CSE15 Abstracts

Abstracts are printed as submitted by the authors.

Society for Industrial and Applied Mathematics 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Telephone: +1-215-382-9800 Fax: +1-215-386-7999 Conference E-mail: [email protected] Conference web: www.siam.org/meetings/ Membership and Customer Service: 800-447-7426 (US & Canada) or +1-215-382-9800 (worldwide) CS15 Abstracts 1

IP1 to a strong earthquake. Graph Data Analytics at Scale: Opportunities and Challenges Shinobu Yoshimura The University of Tokyo The four Vs of Big Data necessitate fundamentally different [email protected] data analytics. A promising strategy toward understand- ing of a complex system’s dynamics and function aims to extract features and relationships between them and to an- IP4 alyze how their evolution causes different functional system Extreme-scale Multigrid in Space and Time responses. Discovery and forecasting of patterns in such feature graphs can provide insights about the vulnerability Multigrid methods are important techniques for efficiently of our nations energy infrastructure to disturbances, the solving huge linear systems and they have already been spread of a cyber-security attack, or the anomalies in in- shown to scale effectively on millions of cores. Future exas- ternode communication in high performance systems. This cale architectures will require solvers to exhibit even higher talk will present some opportunities and challenges in us- levels of concurrency (1B cores), minimize data movement, ing this strategy for computational science and engineering exploit machine heterogeneity, and demonstrate resilience applications. to faults. While considerable research and development remains to be done, multigrid approaches are ideal for ad- Nagiza Samatova dressing these challenges. In this talk, we will discuss ef- North Carolina State University forts to develop extreme-scale multigrid, including a new Oak Ridge National Laboratory parallel time integration approach that has the potential [email protected] for significant speedups over standard time stepping.

Robert Falgout IP2 Center for Applied Scientific Computing Model Reduction - Trouble with Scales? Lawrence Livermore National Laboratory [email protected] Scientific and technological advances call for more and morecomplexmodelsaswellassystematicwaysofcomple- menting them by observational data. Despite the ever in- IP5 creasing computing capacity, ironically, the need for quan- Statistical and Computational Challenges of Con- tifiable model reduction concepts is also gaining increasing straining Greenhouse Gas Budgets importance in numerous application contexts. Examples are large scale design or online optimization tasks, uncer- Predicting future changes to the global carbon cycle (and tainty quantification or inversion problems some of which therefore climate) and quantifying anthropogenic emissions may only become feasible through employing reduced mod- of greenhouse gases (GHGs) both require an understand- els. Starting from a flow scenario with microscales this ing of net GHGs emissions and uptake across a variety of talk highlights several aspects of related model reduction spatial and temporal scales. This talk will explore some of strategies with particular focus on accuracy and stabil- the core scientific questions related to understanding GHG ity guarantees, presence of small scales, singular pertur- budgets through the lens of the statistical and computa- bations, and high dimensionality. We address some of the tional challenges that arise. The focus will be on the use key ingredients, revolving around error-residual relations, of atmospheric observations, and applications will include rate-optimality as a benchmark notion, adaptive or greedy the natural and anthropogenic components of the methane methods, separation of variables. The discussion is illus- and carbon dioxide budgets. The discussion will include is- trated by numerical examples. sues related to the solution of spatiotemporal inverse prob- lems, uncertainty quantification, data fusion, gap filling, Wolfgang Dahmen and issues of “big data” arising from the use of satellite RWTH Aachen observations. IGPM [email protected] Anna Michalak Carnegie Institution for Science Stanford, CA IP3 [email protected] Petascale Finite Element Simulation of Real Worlds Complex Structure with Billions DOFs Model IP6 Scaling Open Systems for Future Computational Leading supercomputers offer the computing power of Challenges petascale, and exascale systems are expected to be avail- able by the end of this decade. Supercomputers with more Computational models are changing rapidly, partially in than tens of thousands of computing nodes, each of which response to growing data size and advances in high- has many cores cause serious problems in practical finite performance computing. Open approaches are well suited element software. We have been developing an open source to this dynamic environment as they provide agile re- parallel finite element software known as ADVENTURE, sponses to complex, evolving code, and support the greater which enables very precise analyses of practical structures goal of ensuring reproducible science. This presentation and machines using over 100 million to billions DOFs mesh. introduces some open initiatives addressing big data and The basic parallel solution algorithms employed are the hi- HPC and the role that software architectures and processes erarchical domain decomposition method with balancing plays in advancing scientific computation. Also discussed domain decomposition as preconditioner. In this talk, I are emerging trends including competitive challenges and explain several key technologies and one practical applica- active publications that will likely play an important role tion, i.e. seismic response of nuclear power plant subjected in the creation, development and deployment of computa- 2 CS15 Abstracts

tional software. technology trends that support accessing and understand- ing our data using intuitive, web-based and query-driven Will Schroeder interfaces are now the norm. In this talk, I will discuss Kitware, Inc. these trends and several freely available, open-source ap- [email protected] proaches that leverage them.

IP7 James Ahrens Los Alamos National Laboratory A Calculus for the Optimal Quantification of Un- [email protected] certainties

The past century has seen a steady increase in the need of estimating and predicting complex systems and making SP1 (possibly critical) decisions with limited information. With Celebrating 15 Years of SIAM CSE this purpose, this talk will describe the development of a form of calculus allowing for the (computational) manip- ulation of infinite dimensional information structures and There can be no doubt that SIAM CSE has been a big its application to the optimal quantification of uncertain- success! We examine the growth of CSE in SIAM, and ties in complex systems and the scientific computation of more broadly as a discipline, and look toward some of the optimal statistical estimators/models. Specific examples challenges and opportunities for the future. will be discussed to illustrate how this form of calculus could also be used to facilitate/guide the process of scien- Linda R. Petzold tific discovery. University of California, Santa Barbara [email protected] Houman Owhadi Applied Mathematics Caltech [email protected] CP1 Computational Molecular Engineering: An Emerg- ing Technology in Process Engineering IP8 The Power of Matrix and Tensor Decompositions Molecular modeling and simulation has become a powerful in Smart Patient Monitoring tool which can be applied to many physical processes and Accurate and automated extraction of clinically relevant properties of fluids on the molecular level. A shift in the information from patient recordings requires an ingenious accessible length and time scales due to massively parallel combination of adequate pretreatment of the data (e.g. high-performance computing has greatly increased its po- artefact removal), feature selection, pattern recognition, tential. The novel molecular dynamics code ls1 mardyn, decision support, up to their embedding into user-friendly which scales excellently on up to 146 000 cores, is pre- user interfaces. The underlying computational problems sented, highlighting the emergence of computational molec- can be solved by making use of matrix and tensor decom- ular engineering as a discipline. positions as building blocks of higher-level signal process- ing algorithms. A major challenge here is how to make Martin T. Horsch, Stephan Werth the mathematical decompositions “interpretable’ such that University of Kaiserslautern, Germany they reveal the underlying medically relevant information Laboratory of Engineering Thermodynamics and improve medical diagnosis. The application of these [email protected], [email protected] decompositions and their benefits will be illustrated in a variety of case studies, including epileptic seizure onset lo- Christoph Niethammer, Colin Glass calisation using adult and neonatal scalp EEG and Event- High Performance Computing Center Stuttgart, Germany related potential analysis during simultaneous EEG-fMRI [email protected], [email protected] acquisition. Wolfgang Eckhardt, Philipp Neumann Sabine Van Huffel Technische Universit¨at M¨unchen, Germany ESAT-SCD(SISTA) Department of Electrical Engineering Scientific Computing in Computer Science Katholieke Universiteit Leuven [email protected], [email protected] sabine.vanhuff[email protected] Hans-Joachim Bungartz IP9 Technische Universit¨at M¨unchen, Department of Informatics Implications of Numerical and Data Intensive Chair of Scientific Computing in Computer Science Technology Trends on Scientific Visualization and [email protected] Analysis

Technology trends in numerically and data intensive com- Jadran Vrabec puting have the potential to reshape and significantly ad- University of Paderborn, Germany vance how we visualize and analyze the results of scientific Thermodynamics and Energy Technology simulations. However, next generation numerically inten- [email protected] sive supercomputers are bound by power and storage con- straints. These require us to transition from standard post- Hans Hasse processing visualization and analysis approaches to intelli- University of Kaiserslautern, Germany gent, automated in-situ ones. In addition, data intensive Laboratory of Engineering Thermodynamics CS15 Abstracts 3

[email protected] [email protected]

CP1 CP2 Dependance of the Convergence of Multigrid A Numerical and Computational Framework Methods on the Used Discretization for Hierarchical Multi-Scale/multi-Physics Simula- tions A lot of effort has been put into analyzing the conver- gence rate of multigrid methods depending on the used Multi-scale modeling (MSM) has become a dominant smoother and coarse grid operator. Effectively, the conver- paradigm in materials modeling. The practical impact of gence rate of the solver is already being influenced when MSM depends on its ability to utilize modern computing the discretization of the PDE is chosen. In order to solve platforms. However, since there are no general numerical PDEs as computationally efficient as possible, the choice of and computational frameworks for MSM, the vast major- the discretization matters. We present analyses of the con- ity of multi-scale material models or simulations are devel- vergence rate and computational cost of multigrid methods oped on a case-by-case basis. We present a formulation of for different discretizations. an adaptive numerical and computational framework for MSM and analyze its performance for a number of chal- Matthias Bolten lenging problems. University of Wuppertal Department of Mathematics Jaroslaw Knap, Oleg Borodin, Carrie E. Spear, [email protected] KENNETH W. Leiter, DAVID A. Powell, RICHARD C. Becker U.S. Army Research Laboratory CP2 [email protected], [email protected], Support Graph Smoothing [email protected], [email protected], [email protected], [email protected] Large scale-free data mining tasks often require an efficient linear solver. Often standard iterative methods struggle do to the large size and complexity of the graphs. Computa- CP1 tion of an optimal preconditioner for CG is challenging for a general scale-free graph. Support graph preconditioners Amr Strategies for Scft Algorithm have been a popular subject of study, but deserve more in depth study within a multilevel setting. We employ a sup- We introduce an adaptive mesh refinement technique for port graph technique that serves as a relaxation method solving the self consistent field theory mean-field optimiza- for AMG. tion for an AB diblock copolymer. We use a 3D octree data structure and a level set based refinement method to Alyson Fox solve a diffusion reaction equation. It reduces the required University of Colorado Boulder number of points for fine polymeric 3D structures and thus [email protected] the data required to store is compressed consequently (1/3) without loss of accuracy on the physical observables. CP2 Gaddiel Ouaknin On Teh Efficiency of Nonlinear Multigrid Methods UCSB Nonlinear multigrid methods such as the Full Approxima- [email protected] tion Scheme (FAS) and Newton-multigrid (Newton-MG) are widely-used as fast solvers for nonlinear PDEs of ellip- Frederic G. Gibou tic and parabolic type. This talk will consider Newton-MG UC Santa Barbara and FAS iterations in a general setting to derive a the- [email protected] oretical approximation of the execution time of the algo- rithms. Specific examples will then be used to demonstrate the sharpness of these estimates for a range of nonlinear CP2 eliiptic and parabolic problems (the latter with implicit time-stepping). Our conclusion is that the Newton-MG Robust Multigrid Methods for Magnetohydrody- approach is almost always the superior choice. namics Peter K. Jimack Magnetohydrodynamic models are used for a wide range School of Computing of plasma physics applications. The system of PDEs that University of Leeds characterizes these models is nonlinear, with strongly cou- [email protected] pled fluid and electromagnetic interactions. The linear systems that result from linearization and discretization are typically difficult to solve. We consider multigrid- CP2 preconditioned GMRES to achieve efficient solution, and Large-Scale Sparse Inverse Covariance Estimation compare results for two potential relaxation methods, both motivated by well-known relaxation techniques for incom- The Sparse Inverse Covariance Estimation problem arises pressible fluid dynamics. in many statistical applications in Machine Learning. In this problem we estimate a sparse inverse of a covariance Thomas Benson matrix of a multivariate normal distribution, by solving Department of Mathematics an l1 regularized optimization problem. Because of mem- Tufts University ory limitations, most algorithms are unable to handle large 4 CS15 Abstracts

scale instances of this problem. We present a block coor- Generation for Discontinuous Galerkin Finite El- dinate descent approach and a multilevel acceleration for ement Methods solving the problem for such large-scale data sets. We fur- ther show that an additional debiasing phase improves the We consider the application of discontinuous Galerkin fi- estimated matrix. nite element methods for the discretization of general fluid flow and multiphysics problems. By exploiting tools from Eran Treister symbolic differentiation, we present a simple programming Technion - Israel Institute of Technology, Israel environment which automatically generates the necessary [email protected] code segments, leading to rapid development and testing of discontinuous Galerkin methods for a wide variety of prob- Javier Turek lems. The proposed computational framework is demon- Computer Science Department strated on a variety of problems arising in both incompress- Technion ible and compressible fluid flows. [email protected] Nathan Sime School of Mathematical Sciences Irad Yavneh University of Nottingham Computer Science Department, Technion [email protected] [email protected] Paul Houston CP3 School of Mathematical Sciences CSE Education at JSC University of Nottingham, UK [email protected] Fostering a sound education of students and young re- searchers at bachelor, master and PhD level in high- performance computing, mathematics and computational CP3 science is an essential task of the J¨ulich Supercomputing PoKiTT: an Efficient, Platform Agnostic Pack- Centre (JSC). This talk will give an overview of the educa- age for Thermodynamics, Kinetics, and Transport tional activities and structures at JSC and informs about Properties within PDE Solvers the guest student programme, the summer/winter schools for PhD students, joint bachelor and master courses with We introduce PoKiTT, a portable, lightweight library for universities and the German Research School for Simula- performing data parallel calculations of thermochemical tion Sciences (GRS). quantities commonly encountered in turbulent reactive flow simulations. PoKiTT uses Nebo, a domain specific Johannes Grotendorst language, to provide a platform agnostic implementation Forschungszentrum Juelich which will be ready for future exascale architectures. We [email protected] demonstrate the performance benefits of using PoKiTT over Cantera in the context of a PDE solver for both CPU and GPU executions. CP3 Automatic Parallel Programming for Scientific Nathan Yonkee Simulation The University of Utah [email protected] HiPro is an automatic parallel programming IDE designed for developing scientific simulation based on JASMIN, a James C. Sutherland domain-specific computational framework. It supports Department of Chemical Engineering parallel programming through GUI and source code gen- The University of Utah eration.The unique parallel part and all interfaces of the [email protected] application are generated and implementation of sequen- tial subroutines is the only part of the code left to be writ- ten manually for a programmer. It combines numerical CP4 mathematics with component-based programming to cre- A Framework for Parallel Fast Matrix Multiplica- ate ontological models for parallel simulations. tion

Li Liao We explore the performance of novel fast (Strassen-like) IAPCM matrix multiplication algorithms in sequential and shared- [email protected] memory parallel environments. We use a code generation framework to automatically implement over twenty fast Aiqing Zhang matrix multiplication algorithms and to rapidly test algo- Institute of Applied Physics and Computational rithmic variations for performance tuning. Our implemen- Mathematics tations outperform Intel MKL for modest problem sizes. zhang [email protected] Furthermore, we find that Strassens algorithm is not al- ways optimal in practice; in particular, other algorithms Zeyao Mo perform better for the multiplication of rectangular matri- Laboratory of Computational Physics, IAPCM ces. P.O. Box 8009, Beijing 100088, P.R. China zeyao [email protected] Austin Benson Stanford University [email protected] CP3 Symbolic Representation and Automated Code Grey Ballard CS15 Abstracts 5

Sandia National Laboratories Ichitaro Yamazaki, Jakub Kurzak [email protected] University of Tennessee, Knoxville [email protected], [email protected]

CP4 Piotr Luszczek Dynamic Runtime Scheduling for Dense Out-of- Department of Electrical Engineering and Computer Core Matrix Computation on the Intel Xeon Phi Science University of Tennessee, Knoxville The talk describes the implementation of dense out-of- [email protected] core matrix computations, such as Cholesky factorization, on the Intel Xeon Phi. The out-of-core algorithm is for- Stanimire Tomov mulated as computation over submatrix tiles where the University of Tennessee, Knoxville dependency is expressed as a directed acyclic graph. A [email protected] multi-threaded runtime system launches asynchronous of- fload computations on the Intel Xeon Phi. Examples and results are presented. Jack J. Dongarra Department of Computer Science Eduardo F. D’Azevedo The University of Tennessee Oak Ridge National Laboratory [email protected] Mathematical Sciences Section [email protected] CP5 Ben Chan, Terrence Chong Variational Bayesian Formulations for High- Chinese University of Hong Kong Dimensional Inverse Problems [email protected], [email protected] The present paper advocates a Variational Bayesian Allan Morales (VB) approach for approximating the posterior density in The George Washington University stochastic inverse problems. In contrast to sampling tech- [email protected] niques (e.g. MCMC, SMC), VB requires much fewer for- ward evaluations. Furthermore it enables learning of a suit- Kwai L. Wong able lower-dimensional subspace where most of the poste- Joint Institute for Computational Science rior probability lies, and reducing dramatically the number University of Tennessee/ORNL of unknowns. We demonstrate the accuracy and efficiency [email protected] of the proposed strategy in nonlinear problems and non- Gaussian posteriors in view of biomedical applications.

CP4 Isabell Franck Technische Universit¨at M¨unchen, Germany Optimization of Singular Vectors Computation [email protected] New SVD routines based on a two-step reduction of a gen- eral matrix to bidiagonal form were developed for IntelR Phaedon S. Koutsourelakis MKL. In this talk we present some details of implemented Technische Universitat Muenchen optimizations: dynamic parallelization of singular vectors [email protected] computations, speculative computations in QR and LQ factorizations, dynamic parallelization of the reduction of banded matrix to bidiagonal form and how these tech- CP5 niques are combined for achieving high performance. Surrogate-Based Bayesian Model Ranking of Atomistic Models Incorporating the Fidelity of Sergey V Kuznetsov, Nadezhda Mozartova Surrogates Intel Corporation [email protected], Approximate modeling of atomistic systems is crucial in [email protected] designing new generation of material since ab initio simu- lations are prohibitively costly. We present how a Bayesian framework can rank a number of competing approximate CP4 models and also provide a basis concurrently exploit mul- Performance Study of a Randomized Dense Low- tiple models for the same system. We make use of Poly- Rank Matrix Approximation Using Multiple Gpus nomial Chaos surrogates to accelerate the calculation and also account for the numerical error that is thus induced. A standard method to compute low-rank approximations for dense matrices is truncated QR factorizations with piv- Hadi Meidani oting, such as LAPACK DGEQP3, an important kernel in University of Southern California many scientific applications. In this talk, we study the per- [email protected] formance of an algorithm based on randomized sampling to compute such factorizations of dense matrices for hybrid CPU/GPU architectures and show it can have comparable Mike Kirby accuracy, better performance and reduced communications University of Utah than DGEQP3. School of Computing [email protected] Theo Mary Universite de Toulouse, INPT ENSEEIHT Dmitry Bedrov [email protected] University of Utah 6 CS15 Abstracts

[email protected] [email protected]

CP5 CP6 Minimal Set of Mechanisms Controlling Type I In- Preconditioner Scaling for Finite Element Models terferon Differential Signaling of Turbulent Air/Water Flow in Coastal and Hy- draulic Applications

Type I interferon ligands differentially trigger a wide range While three-dimensional models of turbulent air/water of cellular responses through a common heterodimeric re- flow are seeing application in coastal and hydraulic engi- ceptor. We seek to identify minimal configurations of cel- neering, the computing resources required for simulating lular mechanisms in interferon signaling that could repro- field problems is a major barrier to widespread adoption of duce this observed behavior. We developed and applied a the overall approach. One route to scalable solvers is ex- Bayesian model selection method tailored for linear steady ploiting the block structure of operators arising from dis- state threshold models. The best models emphasize the cretizations of multi-phase Navier-Stokes equations. We importance of the rate of endocytosis and receptor binding present a study of recently developed approximate Schur dynamics within the endosome for interferon signaling. complement factorizations to a stabilized finite element code for multi-phase flow. Pencho Yordanov ETH Zurich Chris Kees [email protected] U.S. Army Engineer Research and Development Center Coastal and Hydraulics Laboratory Irene Otero-Muras, Joerg Stelling [email protected] Department of Biosystems Science and Engineering, ETH Zurich Aron Ahmadia [email protected], [email protected] US Army Engineer Research and Development Center [email protected]

CP5 Jed Brown Uncertainty Propagation Using Infinite Mixture of Mathematics and Computer Science Division Gaussian Processes and Variational Bayesian Infer- Argonne National Laboratory and CU Boulder ence [email protected]

Uncertainty propagation (UP) is a very challenging mathe- Matthew Farthing matical and computational problem. Among other things, US Army Engineer Research and Development Center UPs difficulty is due to the limited number of model eval- [email protected] uations, the curse of dimensionality, discontinuities, and multivariate responses with non-trivial correlations. In or- Barry F. Smith der to deal with all these problems simultaneously, we de- Argonne National Lab velop an infinite mixture of multi-output Gaussian process MCS Division model. We train the model using variational Bayesian in- [email protected] ference and we obtain highly competing results in porous flow problems. CP6 Peng Chen, Nicholas Zabaras A Scalable Newton-Krylov-Schwarz Method for Cornell University Coupled Fluid-Structure Interaction Problems [email protected], [email protected] Fluid-structure interaction is a challenging multi-physics Ilias Bilionis problem. The difficulties are due to the high nonlinearity Purdue University derived from the convective term of fluid problems, the con- [email protected] stitutive relationship of solid materials, the dependency of the solution on the displacement of the moving fluid mesh, and unbalanced message passings between different proces- CP6 sors resulting from the partition of unstructured meshes into a large number of parts. To overcome the difficul- Data Based Regularization Methods ties, we study an inexact Newton-Krylov algorithm with a Schwarz preconditioner to solve the monolithically cou- Often one is looking for preconditioners with special behav- pled fluid-structure system. We show that the proposed ior on certain subspaces. So in Multigrid methods the pre- algorithm is scalable in terms of the iteration count and conditioner (smoother) should be defined to remove high the total compute time on a supercomputer with a large frequency error components while in regularization prob- number of processors. lems the preconditioner (seminorm) should not recover the noise. In this talk we will present different methods to Fande Kong, Xiao-Chuan Cai obtain such preconditioners especially in connection with Department of Computer Science ill-posed inverse problems by finding data dependent semi- University of Colorado Boulder norms. [email protected], [email protected]

Thomas K. Huckle Institut fuer Informatik CP6 Technische Universitaet Muenchen A Parallel Linear Solver Exploiting the Physical CS15 Abstracts 7

Properties of the Underlying Mechanical Problem Cong Zheng Graduate School of Chinese Academy of Engineering The iterative solution of large systems of equations may Physics benefit from parallel processing. However, using a straight- [email protected] forward domain decomposition in ’layered’ geomechanical finite element models with significantly different stiffnesses Shou Gu may lead to slow or non-converging solutions. Physics- University of Electronic Science and Technology of China based domain decomposition is the answer to such prob- [email protected] lems, as explained in this paper and demonstrated on the basis of a few examples. Together with a two-level pre- Xingping Liu conditioner comprising an additive Schwarz preconditioner Institute of Applied Physics and Computational that operates on the sub-domain level, an algebraic coarse Mathematics grid preconditioner that operates on the global level, and [email protected] additional load balancing measures, the described solver provides an efficient and robust solution of large systems of equations. Although the solver has been developed pri- CP7 marily for geomechanical problems, the ideas are applicable to the solution of other physical problems involving large Spectral Methods in PDE Solving: a Multi-GPU differences in material properties. Framework

Kees Vuik Spectral methods offer unconditionally stable time- Delft University of Technology stepping schemes for solving PDEs numerically. Although [email protected] a parallel spectral scheme necessitates the parallelization of the FFT, all other operations can be executed asyn- chronously. We present a framework utilizing the benefits CP7 of multi-GPU hardwares and demonstrate the advantages and disadvantages of the method on the results obtained Parallel Graph Coloring for Scientific Computing for surfactant assisted liquid phase separation in the wa- ter/CO2/hydrocarbon system, which is of high industrial Graph coloring has many applications in scientific comput- importance nowadays on the field of improved recovery. ing, such as parallel scheduling, sparse matrix reordering, and automatic differentiation. Often the graph coloring Gyula I. Toth itself must be computed in parallel. We describe new soft- Wignes Research Centre for Physics ware for parallel graph coloring on multicore and manycore Budapest, Hungary architectures. Our implementation is based on the Kokkos [email protected] library, which makes the code portable to many platforms, including Intel MIC and GPUs. We discuss algorithmic issues and show some preliminary results. Tatjana Kuztensova, Bjorn Kvamme Department of Physics and Technology Erik G. Boman University of Bergen Sandia National Labs, NM [email protected], [email protected] Scalable Algorithms Dept. [email protected] CP7 Direct Hierarchical Schur Method for Nested Dis- CP7 section Reordered Linear Systems on Multi-GPUs Solving Sparse Linear Systems on GPUs Based on the Biell Storage Format We propose a direct hierarchical Schur complement method to solve sparse symmetric positive-definite linear systems Nowadays, the GPU has evolved into a highly parallel on multinode GPU clusters. By exploring the structures of coprocessor which is suited to compute-intensive, highly the reordered coefficient matrices and developing a scheme parallel computation. Solving sparse linear systems is to distribute data and schedule tasks, we can solve the one of basic task for scientific and engineering comput- problem efficiently. Our method solves the diagonal block ing. Achieving high performance of this task on GPUs and Schur subproblems by GPU-based Cholesky factoriza- is relatively challenging, especially when the matrix has no tion to gain accelerated performance. Numerical results specific structure. For the general sparse matrices, we have suggest the method is scalable for GPU-clusters with dif- proposed a new data structure based on the BiELL (bisec- ferent node numbers. tion ELLPACK) format, which is designed to realize the load balance better and thus improve the performance of Cheming Chu the SpMV (sparse matrix-vector multiplication) on GPUs. Department of Mathematics, National Taiwan University Now, we use this new format in iterative methods and pre- [email protected] conditioning techniques for solving sparse linear systems. Numerical results on various matrices show that GMRES, Pochuan Wang CG and some preconditioning techniques using this new Institute of Applied Mathematical Sciences, National format have higher performance than that of using other Taiwan formats on GPUs and their CPU counterparts. University [email protected] Tongxiang Gu Computer Network Information Center, Weichung Wang Chinese Academy of Science Institute of Applied Mathematical Sciences gu [email protected] National Taiwan University 8 CS15 Abstracts

[email protected] tiplications performed during the setup phase of alge- braic multigrid. In particular, we show that the most commonly used parallel algorithm is often not the most CP7 communication-efficient one for all of the matrix-matrix Optimizing Structured Grid Numerical Simula- multiplications involved. By using an alternative algo- tions for Numa-Multicore Systems rithm, we show that the communication costs are reduced (in theory and practice), and we demonstrate the perfor- NUMA-multicore systems are now ubiquitous. Optimal mance benefit for both model and real problems on large- data placement and data move are crucial to fully utilize scale distributed-memory parallel systems. these systems. In this talk, we share our experience in optimizing JASMIN framework for these systems. Firstly, Grey Ballard we developed an efficient NUMA-aware heap manager to Sandia National Laboratories enforce data locality. Secondly, we designed a scalable [email protected] NUMA-aware algorithm for structured grid data communi- cations. These technologies are then integrated into JAS- Jonathan J. Hu MIN framework and numerical results shows that our ap- Sandia National Laboratories proach improves significantly the performance of real-word Livermore, CA 94551 applications on typical NUMA-multicore systems with 10K [email protected] CPU cores. Christopher Siefert Zhang Yang Sandia National Laboratories Institute of Applied Physics and Computational [email protected] Mathematics China Academy of Engineering Physics yang [email protected] CP8 Avoiding Communication and Synchronization in Aiqing Zhang Krylov Eigensolvers Institute of Applied Physics and Computational Mathematics Solving sparse eigenproblems is an important task in many zhang [email protected] engineering problems; Krylov subspace methods, e.g. IR- LAN, TRLAN, are frequent solvers of choice. Krylov sub- Zeyao Mo space eigensolvers have well-known difficulties scaling be- Laboratory of Computational Physics, IAPCM yond 10,000 processors. This bottleneck is due to commu- P.O. Box 8009, Beijing 100088, P.R. China nication from dot products at each iteration rather than zeyao [email protected] matrix-vector products. When matrix-vector products scale well, judiciously-applied preconditioners reduce to- tal iterations; they shift work from globally-communicating CP8 dot products to locally-communicating matrix-vector prod- Scalable Alternative to Domain Decomposition ucts, and we witness improvements in scalability.

We present a novel algorithm based on decomposing the Alexander Breuer, Claire Eisner, Jaroslaw Knap, Kenneth range of a PDE instead of the error. The method allows Leiter efficient use of W and full multigrid cycles in a parallel U.S. Army Research Laboratory setting. A performance model predicts extreme weak scal- [email protected], ability of the algorithm and numerical tests up to 1000 [email protected], [email protected], cores confirm the predicted scalability. [email protected]

David A. Appelhans University of Colorado, Boulder CP8 [email protected] αSetup-Amg: An Adaptive Setup Based Amg Solver for Large-Scale Simulations with Long Time- Thomas Manteuffel Stepping University of Colorado Coarse-level visiting is the main reason that causes loss of [email protected] scalability for AMG solver on massive parallel computer. In our presented adaptive setup strategy, coarsening is per- Steve McCormick formed based on the smoothing behavior on each level, in- Department of Applied Math stead of constructing via an independent setup phase in CU-Boulder traditional procedure. As a results, doing relaxations on [email protected] finer-levels as much as possible, while the required coarse- levels as less as possible. Realistic simulations on O(104) John Ruge cores show the improved scalability. University of Colorado [email protected] Xiaowen Xu Institute of Applied Physics and Computational Mathematics CP8 [email protected] Reducing Communication Costs for Sparse Matrix Multiplication within Algebraic Multigrid CP9 We consider the sequence of sparse matrix-matrix mul- A Multiscale Finite Volume with Oversampling CS15 Abstracts 9

Method to Simulate Low-Frequency Electromag- ing the domain of interest for all times that adapts to the netic Geophysical Responses geometry of the immersed domain by adjusting a small number of mesh elements in the neighborhood of the mov- In Geophysics, simulation of low-frequency Electromag- ing boundary. We illustrate the approach and compare netic (EM) fields in highly heterogeneous, anisotropic me- it with conventional arbitrary Lagrangian Eulerian (ALE) dia is computationally expensive. One reason being the schemes via numerical examples involving fluid-structure multiple length scales that coexist in a given realistic set- interaction. ting. Discrete models require very fine meshes leading to solve large linear systems of equations. Here, we develop a Evan S. Gawlik multiscale finite-volume method with oversampling to re- Stanford University duce the size of the system of equations to be solved while Institute for Computational and Mathematical retaining a good level of accuracy in the solution. Engineering [email protected] Luz Angelica A. Caudillo Mata Earth, Ocean and Atmospherical Sciences Department Adrian Lew University of British Columbia Stanford University [email protected] Mechanical Engineering [email protected] Eldad Haber Department of Mathematics The University of British Columbia CP9 [email protected] Numerical Simulations of Biological Invasions

Lars Ruthotto Biological invasions occur when there is a road on which an Department of Mathematics and Computer Science epidemic propagates faster than in the outlying fields adja- Emory University cent to the roads. These types of invasions can be modeled [email protected] using reaction-diffusion equations with varying parameters on the roads and in the outlying areas with coupling be- tween the two. We will present a numerical method to Christoph Schwarzbach study this problem. Comparisons with previous analyti- University of British Columbia cal work with a straight road will be presented, as well as [email protected] numerical simulations of more complex road shapes.

Shilpa Khatri CP9 Department of Mathematics A Computational Shock-Tube for Reproducible University of North Carolina at Chapel Hill Computational Experiments in Traumatic Brain [email protected] Injury Anna-Karin Tornberg We developed a computational shock tube with conser- KTH vative finite volume methods and interface-shock interac- [email protected] tion to complement experiments in traumatic brain in- jury(TBI). The 3D model was implemented using com- pressible Euler equations coupled with a Tammann-EOS. CP9 An experimental setup was simulated and yielded insights Asymptotic-Preserving Space-Time Discontinuous not available by experimental means, emphasizing the im- Galerkin Schemes for a Class of Relaxation Systems portance of geometry and yielding cavitation as a possible damage mechanism. The code is open-source to promote We consider in this work a class of singularly perturbed reproducible research. hyperbolic balance laws that admit a diffusive limit. Such systems arise naturally in radiative transport applications Mauricio J. Del Razo if one starts with a Boltzmann description and expands the University of Washington distribution function in spherical harmonics (i.e., the Pn mauricio [email protected] approximation). One key difficulty in solving such systems is that standard numerical schemes have maximum time- Randall LeVeque step restrictions that vanish in the singular limit. Sev- University of Washington eral approaches have been proposed in the literature to Applied Math overcome this difficulty, many of which are based on split- [email protected] ting the equation into stiff and non-stiff pieces and using appropriate semi-implicit time-stepping methods. In this David Cook work we employ a different strategy in order to achieve VA Hospital asymptotic-preservation. We develop a scheme using a [email protected] space-time discontinuous Galerkin approach. Several nu- merical test cases are used to validate the proposed scheme.

CP9 Universal Meshes for Problems with Moving Anna Lischke Boundaries Iowa State University [email protected] We develop a framework for the design of high-order finite element methods for moving-boundary problems using a James A. Rossmanith universal mesh: a stationary background mesh contain- Iowa State University 10 CS15 Abstracts

Deparment of Mathematics sition, and employ techniques from differential/algebraic [email protected] equations. We shall also provide a systematic theoretical study of these methods. Several numerical examples will be shown to illustrate the theoretical findings and the salient CP10 features of the proposed methods. Finite-Difference Frequency-Domain Analysis of Photonic Devices with Periodic Structures Based Saeid Karimi on Domain Decomposition University of Houston [email protected] We present an efficient algorithm and implementation of 3D finite-difference frequency-domain simulation of pho- Kalyana Nakshatrala tonic devices. By proposing a new matrix-reordering University Of Houston - Main Campus scheme in the domain decomposition framework, our [email protected] method exploits the homogeneous and periodic structures in photonic devices with Yee’s mesh and achieves com- puting resources saving in memory usage and total run- CP11 time. The linear system solver is capable of solving the ill- A Parallel Fast Sweeping Method for Quadtrees conditioned problems and suitable for parallel computation and Octrees via high-performance computers with GPU or many-core accelerators. We present a hybrid shared memory and message pass- ing algorithm for the fast sweeping method on tree based Cheng-Han Du adaptive grids. We utilize graph theory to decompose the Department of Mathematics, National Taiwan University tree into clusters of nodes that can be updated simulta- [email protected] neously via a shared memory parallelization model. Large scale parallelization is accomplished by domain decompo- Pochuan Wang sition with a message passing model. We present scaling Institute of Applied Mathematical Sciences, National results on a number of time-independent Hamilton Jacobi Taiwan equations. University [email protected] Miles L. Detrixhe University of California Santa Barbara Weichung Wang [email protected] Institute of Applied Mathematical Sciences National Taiwan University [email protected] CP11 A Communication Algorithm for the Patch-Based Multiblock Structured Mesh Applications CP10 High Order Schemes Based on Operator Splitting Multiblock structured mesh allows to handle complex and Deferred Corrections for Stiff Time Dependent configurations which are widely existed in computational Pdes physics applications. A Patch-based data structure is al- ways used in applications with multiblock structured mesh We consider quadrature formulas of high order in time to get satisfying parallel performance. However, such based on Radau–type, L–stable implicit Runge–Kutta Patch-based data structure seriously challenges the block schemes to solve time dependent stiff PDEs. Instead of to block data communications. This talk presents an algo- solving a large nonlinear system of equations, we develop rithm for such communication and introduces its integra- a method that performs iterative deferred corrections to tion to JASMIN infrastructure to support the peta-scale compute the solution at the collocation nodes. The numeri- simulations while tens of thousands of processors are used. cal stability is guaranteed by a dedicated operator splitting Performance results show its robustness. technique that efficiently handles the stiffness of the PDEs and provides initial and intermediate solutions to the iter- Hong Guo ative scheme. Institute of Applied Physics and Computational Mathematics Max Duarte guo [email protected] Center for Computational Sciences and Engineering Lawrence Berkeley National Laboratory [email protected] CP11 Scalable Parallel Assembly for High-Performance Matthew Emmett Computing with Isogeometric and Higher-Order Lawrence Berkeley National Laboratory Finite Elements Center for Computational Sciences and Engineering [email protected] Isogeometric and higher-order finite element methods lead to system matrices whose parallel assembly requires exten- sive communication. We introduce a distributed-memory CP10 domain decomposition strategy, which uniquely assigns Monolithic Multi-Time-Step Coupling Methods for each degree of freedom to one processor, therefore elimi- Transient Systems nating communication completely. We show that although contributions from interface elements need to be computed We shall present new multi-time-step coupling methods several times on different processors, our approach leads to for first- and second-order transient systems. The pro- a scalable and efficient parallel assembly. Algorithmic de- posed methods are based on dual Schur domain decompo- tails and performance measurements for different examples CS15 Abstracts 11

are presented. case.

Vasco Varduhn Stephane Brull Technische Universit¨at M¨unchen Institut de Math´ematiques de Bordeaux UMR 5251 [email protected] Universit´e Bordeaux [email protected] Dominik Schillinger University of Minnesota Bruno Dubroca, d’Humi`ere Emmanuel, Guisset S´ebastien [email protected] CELIA [email protected], [email protected] bordeaux1.fr, [email protected] CP11 Exploring Communication Options with Adaptive CP12 Mesh Refinement Coarse Multiscale Timestepping for Problems in Finite difference and volume based codes comprise a signif- Plasma Physics with Equation-Free Projective In- icant portion of the workload on modern high performance tegration computers. Many of these codes use Adaptive Mesh Re- finement (AMR) as a computational strategy. We have Multiscale plasma problems are hard to simulate because developed miniAMR, a miniapp in the Mantevo suite, to the physics of micro and macro-scales are strongly linked. explore AMR communication issues. We compare mini- We propose a coarse-grained numerical scheme, based on AMR to CTH, a shock hydrodynamics code, and use mini- equation-free projective integration, for a kinetic plasma AMR to explore some communication strategies that may system modelled by the Vlasov-Poisson equations, follow- be necessary as we move to future architectures. ing the idea of [Shay, Drake, Dorland 2006]. A particle-in- cell (PIC) code is used to simulate the micro scale dynam- Courtenay T. Vaughan, Richard Barrett ics. As a first test case, we simulate the propagation and Sandia National Laboratories steepening of a nonlinear ion acoustic wave. [email protected], [email protected] Paul Cazeaux,JanHesthaven EPFL [email protected], jan.hesthaven@epfl.ch CP11 A Communication Staging Technique for a Hierar- chical Ocean Model CP12 Semi-Lagrangian Discontinuous Galerkin Schemes We study a communications staging technique applied to for the Relativistic Vlasov-Maxwell System an algorithmically accelerated, free-surface, z-level ocean model. The ocean model is a hierarchical high-order / The Vlasov-Maxwell system describes the evolution of a low-order model, which allows mapping to heterogeneous collisionless plasma, represented through a probability den- architectures and exploitation of advanced communication sity function (PDF) that self-interacts via the electromag- algorithms. We compare the benefit of communication netic force. One of the main difficulties in numerically solv- staging between a current numerical method and a re- ing this system is the severe time-step restriction that arises search method under development, within this high-order from parts of the PDF associated with moderate-to-large / low-order framework. We provide numerical examples to velocities. The dominant approach in the plasma physics support our study and compare to traditional implemen- community is the so-called particle-in-cell method. The tations. focus of the current work is on semi-Lagrangian methods. In particular, we develop a method based on high-order Geoff Womeldorff, Chris Newman, Dana Knoll, Luis discontinuous Galerkin (DG) scheme in phase space, and Chac´on an operator split, semi-Lagrangian method in time. The Los Alamos National Laboratory method is designed to be (1) high-order accurate, (2) mass [email protected], [email protected], [email protected], cha- conservative, and (3) positivity-preserving. The resulting [email protected] scheme is applied to laser-plasma acceleration problems.

Pierson Guthrey CP12 Iowa State University Asymptotic-Preserving Scheme for the Fokker- Department of Mathematics Planck-Landau-Maxwell System in the Quasi- [email protected] Neutral Regime James A. Rossmanith This work deals with the numerical resolution of the Iowa State University Fokker-Planck-Maxwell system in the quasi-neutral regime. Deparment of Mathematics In this regime the stiffness of the stability constraints of [email protected] classic schemes causes huge calculation times. That is why, we introduce a new stable numerical scheme consistent with the transitional and limit models. Such schemes are CP12 called Asymptotic-Preserving schemes in literature. This Discontinuous Galerkin Deterministic Solvers of new scheme is able to handle the quasi-neutrality limit Boltzmann-Poisson Models of Hot Electronic regime without any restrictions on time and space steps. Transport Using Empirical Pseudopotential Meth- Next, this approach can be easily applied to angular mo- ods ment models by using a moments extraction. Finally, the efficientcy of the scheme is validated on the Batishev test We develop Discontinous Galerkin deterministic solvers of 12 CS15 Abstracts

Boltzmann-Poisson models of electronic transport, incor- [email protected] porating numerical full energy bands obtained from Empir- ical Pseudopotential Methods (EPM), to improve the semi- conductor physical modeling related to energy bandstruc- CP13 ture, charge carrier group velocity and scatterings. We will present the DG schemes related to electronic transport in Parallel Methods for Accelerated Multilevel Monte both a conduction band and multi-band system. Simula- Carlo for Partial Differential Equations with Ran- tions related to nano-devices such as n+ − n − n+ diodes dom Input and double gated MOSFETS will be presented. An improvement on previous work where MLMC for PDEs using finite element iterative solvers was accelerated by im- Jose A. Morales Escalante proving the initial guess during sampling. Using informa- ICES, The University of Texas at Austin tion gathered at previous samples, the number of iterations [email protected] per Monte Carlo sample were greatly reduced. However, these methods did not allow for any parallel computation. Irene M. Gamba In this work we propose alternate methods which can ben- Department of Mathematics and ICES efit from parallel processing. University of Texas [email protected] Zane Colgin Middle Tennessee State University Yingda Cheng [email protected] Department of Mathematics Michigan State University [email protected] CP13 Armando Majorana Topology Optimization under Manufacturing Un- Dipartimento di Matematica e Informatica certainties University of Catania - Italy [email protected] The focus of this work is on incorporating manufacturing uncertainties in the topology optimization of micro and Chi-Wang Shu nano devices. The considered microfabrication process is Brown University photolithography, which transfers a mask pattern onto a Div of Applied Mathematics substrate. Deviations between the print and the design [email protected] occur due to light diffraction and process variations and these can change severely the design performance. Robust James R. Chelikowsky solutions can be obtained by including uncertainties in the Institute for Computational Engineering and Sciences design process. The modification increases significantly the University of Texas at AUstin computational cost and different strategies for its reduction [email protected] are discussed. Boyan S. Lazarov Department of Mechanical Engineering CP12 Technical University of Denmark [email protected] Vlasov-Poisson Simulations of Magnetized Plasmas Using High-Order Continuum Methods CP13 The Vlasov-Poisson equation system, which describes col- Reducing Dimensionality Through Active Sub- lisionless plasma dynamics, can be solved in conservation- spaces, and the Effect of Gradient Approximations law form using continuum methods. A fourth-order accu- on the Associated Eigenpairs rate finite volume method has been implemented using the Chombo library to solve the governing equations in two spatial and two velocity dimensions. A new benchmark Uncertainty quantification studies struggle in high dimen- based on the Dory-Guest-Harris instability has been de- sions; active subspaces are new tools for dimension reduc- veloped for validating magnetized plasma simulations in tion. Finding active subspaces requires gradient informa- higher dimensional phase space. Extension of the method tion which in practice is often unknown. To work around to cylindrical coordinates is described. this problem, we can approximate gradients by fitting mod- els to the data and computing the gradients associated with the models. We illustrate this principle using Local Linear Genia Vogman Regressions, and investigate how approximation errors in University of California - Berkeley the gradients affect the estimates of the eigenpairs. Exam- [email protected] ples are shown for selected test functions

Phillip Colella Uno B. Vaaland Lawrence Berkeley National Laboratory Norwegian University of Science and Technology, Norway [email protected] [email protected]

Uri Shumlak Paul Constantine Aerospace and Energetics Research Program Colorado School of Mines University of Washington Applied Mathematics and Statistics CS15 Abstracts 13

[email protected] alyzed. The state and co-state variables are approximated by the piecewise linear functions and the control is ap- proximated by piecewise constant functions. We derive, a CP13 priori error estimates for both the control variable and the A Multi-Model Approach for Uncertainty Propaga- state variables. We illustrate with a numerical example to tion and Model Calibration in CFD Applications confirm our theoretical results.

Monte Carlo-based uncertainty propagations are computa- Manickam Kandasamy tionally expensive or even impractical for complex systems Periyar University, Salem 636011, INDIA such as turbulent flows. Efforts to reduce sampling errors [email protected] and modeling errors often compete for limited computa- tional resources. Here we propose a multi-model Monte Periasamy Prakash Carlo method that combines models of multiple fidelities Department of Mathematics,Periyar University to propagate uncertainties. A Gaussian process is used to Salem, INDIIA construct the model discrepancy between high- and low- [email protected] fidelity models to improve the results.

Jianxun Wang,HengXiao CP14 Dept. of Aerospace and Ocean Engineering, Virginia Tech Optimal Order Multigrid Preconditioners for Lin- [email protected], [email protected] ear Systems Arising in the Semismooth Newton Method Solution Process of a Class of Control- CP13 Constrained Problems Detecting Discontinuities and Localized Features In this work we discuss multigrid preconditioners for Using Gaussian Processes control-constrained optimal control problems constrained Constructing surrogates of physical models can be ex- by semilinear elliptic PDEs. Building upon the existing tremely difficult, especially when they exhibit sharp, or work from linear-quadratic case, we study preconditoners even discontinuous, variations. Iteratively-built tree- for the submatrices of the reduced Hessian arising in the decompositions, or two-stage classification-regression ap- semismooth Newton solution process. The control is dis- proaches, have been able to partially deal with this prob- cretized using piecewise constant finite elements. It is ob- lem. However, virtually all such techniques rely on intuitive served that the resulting preconditioner is of optimal order ideas. Here, we develop a two-level-deep, potentially infi- with respect to the discretization. Analytical and numeri- nite mixture of Gaussian processes that can automatically cal results are presented. detect local features with no ad hoc assumptions. Jyoti Saraswat Ilias Bilionis Thomas More College Purdue University [email protected] [email protected] Andrei Draganescu Nicholas Zabaras Department of Mathematics and Statistics, UMBC Cornell University University of Maryland, Baltimore County [email protected] [email protected]

CP14 CP14 Optimal Control of Level Sets Multigrid Preconditioners for Stochastic Optimal Control Problems with Elliptic Spde Constraints We present two level set approaches for numerical simula- tion of evolving interfaces, each based on PDE-constrained We consider an optimal control problem constrained by an optimization problems. In the first one the optimal control elliptic SPDE, with a stochastic cost functional of tracking procedure constrains the level set function so as to satisfy type. We use a sparse grid stochastic collocation approach a conservation law and thus produces a mass conservative to discretize in the probability space and finite elements numerical solution. The second approach is designed to to discretize in the physical space. To accelerate the solu- preserve the signed distance function property of the level tion process, we propose a deterministic multigrid precon- set function by incorporating the residual of the Eikonal ditioner for the stochastic reduced KKT system, similar to equation into the cost functional and prescribing a bilinear the preconditioners introduced by Draganescu and Dupont state equation. Both approaches are evaluated numerically. for the deterministic PDE constrained problem. Christopher Basting,DmitriKuzmin Ana Maria Soane Dortmund University of Technology Towson University [email protected], Department of Mathematics [email protected] dortmund.de [email protected]

CP14 CP14 Fractional Powers of Finite Element Approxima- Numerical Realization of the Open Pit Mine Plan- tion for An Parabolic Optimal Control Problems ning Problem In this paper, a numerical theory based on fractional fi- By reformulating a model for open pit mine planning due to nite element approximations for an optimal control prob- [F. Alvarez et al., 2011], we obtain an optimization problem lem with pointwise control constraints is presented and an- subject to viscosity solutions of an underlying Hamilton- 14 CS15 Abstracts

Jacobi PDE. We apply a monotone discretization scheme, [email protected] which yields an optimal control problem of a system of ODEs. We present the algorithmic treatment and numeri- Vrushali Bokil, Nathan L. Gibson cal results of this problem under consideration of the effort Oregon State University constraint, which is of non-incremetal type. [email protected], [email protected] Nikolai Strogies Humbold Universit¨at zu Berlin Charles Woodside Matheon Mathematics for key technologies National Energy Technology Laboratory [email protected] [email protected] Andreas Griewank HU Berlin, Germany CP16 [email protected] Data-Driven Uncertainty Quantification with Adaptive Sparse Grids in Subsurface Flow Simu- CP15 lations Fast Supercomputing Algorithms for Power Sys- We present a novel data-driven approach to propagate un- tem Operation and Control certainty through an expensive subsurface flow simulation. We remove the gap between the subjective approximation We have developed new supercomputing algorithms for of the input’s uncertainty and the unknown real distri- multicore architectures for the state estimation and power bution by applying sparse grid density estimation. We flow problems that present a step towards the real time link the estimation to the adaptive sparse grid collocation power grid optimization and control. We have also devel- method to propagate the uncertainty and obtain new re- oped allocation algorithms for Phasor Measurement Units finement criteria. Our approach excels by speed, flexibility (PMUs) for estimating the state of a nonlinear power sys- and thus can be applied in many fields from environmental tem in real time. These algorithms involve partitioning of to financial sciences. large power systems into several sub-systems, and multi- threaded solving with PMU data constraints. Fabian Franzelin Universit¨at Stuttgart Eugene A. Feinberg [email protected] Stony Brook University [email protected] Sergey Oldayshkin University of Stuttgart Bruce Fardanesh [email protected] New York Power Authority [email protected] Benjamin Peherstorfer ACDL, Department of Aeronautics & Astronautics Muqi Li, Roman Samulyak Massachusetts Institute of Technology Stony Brook University [email protected] [email protected], [email protected] Dirk Pfl¨uger University of Stuttgart George Stefopoulos Dirk.Pfl[email protected] New York Power Authority [email protected] CP16 Gaurish Telang HPC and Model Reduction Algorithms for Large- Stony Brook University Scale Simulation of Stochastic Wave Propagation [email protected] Models

We discuss a new class of efficient iterative high-order CP15 high performance computing (HPC) model reduction algo- Simulation-based Current Estimation in Magneto- rithm for simulating wave propagation exterior to stochas- hydrodynamic Generators tic configurations containing very large numbers of parti- cles. Such simulations are crucial in important medical ap- Direct power generation via magnetohydrodynamic princi- plications such as in vivo and in vitro blood measurements pals offers an increase in efficiency over traditional turbo- using light scattering of blood cells, and topical climate machinery systems but commercialization is impeded by science applications such as light scattering and absorption high lifecycle costs. The generators electrodes are dam- by atmospheric aerosols. Even simulation for a single de- aged by the formation of high current density arcs. How- terministic configuration with a large number of particles ever, these arcs induce magnetic fields which are measur- is a large-scale computational challenge. The stochastic able nearby. The development of sensors to detect these nature of the configuration leads to a larger dimensional arcs is critical in controlling the phenomenon. We produce model involving three spatial and several stochastic vari- simulations using the Mimetic Finite Differences and per- ables. Our approach provides a practically feasible HPC form inversion by simulation-based parameter estimation. framework to compute highly accurate statistical moments to quantify uncertainties in stochastic configurations. Duncan A. Mcgregor Oregon State University Mahadevan Ganesh Department of Mathematics Colorado School of Mines CS15 Abstracts 15

[email protected] other existing models.

Hansong Tang,KeQu CP16 Dept. of Civil Eng., City College of NewYork, CUNY Quantification of Structural Uncertainty in a Land [email protected], [email protected] Surface Model

This study identifies and quantifies model structural un- CP17 certainty in the Community Land Model, by fully explor- An Efficient, Pressure Projection Method for Re- ing the high-dimensional model parameter space with ef- acting Low-Mach Flow Simulations ficient sampling and then evaluating the discrepancies be- tween the corresponding numerical simulations and obser- A new explicit variable-density pressure projection method vations using wavelet decomposition and other spatiotem- is proposed with a focus on transient low-Mach-number re- poral analysis approaches. The power spectra, dominant acting flows. This method introduces a new form of the temporal scales and energy, and characteristic phase shift, pressure Poisson equation suitable for use with an explicit are summarized to help quantify model structural uncer- algorithm. The density, assumed to be a function of an tainty and identify the major processes contributing to arbitrary set of transported scalars, is determined by solv- such uncertainty. ing a non-linear system of equations at each point in the domain. The proposed method is evaluated using several Zhangshuan Hou, Maoyi Huang time-varying, variable-density test cases as well as an an- Pacific Northwest National Lab nular jet flow. [email protected], [email protected] Amir Biglari Jaideep Ray The Institute for Clean and Secure Energy Sandia National Laboratories, Livermore, CA Department of Chemical Engineering, University of Utah [email protected] [email protected]

Laura Swiler Tony Saad Sandia National Laboratories Institute for Clean and Secure Energy Albuquerque, New Mexico 87185 University of Utah [email protected] [email protected]

James C. Sutherland CP16 Department of Chemical Engineering PDE-Constrained Optimization Applied to Core The University of Utah Flooding from Reservoir Engineering [email protected]

This talk explores the impact of PDE-constrained opti- mization on the core flooding problem to determine rock- CP17 fluid parameters essential to effective reservoir simulation. Energy-Stable Open Boundary Conditions for Current core flooding technologies are time-consuming and Two-Phase Flows involve manual inversion for parameters of interest on sim- plified physical models of fluid flow. We demonstrate, on We present an effective open boundary condition, and simple model problems, that PDE-constrained optimiza- an associated numerical algorithm, within the phase field tion can automate the process and do so in a robust way framework for dealing with two-phase outflows or open that incorporates more realistic physical fluid flow model- boundaries. Two-phase outflows refer to situations where ing. the interface between two immiscible incompressible flu- ids passes through open portions of the domain boundary. Caleb C. Magruder The proposed open boundary conditions ensure the energy Rice University, Computational and Applied Mathematics stability of the two-phase system, even in situations where [email protected] strong backflows or vortices occur at the two-phase out- flow boundaries. Numerical examples involving two-phase Jeremy Brandman, Shivakumar Kameswaran inflows/outflows will be presented to demonstrate the ef- ExxonMobil Corporate Strategic Research fectiveness of the method when large density ratios and [email protected], shivaku- large viscosity ratios are involved and when strong back- [email protected] flows occur at the two-phase outflow boundaries.

Suchuan Dong CP16 Purdue University Integration of Geophysical Fluid Dynamics and [email protected] Fully 3D Fluid Dynamics to Simulate Multiphysics Coastal Ocean Flows CP17 An integration of geophysical fluid dynamics and fully 3D A Low Mach Number Model for Moist Atmo- fluid dynamics models is proposed to simulate multiphysics spheric Flows coastal ocean flows. This integration is the first of its kind and able to capture flow phenomena at spatial scales O We introduce a low Mach number model for moist atmo- (1) m – O (10,000) km. The approachs methodology and spheric flows that accurately incorporates reversible moist software development are discussed, and its unprecedented processes in flows whose features of interest occur on ad- capabilities will be demonstrated in its applications to cru- vective rather than acoustic time scales. We numerically cially important problems that are beyond the reach of assess the validity of the more computationally efficient low 16 CS15 Abstracts

Mach number approximation for moist atmospheric flows finite elements to reach to a stable space based on the inf- by contrasting the low Mach number solution to reference sup condition. In the meanwhile, we cast the computation solutions computed with a fully compressible formulation for material state update as a successive convex optimiza- for a variety of test problems. tion problem.

Max Duarte Zahra S. Lotfian, Mettupalayam Sivaselvan Center for Computational Sciences and Engineering SUNY at Buffalo Lawrence Berkeley National Laboratory zahrasad@buffalo.edu, mvs@buffalo.edu [email protected]

Ann S. Almgren CP18 Lawrence Berkeley National Laboratory Physically Motivated and Certified Approximation [email protected] of Large Elastic Structures in Real-Time

John B. Bell We introduce a physically motivated, certified model re- CCSE duction approach for the simulation of large component- Lawrence Berkeley Laboratory based elastic structures as bridges. We build the system [email protected] from a library of interoperable, parametrized components and apply a domain decomposition method. We compute the displacement field in real-time at a high FEA by using CP17 a reduced basis approximation within the component and physical modes on the interfaces/ports. The approxima- A Stable Projection Method for the Incompressible tion is certified by error bounds based on local, component- Navier-Stokes Equations on Arbitrary Geometries wise error indicators. and Adaptive Quad/oc-Trees Kathrin Smetana We present a novel stable projection method for the incom- Department of Mechanical Engineering pressible Navier-Stokes equations on non-graded adaptive Massachusetts Institute of Technology quad/oc-trees with arbitrary geometries. The viscosity is [email protected] treated implicitly through a finite volume approach based on Voronoi partitions and the convective term is discretized with a semi-Lagrangian scheme, thus relaxing the time step Phuong Huynh, David Knezevic restrictions. Akselos [email protected], [email protected] Arthur Guittet UCSB Anthony T. Patera [email protected] Massachusetts Institute of Technology Department of Mechanical Engineering [email protected] CP18 Dual-Mixed Finite Element Methods for the Brinkman Problem CP18 A Variational Multi-Scale Approach Using Linear We develop a dual-mixed finite element method for the Simplicial Finite Elements for Transient Viscoelas- Brinkman problem of viscous flow in porous media. The tic Solid Mechanics primary unknowns are the fluid velocity, the fluid stress, and the deviatoric part of the velocity gradient. The We present a variational multi-scale (VMS) approach for method is stable and accurate for a wide range of problem linear and nonlinear transient viscoelastic solid mechanics. parameters, including both the Stokes and Darcy limiting The method is stable and second-order accurate on linear cases. simplicial finite elements (including in the incompressible limit), with only one additional equation for pressure. Us- Jason Howell ing a VMS decomposition, we model the fine-scale variables College of Charleston by residual-consistent formulations to maintain the accu- [email protected] racy. We assess the performance of the method by using manufactured solutions, and test it on 3D problems with Noel J. Walkington complex geometries. Department of Mathematical Sciences Carnegie Mellon University Xianyi Zeng, Guglielmo Scovazzi [email protected] Duke University [email protected], [email protected]

CP18 Numerical Modeling of Non-Associated Flow CP18 Model by Successive Convex Optimization: Appli- High-Order Mixed Finite Elements for a Pressure cation in Incompressible Porous Media Poisson Equation Reformulation of the Navier- Stokes Equations with Electric Boundary Condi- In this study, we propose a numerical method to solve the tions PDEs of incompressible saturated porous media under dy- namic condition and material nonlinearity. Two parallel Pressure Poisson equation (PPE) reformulations for the schemes are implemented to handle the incompressibility Navier-Stokes equations represent a class of methods that condition and the non associated flow material model. The replace the incompressibility constraint by a Poisson equa- approach couples the Raviart-Thomas mixed and Galerkin tion for the pressure, with a suitable choice of the bound- CS15 Abstracts 17

ary conditions so that the incompressibility is maintained. approach. In this talk we present a mixed finite element methods for the Shirokoff-Rosales PPE reformulation, and demonstrate Johan S. Hysing that this approach allows for arbitrary order of accuracy Tokto Inst. of Technology both in space and in time. Aoki Laboratory [email protected] Dong Zhou Temple University CP19 [email protected] An Anchored Analysis of Variance Petrov-Galerkin David Shirokoff Projection Scheme for a Class of High Dimensional New Jersey Institute of Technology Elliptic Partial Differential Equations david.g.shirokoff@njit.edu High dimensional operator equations from state space es- timation, molecular dynamics, and mathematical finance Benjamin Seibold present an interesting numerical challenge because their Temple University dimensionality necessitates schemes beyond classical mesh [email protected] based methods. In this work, we propose a novel anchored separation of variables function decomposition in conjuc- Rodolfo R. Rosales tion with a Petrov-Galerkin projection scheme to overcome Massachusetts Inst of Tech this “curse of dimensionality’. A class of model high dimen- Department of Mathematics sional elliptic partial differential equations are considered [email protected] and numerical results using this nonlinear approximation are presented. Prince Chidyagwai Loyola University Maryland Matthew T. Li Department of Mathematics and Statistics University of Toronto Institute for Aerospace Studies [email protected] [email protected]

Christophe Audouze CP19 University of Toronto Institute for Aerospace Studies Hierarchical Hpk-Adaptivity for Isogeometric [email protected] Analysis Prasanth B. Nair Input your abstract, including TeX commands, here. Hier- University of Toronto archical h-adaptivity has since been implemented for ten- [email protected] sor product B-splines, NURBS, and T-splines in the con- text of isogeometric analysis. We have implemented hpk- adaptivity in the hierarchical unstructured regime. We CP20 present several benchmark examples, which highlight the Ground States and Dynamics of Spin-Orbit- advantages of local hierarchical refinement, the necessity Coupled Bose-Einstein Condensates of multiple types of refinement, and the power of mixed refinement types. We present convergence results for hier- We study analytically and asymptotically as well as numer- archical hpk-refinements, as well as efficient algorithms for ically ground states and dynamics of two-component spin- handling hierarchical hpk-adaptivity. orbit-coupled Bose-Einstein condensates (BECs) modeled by the coupled Gross-Pitaevskii equations (CGPEs). In Emily Evans fact, due to the appearance of the spin-orbit (SO) coupling Mathematics Department in the two-component BEC with a Raman coupling, the Brigham Young University ground state structures and dynamical properties become [email protected] very rich and complicated.

Kevin Tew Yongyong Cai Brigham Young University University of Wisconsin-Madison kevin [email protected] [email protected]

Weizhu Bao CP19 Dept. of Mathematics and Center for Computational Science an A Stencil Based Finite Element Method [email protected]

A Stencil based FEM approach will be introduced which employs tensor-product grids with FEM discretizations. CP20 This approach eliminates costly FEM assembly, allows for Fast Ewald Summation for Mixed Periodic Bound- stencil based computations which further reduces the need ary Conditions Based on the Nonuniform Fft for sparse matrix storage and indirect memory access, and moreover is highly suitable for efficient geometric multigrid We introduce a generalization of the NFFT based fast solvers. Complex boundaries and immersed (and moving) Ewald summation to mixed periodic boundary conditions. interfaces are treated locally with a new macro grid align- In our approach, we combine the corresponding Ewald for- ment technique. Examples and computational results will mulas with the NFFT based fast summation. The new be presented to show the computational effectiveness of the algorithms can be tuned to high accuracy and the perfor- 18 CS15 Abstracts

mance can be compared to those of well established meth- sofi[email protected] ods for the fully periodic case (P3M, P2NFFT). In our talk we will present the main ideas and show numerical results. Simona Perotto MOX - Modeling and Scientific Computing Franziska Nestler, Michael Pippig Dipartimento di Matematica Chemnitz University of Technology [email protected] Department of Mathematics [email protected], [email protected] Alessandro Veneziani MathCS, Emory University, Atlanta, GA [email protected] CP20 Parallel Replica Dynamics with Spatial Paralleliza- CP21 tion for a Driven System Interaction Between Toroidal Swimmers in Stokes We explore the parallel efficiency and speedup for paral- Flow lel replica dynamics (PRD) with spatial parallelization. In traditional PRD, each replica is assigned to an individual The focus of this research has been devoted to study the in- processor, which extends the time domain for the simula- teraction between two or more self-propelled toroidal swim- tion. By adding spatial parallelization of replicas, we are mers in Stokes flow by applying the method of regularized able to simulate larger systems over the same extended Stokeslets. In the study of the interaction between two time domain. Numerical results on a driven system indi- or more toroidal swimmers, we interpret these as three- cate that this approach can lead to more efficient solutions dimensional, zero Reynolds number analogues of finite vor- for realistic physical systems. tex dipoles in an ideal fluid. Then, we examine the stabil- ity of relative equilibria that can form for these swimmers MichaelT.Stobb,JuanMeza when they are initially placed in tandem or abreast. University of California, Merced [email protected], [email protected] Jianjun Huang Worcester Polytechnic Institute Ashlie Martini [email protected] University of California Merced Lisa J. Fauci [email protected] Tulane University Department of Mathematics [email protected] CP21 Simulating Non-Dilute Transport in Porous Media Using a Tcat-Based Model CP21 Brownian and Hydrodynamic Motion of Complex Predicting the transport of non-dilute species in fluids of Shaped Particles in Straight and Branching Blood variable density in porous media is a challenging problem. Vessels We use a thermodynamically constrained averaging theory (TCAT)-based model, which consists of a flow equation, We develop a computational methodology for the study of a species transport equation, and closure relations. We the motion of complex shaped nanoparticles within straight rewrite the model as a system of two partial differential- and branching vessels subject to thermal fluctuations. A algebraic equations. We use a stiff temporal integrator to framework based on Markovian fluctuating hydrodynamics perform 1D simulations. The model is nonlinear and non- of the fluid together with a non-Markovian Langevin dy- smooth. We will discuss results and numerical difficulties. namics perturbing motion of the particle is adopted. An important application of the method is the transport of nanocarriers within a blood vessel for targeted drug deliv- Deena H. Giffen ery. Supported by NIH through grant U01-B016027. North Carolina State University [email protected] Yaohong Wang Department of Mathematics UCSB CP21 [email protected] Hierarchical Model Reduction of the Navier-Stokes Equations for Incompressible Flows in Pipes David Eckmann Department of Anesthesiology and Critical Care Hierarchical Model Reduction is a novel technique designed University of Pennsylvania for reducing computational costs when solving incompress- [email protected] ible flows in networks of pipes. It consists of a separate discretization of the axial and the transversal components of the flow. The former is approximated by finite elements, Ravi Radhakrish the latter by spectral methods. The local accuracy of the Department of Bioengineering transversal discretization can be adaptively modulated. In University of Pennsylvania this talk we present analysis and numerical results, having [email protected] hemodynamics as reference application. Helena Vitoshki, Portonovo Ayyaswamy Sofia Guzzetti Department of Mechanical Engineering and Applied Emory University Mechanics Department of Mathematics and Computer Science University of Pennsylvania CS15 Abstracts 19

[email protected], [email protected] ferential Equations with High Dimensional Ran- dom Inputs

CP21 We present a localized PC expansion for PDEs with An ALE-Phase-Field Method for Dynamic Wetting random inputs, where most existing methods incur pro- of Moving Particles hibitively high simulation cost. The local polynomial chaos method employs a domain decomposition technique to ap- A hybrid method that uses an arbitrary Lagrangian- proximate the stochastic solution locally in a much lower Eulerian technique to track solid particles and a phase-field dimensional random space. Our method applies the cou- method to capture fluid interfaces as well as moving con- pling conditions at the interfaces of the subdomains along tact lines is developed. The Navier-Stokes and the Cahn- with accurate samples to ensure both accuracy and high ef- Hilliard equations are are solved by a mixed finite element ficiency. We present the general mathematical framework method on an adaptive triangular moving mesh. Numer- of our methodology. ical results on the interactions between floating particles, also known as the cheerio effect, and the effect of dynamic Yi Chen wetting in water-entry problems will be presented. Purdue University [email protected] Pengtao Yue Virginia Polytechnic Institute and State University Dongbin Xiu [email protected] University of Utah [email protected]

CP22 John D. Jakeman Anchored ANOVA Petrov-Galerkin (AAPG) Pro- Sandia National Labs jection Schemes for Parabolic Stochastic Partial [email protected] Differential Equations claude gittelson We present an intrusive method based on the combina- ETH Zurich tion of Hoeffding functional ANOVA decomposition with [email protected] stochastic Galerkin projection for solving a class of high- dimensional parabolic stochastic PDEs. Enforcing the component functions of the approximate solution to be or- CP22 thogonal with respect to an appropriate measure and using Variance Reduction in the Simulation of Stochastic adapted test functions, the stochastic weak formulation is Differential Equations decoupled into independent low-dimensional subproblems. An a priori error analysis and numerical studies for stochas- Variance reduction techniques are commonly used to en- tic diffusion models are provided. hance the efficiency of Monte Carlo simulations. This talk focuses on variance reduction for single and coupled sys- Christophe Audouze tems of stochastic ordinary differential equations. Variance University of Toronto reduction techniques such as antithetic variates and control Institute for Aerospace Studies variates will be described and results presented. [email protected] David J. Horntrop Prasanth B. Nair Dept of Mathematical Sciences, Center for Applied Math University of Toronto New Jersey Institute of Technology [email protected] [email protected]

CP22 CP22 Stochastic Low-Dimensional Modeling of Natural Fully Implicit Runge-Kutta Methods for Multi- Convection Using Dynamically Orthogonal Decom- Channel Stiff Stochastic Differential Systems with position Jumps

An efficient numerical method for studying the effect of We discuss systems of ordinary SDEs with non- stochastic parameters on natural convection is presented. commutative multi-channel noise including jump-diffusion In this methodology, the solution is approximated by a gen- processes. Such systems arise in biochemical networks that eralized Karhunen-Loeve expansion. The elements of the involve reactions at different time scales. They are in- basis remain orthogonal for all times and they evolve ac- herently stiff, both in deterministic and stochastic compo- cording to the system dynamics to capture the energetically nents, and change their stiffness with uncertainty. To re- dominant stochastic subspace. The stochasticity can be in- solve this issue we consider fully implicit split-step stochas- troduced at the boundary conditions and source terms, a tic balanced Runge-Kutta methods and investigate their problem setup that includes a wide range of engineering convergence, stability and positivity preserving properties. problems. Numerical examples are provided to show the effectiveness of these methods. Hessameddin Babaee MIT Viktor Reshniak, Abdul Khaliq [email protected] Middle Tennessee State University [email protected], [email protected]

CP22 Guannan Zhang Local Polynomial Chaos Expansion for Linear Dif- Oak Ridge National Laboratory 20 CS15 Abstracts

[email protected] utilized to guide right time-steps to ensure error diminish- ing discretizations. Results for 1D heat and hyperbolic David A. Voss conservation laws will be demonstrated. Western Illinois University [email protected] Yaw Kyei North Carolina A&T State University Greensboro, NC 27401 CP23 [email protected] Space-Time Adaptive Multiresolution Simulations of the Compressible Euler Equations CP23 Fully space-time adaptive multiresolution simulations of A Runge-Kutta Discontinuous Galerkin Method the compressible Euler equations applied to 2d and 3d Rie- for Modeling Storm-Water Flow in Networks of mann problems will be presented. A new higher order local Drainage Channels time stepping strategy is also proposed. The computa- tional efficieny in terms of CPU time and memory com- A unique hybrid 1D/2D approach is presented to model pression will be assessed. The accuracy of the adaptive water flow in networks of channels that naturally exist in simulations with respect to fine grid computations will be coastal areas. The governing 1D and 2D shallow water studied. equations are discretized using an RKDG method. Flows in individual channel branches are treated as 1D flows. These Margarete O. Domingues branches are conservatively coupled together at junctions Instituto Nacional de Pesquisas Espaciais (INPE) using 2D elements. The accuracy of the model is estab- [email protected] lished by comparing the simulation results to experimental data and other numerical models.

Muller Lopes, Odim Mendes Prapti Neupane INPE, Sao Jose dos Campos, Brazil Institute for Computation, Engineering and Science [email protected], [email protected] University of Texas at Austin [email protected] Kai Schneider Universite de Provence, Aix-Marseille Clint Dawson Centre de Mathematiques et Informatique Institute for Computational Engineering and Sciences [email protected] University of Texas at Austin [email protected] CP23 Cubic B-Spline Quasi-Interpolation Based Numer- CP23 ical Scheme for Hyperbolic Conservation Laws Lagrangian Particle Method for Complex Flows

The present work analyzes the Cubic B-Spline Quasi- A new Lagrangian particle method improving the smooth Interpolation (CBSQI) based explicit numerical schemes particle hydrodynamics (SPH) has been developed for for hyperbolic conservation laws. To improve the stability equations of compressible flows. The method eliminates of the proposed numerical scheme, we modify the CBSQI two major deficiencies of SPH: the dependence on parame- scheme by adding an artificial diffusion to the numerical ter called the smoothening length and the presence of large scheme through a diffusion parameter b. We derive a rela- linear errors of SPH differential operators. Particle-based tion between the CFL condition and b, which ensures the stable, high order upwinding schemes have been developed monotonicity of the proposed numerical scheme. Further, ∞ using moving weighted least squares. Rigorous verification the L -error and the TVD property of the modified BSQI tests and applications to complex free surface flows will be scheme are established. discussed.

Rakesh Kumar Roman Samulyak, Hsin-Chiang Chen, Wei Li IIT Bombay Stony Brook University [email protected] [email protected], [email protected], [email protected] Sambandam Baskar Indian Institute of Technology Bombay [email protected] CP24 Quantifying Scale Coupling and Energy Pathways in the Ocean CP23 A Space-Time Finite Volume Differencing Method The oceans display energetic dynamics across a wide range for Robust Higher Order Schemes for Transport of spatial scales, and researchers have long worked to bet- Equations ter understand the energy coupling between these various scales. While there have been previous attempts to under- A space-time discretization method is applied to construct stand energy pathways, assumptions of homogeneity and robust higher-order schemes for transport equations. A isotropy have presented a limitation upon the applicability unified space-time error for integral formulations are con- of the analyses. Here we present a more general technique, structed using general weighted quadratures for flux inte- unrestricted by the usual assumptions of homogeneity or grals. Efficient quadrature approximations of sources are isotropy, which allows one to simultaneously probe the dy- then sought to account for local space-time fluxes through a namics in both space and time. We makes use of a novel constrained minimization of error. Residual errors are then coarse-graining framework, which accounts for the spheri- CS15 Abstracts 21

cal geometry of the problem, to directly analyze the cou- [email protected] pling between scales. We apply this technique to strongly eddying high-resolution simulations using LANLs Paral- lel Ocean Program. We examine the extent to which the CP24 traditional paradigm for such pathways is valid at various Free Surface Waves on a Horizontal Shear Flow locations such as in western boundary currents, near the equator, and in the deep ocean. Free surface waves on a non-uniform mean flow are con- sidered. The mean flow U(y) varies with the transverse coordinate y but not the vertical. The domain is bounded Hussein Aluie, Matthew Hecht on one side by a flat rigid vertical wall and unbounded Los Alamos National Laboratory on the other side. The mean flows considered are nonzero [email protected], [email protected] near the vertical wall and approach zero far from the wall, e.g. U = ey.Forlargey where the mean flow is near- Geoffrey Vallis zero the waves are merely irrotational Stokes’ waves. Near University of Exeter the wall the mean flow and the waves are rotational but [email protected] still inviscid. Solutions are obtained using a nonuniform coordinate transformation that converts the free surface boundary condition into a modified Bessel equation. The CP24 solution for linear waves that are periodic along the wall is an expansion in Bessel of imaginary argument and imagi- A Numerical Simulation of the Sediment Dynamics nary order. Eigenvalues are found numerically. in a Three Dimensional Fluid Flow John P. Mchugh University of New Hampshire In this study we use NaSt3D as fluid solver for incom- [email protected] pressible two-phase flow problems in three dimensions. We apply this fluid solver to the problem of sediment transport Gary Lapham processes. The main parts in sediment transport are bed Maine Maritime Academy load and suspension load. Both parts are calculated from [email protected] the fluid velocities and are used to compute the transport of sediment masses. Single phase examples like dunes and ripples as well as two-phase phenomena like scouring at an CP24 obstacle can be reproduced by this model. Three-Dimensional Wavelet-Based Adaptive Mesh Refinement Algorithm for Numerical Simulation of Markus Burkow Atmospheric Global Chemical Transport Institute for Numerical Simulation University Bonn Accurate numerical modeling of multi-scale Global Chem- [email protected] ical Transport Models (GCTMs) is a challenging task. Here we present Wavelet-based Adaptive Mesh Refinement Michael Griebel (WAMR) method that allows efficient numerical simulation Universitat Bonn of the GCTMs by permitting two-three orders of magni- Inst fur Angewandte Mathematik tude finer local resolution than static-grid GCTMs for the [email protected] same number of grid points. Therefore, WAMR provides a realistic opportunity to model efficiently challenging multi- scale GCTMs on existing computers by producing accurate results at a relatively low computational cost. Supported CP24 by NSF grant HRD-1036563

Openfoam Implementation of a New Subgrid-Scale Artem N. Semakin, Yevgenii Rastigejev Model for Large Eddy Simulation North Carolina A&T State University [email protected], ye [email protected] We have recently proposed a novel subgrid scale model based on random vortex structures for large eddy simula- CP25 tion of the ocean. It is developed for homogeneous and in- compressible flows. In this study, we validate the model by Tensor Rank Prediction via Cross Validation numerical simulations and compare with well-known sub- grid scale models and direct numerical simulation. Tur- The use of higher order tensors in machine learning has bulent channel flow is solved at different Reynolds num- become increasingly popular in recent years. Traditional bers using OpenFOAM software. The results indicate the techniques like clustering and principle component analy- strengths of our model and the directions for improvement. sis can be extended to N-way data through the Canonical Polyadic (CP) tensor decomposition, but only if the rank is known ahead of time. Although computing the rank is NP-hard, we approximate it using cross validation, a sta- Rukiye Kara tistical technique used to choose model complexity. We Department of Mathematics present results for dense, normally distributed data. Mimar Sinan Fine Arts University [email protected] Woody N. Austin University of Texas - Austin Mine Caglar [email protected] Department of Mathematics Koc University Tamara G. Kolda, Todd Plantenga 22 CS15 Abstracts

Sandia National Laboratories Department of Mathematics [email protected], [email protected] [email protected]

Setephen Shank CP25 Massachussets Instittute of Technology Lu and Partial Orthogonalization Precondition- [email protected] ing for Conjugate Gradient Solution of Overdeter- mined Sparse Least Squares Problems Valeria Simoncini Universita’ di Bologna Let PLU = AQ be a decomposition of a sparse rank n [email protected] matrix A with m rows and n columns, m>n.Conju- gate gradient iteration on the system LT L can be used to find x minimizing ||Ax − b||2.WecompareLU and par- CP25 tial orthogonalization preconditionings and also a hybrid An Implementation and Analysis of the Refined scheme using both techniques. Automated conversion to Projection Method For (Jacobi-)Davidson Type C++ from Matlab and Octave scripts is explored. Methods Gary W. Howell The computation of interior eigenvalues of large sparse ma- North Carolina State University trices remains a challenging problem. Compared to the gary [email protected] Rayleigh-Ritz projection, the refined projection method is a more effective way to extract Ritz pairs and achieve Marc Baboulin monotonic convergence but with a much higher compu- University of Paris-Sud/INRIA tational cost. We analyze four different implementations [email protected] of refined projection and present a new efficient approach to compute interior eigenvalues accurately for (Jacobi- )Davidson type methods. Numerical experiments demon- CP25 strate the effectiveness and accuracy of the presented On a priori and a posteriori Eigenvalue/eigenvector method. Error Estimates for Nonlinear Eigenvalue Prob- lems Lingfei Wu Department of Computer Science In this talk we present the recent results in finite element College of William & Mary approximations for nonlinear eigenvalue problems, with [email protected] nonlinearity in the spectral parameter. New a priori and a posteriori eigenvalue/eigenvector error estimates are in- Andreas Stathopoulos troduced and verified using the Residual Inverse Iteration College of William & Mary Method (RINVIT) for nonlinear eigenvalue problems. Var- Department of Computer Science ious numerical examples arising from applications in struc- [email protected] tural mechanics and electromagnetics are discussed to dis- play the performance of our approach. This is a joint work with Daniel Kressner (EPF Lausanne). CP26 Updating and Downdating Techniques for Net- Agnieszka Miedlar works TU Berlin [email protected] The total communicability of a network is the sum of the entries in the exponential of its adjacency matrix. This Daniel Kressner quantity offers a good measure of connectivity and can be EPFL Lausanne useful in the design of networks having certain desirable Mathicse properties. I will discuss algorithms that can be used to daniel.kressner@epfl.ch construct networks that are sparse and have a large total communicability. Computational results will be provided.

CP25 Efficient Low-Rank Solutions of Generalized Lya- Francesca Arrigo punov Equations Universit`a degli Studi dell’Insubria [email protected] An iterative method for the low-rank approximate solu- tion of a class of generalized Lyapunov equations is stud- Michele Benzi ied. At each iteration, a standard Lyapunov is solved us- Department of Mathematics and Computer Science ing Galerkin projection with an extended Krylov subspace Emory University method. This Lyapunov equation is solved inexactly, thus [email protected] producing a nonstationary iteration. The inexactness cri- teria for convergence is provided by a new theorem. These tools, together with others presented, comprise an effi- CP26 cient algorithm. Numerical experiments indicate that this Dynamic Causal Modelling of Brain-Behaviour Re- method is competitive vis-`a-vis the current state-of-the-art lationships methods, both in terms of computational times and storage needs. Dynamic Causal Modelling (DCM) of neuroimaging data has become a standard tool for identifying the structure Daniel B. Szyld and plasticity of brain networks that respond to the ex- Temple University perimental manipulation (e.g., sensory stimuli or task de- CS15 Abstracts 23

mands). DCM, however, does not explain how distributed munity detection. brain responses are causally involved in the production of behaviour. Here, we propose a generic extension of DCM David F. Gleich that captures how experimental manipulations are trans- Purdue University formed, through large-scale brain networks, into behaviour [email protected] (e.g. choices, reaction times).

Jean Daunizeau,LionelRigoux MS1 ICM Identifying the Largest Entries in Matrix Multipli- [email protected], [email protected] cation Consider matrices A and B of size m × p and p × n.We CP26 wish to determine the indices of the largest entries in the m × n product matrix C = AB without explicitly calcu- Using Space Filling Curves to Find An Element lating C. For instance, if A represents an adjacency net- That Contains a Given Point work of social connections, then C = AA (i.e., B = A) represents the number of common neighbors for any pair Many techniques used in computational science and engi- of nodes. The largest entries correspond to those pairs neering use a 2D triangulation or 3D tesselation of given with the most common neighbors. Alternatively, it may region, for example finite element analysis or computer be the case that A and B are latent variables in a predic- graphics. Often one needs to locate a triangle or tetrahe- tion task, and the largest entries in C = AB correspond dron that contains a given point. For example, to evalute a to the most likely pairings. The matrices A and B may be finite element solution at an arbitrary point, a containing dense with p m, n or general sparse matrices (in which element must be located. We present a new fast algorithm case C may or may not be dense). We propose a sampling- for this operation which is based on space filling curves. based method to efficiently identify the largest entries in C. Each sample produces a pair (i, j), and the pairs that William F. Mitchell are sampled most frequently correspond to the largest en- NIST, Gaithersburg, MD tries in C in expectation. Specifically, the probability of [email protected] 2 choosing pair (i, j) is proportional to cij .Thenumberof samples for a given confidence level is independent of the CP26 size of the matrices, and in practice s mn.Thecostof the method is O(nnz(A) + nnz(B)) for preprocessing and Topology Backs Holistic Medicine O(log(nnz(A)) + log(m)+log(n)) per sample. The holistic concept in alternative medical practice up- Grey Ballard, Tamara G. Kolda holds that “all of people’s needs should be taken into ac- Sandia National Laboratories count.” In other words, the body is seen as a whole. The [email protected], [email protected] holistic point of view can be scientifically validated by de- termining whether different bodily variables are related to Ali Pinar one another. In this study we provide strong evidence sup- Sandia National Labs porting this claim. We establish the existence of at least [email protected] one fully non-linear relationship involving two bodily vari- ables. C. Seshadhri Fernando Schwartz Univ. California Santa Cruz Department of Mathematics [email protected] University of Tennessee [email protected] MS1 Mining Uncertain Networks Louis Xiang The Chinese University of Hong Kong Abstract not available at time of publication. [email protected] Evamaria Terzi Kwai L. Wong Boston University Joint Institute for Computational Science [email protected] University of Tennessee/ORNL [email protected] MS1 Network Science of Brain Networks MS1 Abstract not available at time of publication. Local Methods in Network Science Zoltan Toroczkai Local methods for methods for network analysis return a University of Notre-Dame property of the network without looking even at the entire [email protected] network. Thus, their runtimes are typically sublinear in the size of the input network. I’ll discuss recent work on using local methods to compute centrality vectors such as MS2 the PageRank vector and the heat kernel vector. These Convex Biclustering involve approximately solving linear systems and approxi- mate matrix exponentials, respectively. We’ll also see how In the biclustering problem, we seek to simultaneously these primitives give highly scalable algorithms for com- group observations and features. We present a convex 24 CS15 Abstracts

formulation of the biclustering problem that possesses a Chalmers University of Technology unique global minimizer and an iterative algorithm, CO- [email protected], [email protected] BRA, that is guaranteed to identify it. The key contri- butions of our work are its simplicity, interpretability, and Yujun Cao algorithmic guarantees. We demonstrate the advantages Institute PPRIME, ENSMA of our approach, which includes stably and reproducibly RENAULT, France identifying biclusterings, on simulated and real microarray [email protected] data. Jacques Boree Eric Chi Institute PPRIME, ENSMA Rice University [email protected] [email protected] Robert K. Niven Richard G. Baraniuk UNSW/ADFA, Australia Rice University [email protected] Electrical and Computer Engineering Department [email protected] Louis N. Cattafesta FCAAP, Florida State University, USA Genevera Allen [email protected] Rice University [email protected] MS2 Ronald Coifman Yale University Self-Tuning Complex Systems Department of Computer Science [email protected] Abstract not available at time of publication. J. Nathan Kutz MS2 University of Washington Dept of Applied Mathematics Cluster-based Reduced-order Modelling: From [email protected] Shear Flows to Engine Tumble Motion

We propose a cluster-based ROM strategy to distil nonlin- MS2 ear mechanisms in an unsupervised manner. This strat- egy uses cluster analysis to partition snapshot data into a The Impact of L1 optimization in Nonlinear PDE small number of representative states in the state space. The transitions between the states are dynamically mod- At this time almost everyone interested in finding sparse elled as Markov process. CROM has potential applications solutions to discrete equations is aware that l1 optimiza- for the systematic identification of physical mechanisms of tion plays a key role. However that fact that L1 optimiza- complex dynamics, for the identification of precursors to tion, using the techniques developed for l1, is a very pow- desirable and undesirable events, and for flow control de- erful tool in nonlinear PDE and numerical analysis is less sign exploiting nonlinearities. widely known. H. Brezis, in 1974, showed that adding an L1 type penalty to calculus of variations problems which Eurika Kaiser lead to elliptic equations plus a signum type terms gives Institute PPRIME, CNRS solutions with compact support. I will discuss this, numer- [email protected] ical aspects, applications to Schrodinger equations, obsta- cle problems, numerical homogenization and certain high Bernd R. Noack dimensional PDE’s. Institut PPRIME, CNRS [email protected] Stanley J. Osher University of California Department of Mathematics Laurent Cordier, Laurent Cordier [email protected] Institute PPRIME, CNRS [email protected], [email protected] MS3 Andreas Spohn Modulus of Families of Walks on Graphs Institute PPRIME, ENSMA [email protected] The modulus of a family of paths in a continuum provides a quantitative assessment of the “richness’ of the family: large families of short paths have larger modulus than small Marc Segond, Markus W Abel families of long paths. In the discrete setting, the concept Ambrosys GmbH of modulus can be linked to several graph-theoretic quan- [email protected], [email protected] tities including shortest path, minimum cut, and effective resistance. This talk will cover connections among these Guillaume Daviller concepts, some applications, and a numerical algorithm for CERFACS, France computing the modulus. [email protected] Nathan Albin Jan sth, Sinisa Krajnovic Kansas State University CS15 Abstracts 25

[email protected] via Basis Splitting

This talk discusses a method to adaptively refine reduced- MS3 order models a posteriori without requiring additional full- Graph Directed Topic Modeling order-model solves. The technique is analogous to mesh- adaptive h-refinement: it enriches the reduced-basis space Recent advancements in dictionary learning or topic mod- online by ‘splitting’ a given basis vector into several vec- eling algorithms find data representations using sparse cod- tors with disjoint support. The splitting scheme is de- ing techniques such as L1 or non-parametric Bayesian reg- fined by a tree structure constructed offline via recursive ularizations. Concurrently, the graph community has de- k-means clustering of the state variables using snapshot veloped algorithms to segment data into clusters using sim- data. The method identifies the vectors to split online ilarity measures. In this work, we integrate the graphical using a dual-weighted-residual approach that aims to re- models and dictionary learning concepts to infer represen- duce error in an output quantity of interest. The resulting tations directed by a graphical structure, enforcing prior method generates a hierarchy of subspaces online without correlations among documents. The utility of this tech- requiring large-scale operations or full-order-model solves. nique is demonstrated on text and image data. Further, it enables the reduced-order model to satisfy any prescribed error tolerance regardless of its original fidelity, Arjuna Flenner as a completely refined reduced-order model is mathemat- Naval Air Weapons Station ically equivalent to the original full-order model. afl[email protected] Kevin T. Carlberg Cristina Garcia-Cardona Sandia National Laboratories Los Alamos National Laboratory [email protected] [email protected]

MS3 MS4 Building Graphs to Analyze Big Data Online-Adaptive Reduced Bases for Parametric Problems There has been increasing demand to understand the data around us. The flood of social media requires new math- We address the topic of projection-based model order re- ematics, methodologies and procedures to extract knowl- duction for parametric systems. If the solution manifold edge from massive datasets. Spectral methods are graph under varying parameters or time is complex, single re- based techniques that uses eigenfunctions of a graph to duced projection spaces are not sufficient to achieve global extract the underlying global structure of a dataset. The accurate approximation. Locality with respect to param- construction of these, application dependent, graphs re- eter or time for generating submodels in the offline phase quire new mathematical ideas that extend data represen- is a solution but may be misleading or yield redundant tation, distance, topic modeling and sparsity. The product models. Therefore, we propose to generate reduced mod- is often massive matrices that push the limits of matrix els by online-greedy procedures from dictionaries of basis computation. This talk looks at applications to analyzing elements. text, images, Twitter microblogs and content based search.

Blake Hunter Bernard Haasdonk UCLA Mathematics Department University of Stuttgart [email protected] [email protected]

MS3 MS4 An Incremental Reseeding Strategy for Clustering A Nonlinear Trust Region Framework for PDE- Constrained Optimization Using Progressively- In this work we propose a simple and easily parallelizable Constructed Reduced-Order Models algorithm for multiway graph partitioning. The algorithm alternates between three basic components: diffusing seed vertices over the graph, thresholding the diffused seeds, The large computational cost associated with high-fidelity and then randomly reseeding the thresholded clusters. We simulations has limited their use in many-query scenarios demonstrate experimentally that the proper combination (optimization and UQ). A nonlinear trust-region frame- of these ingredients leads to an algorithm that achieves work using Reduced-Order Models (ROMs) is introduced state-of-the-art performance in terms of cluster purity on as a means to accelerate PDE-constrained optimization. A standard benchmarks datasets. Moreover, the algorithm progressive approach is employed to construct a ROM dur- runs an order of magnitude faster than the other algorithms ing the optimization procedure. On problems from aero- that achieve comparable results in terms of accuracy. This dynamic shape optimization, the framework reduces the a joint work with X. Bresson, H. Hu, A. Szlam and J. von number of queries to the high-dimensional model by a fac- Brecht. tor of 4 with no loss in accuracy.

Thomas Laurent Matthew J. Zahr Loyola Marymount University Stanford University [email protected] University of California, Berkeley [email protected]

MS4 Charbel Farhat Adaptive h-refinement for Reduced-order Models Stanford University 26 CS15 Abstracts

[email protected] Patrick Guidotti University of California at Irvine [email protected] MS5 A Bound-Plus-Equality Constrained Quadratic Yunho Kim Minimization Algorithm for Inverse Problems Ulsan National Institute of Science and Technology Department of Mathematical Sciences Solutions of inverse problems are often obtained by solving [email protected] a quadratic minimization problem, e.g., the least squares solution in linear cases. Prior information can be in- corporated into such problems by adding constraints to MS5 1 the quadratic minimization. Moreover, L regularization Recycling Krylov Subspaces for Parametric Linear methods, such as total variation and wavelet-based regu- Systems Arising from Hyperspectral Diffuse Opti- larization, can be implemented by solving a constrained cal Tomography quadratic minimization problem. In this talk, we present an algorithm for solving bound-plus-equality constrained The imaging of chromophore concentrations using Diffuse quadratic minimization problems, with applications in Optical Tomography (DOT) data can be mathematically imaging. described as an ill-posed and non-linear inverse problem. The reconstruction algorithm for hyperspectral data even Johnathan M. Bardsley using a linearized Born model is prohibitively expensive, University of Montana both in terms of computation and memory. We discuss [email protected] novel computational strategies for reducing the computa- tional cost based on a recycling Krylov subspace approach Marylesa Howard for a class of parameteric linear systems. We will demon- National Security Technologies, LLC strate the resulting computational gains and the validity of [email protected] our approach by comparison with synthetic experiments.

Arvind Saibaba MS5 Department of Electrical and Computer Engineering Statistically Motivated Preconditioners and Stop- Tufts University ping Criteria for Biomedical Inverse Problems [email protected]

The solution of large-scale, ill-posed, possibly underdeter- Misha E. Kilmer, Eric Miller mined linear systems of equation arises in many applica- Tufts University tion to linear and nonlinear biomedical inverse problems. [email protected], [email protected] In this talk we show how statistical a-priori expectation about the solution and statistical description of the noise in the right-hand side can be exploited to improve the res- MS6 olution of the linear system and design solid stopping rules The Dirichlet-Neumann Iteration and Unsteady for Krylov-type iterative methods. Thermal Fluid Structure Interaction

Daniela Calvetti We consider unsteady thermal fluid structure interaction Case Western Reserve Univ to model industrial gas quenching in steel forging, where Department of Mathematics steel is cooled using high pressured gas. The models are [email protected] the compressible Navier-Stokes equations and the nonlin- ear heat equation. In time, a previously developed efficient Erkki Somersalo adaptive higher order time integration scheme with lin- Case Western Reserve University ear extrapolation within a partitioned Dirichlet-Neumann [email protected] framework for the coupling is considered. The iteration is surprisingly fast and we present some analysis that explains this phenomenon. MS5 Numerical Implementation of a New Class of Philipp Birken Forward-Backward-Forward Diffusion Equations Department 10, Mathematics and Natural Sciences for Image Restoration University of Kassel, Germany [email protected] In this talk, we present the implementation and numer- ical experiments demonstrating new forward-backward- Azahar Monge Sanchez forward nonlinear diffusion equations for noise reduction Lund University and deblurring, developed in collaboration with Patrick Centre for the Mathematical Sciences Guidotti and Yunho Kim. The new models preserve and [email protected] enhance the most desirable aspects of the closely-related Perona-Malik equation without allowing staircasing. By using a Krylov subspace spectral (KSS) method for time- MS6 stepping, the properties of the new models are preserved Multi-level Acceleration of Strongly Coupled without sacrificing efficiency. Fluid-structure Interaction with Manifold Map- ping James V. Lambers University of Southern Mississippi Strongly coupled partitioned fluid-structure interaction Department of Mathematics problems require multiple coupling iterations per time step. [email protected] In order to reduce the number of coupling iterations, the CS15 Abstracts 27

manifold mapping algorithm is applied, which originates tion in Multivariate Statistics from multi-fidelity optimization. Preliminary computa- tions showed a gain of factor four in terms of the number An envelope is a nascent construct for increasing efficiency of coupling iterations with two grid levels. To gain a larger in multivariate statistics. Improvements in efficiency are speedup, the use of more than two levels is investigated for made possible by recognizing that the data may contain a three-dimensional engineering case, namely a hydrofoil. extraneous variation that is immaterial to the purpose of the analysis. This leads to an active subspace – an enve- David Blom lope – for enveloping the material information and thereby Delft University of Technology reducing variation. Beginning with the multivariate lin- [email protected] ear model, we will discuss various types envelopes and how they act to improve efficiency. Alexander H. van Zuijlen, Hester Bijl Faculty Aerospace Engineering Dennis Cook Delft University of Technology, NL University of Minnesota [email protected], [email protected] [email protected]

MS6 MS7 Multirate GARK Schemes Active Subspaces in Theory and Practice

Multirate GARK schemes define a multirate extension We review the theory of the active subspace method from of GARK schemes, generalized additive Runge-Kutta a dimensionality reduction perspective. We describe how schemes. These allow for exploiting multirate behaviour a space with lower dimension than the input space can be in both the right-hand sides and in the components in a constructed using gradient information for the quantities rather general setting, and are thus especially useful for of interest. Bounds are constructed that relate the error coupled problems in a multiphysics setting. We discuss two in reduced order models of the quantities of interest to types of MGARK schemes: IMEX methods, which makes the SVD of the Covariance matrix of the input-output Ja- fully use of the different dynamics and stability properties cobian. Applications from aerospace engineering and oil of the coupled system; and fully implicit schemes, which in- reservoir simulation will be presented. herit the stability properties from both underlying schemes Eric Dow without any coupling constraint. Massachusetts Institute of Technology [email protected] Michael Guenther Bergische Universitaet Wuppertal [email protected] MS7 Adrian Sandu Mathematical Foundations of Subspace Selections Virginia Polytechnic Institute and State University In this talk we present and analyze algorithms which al- [email protected] low us to detect the relevant subspaces characterizing a certain nonlinear phenomenon, exclusively from random collections of relatively few data. We discuss the theoreti- MS6 cal guarantees given by these algorithms both for samples drawn at random according to specific clustering distribu- Partitioned Fluid-Structure Interaction on Mas- tions and for samples drawn without any specific cluster- sively Parallel Systems ing. We show applications in determining regularization parameters in image denoising, without need of knowing Multi-physics applictions such as fluid-structure interac- the noise level a priori. tion (FSI) need massively parallel computations to resolve all relevant spatial and temporal scales. Yet, many classical Massimo Fornasier coupling approaches limit the scalability of the overall sim- Technical University Munich ulation. A partitioned approach allows to reuse highly scal- [email protected] able single-physics codes. We discuss different milestones towards massively parallel FSI, including inter-solver par- Valeriya Naumova allelism, parallel communication, and parallel data map- Simula Research Laboratory ping. All methods are implemented in the coupling library [email protected] preCICE. Test cases with different solvers are presented.

Florian Lindner, Miriam Mehl MS7 Universit¨at Stuttgart fl[email protected], Order Determination for Dimension Reduction Us- [email protected] ing An Alternating Pattern of Spectral Variability Similar eigenvalues in random matrices leads to highly vari- Benjamin Uekermann able eigenvectors; otherwise, eigenvector variability tends TU Munich to be small. We exploit this phenomenon to estimate the [email protected] rank of a fixed, unknown matrix. The proposed method combines eigenvalue drops and eigenvector variability to pinpoint the rank. Under general conditions, we establish MS7 the consistency of the new estimator. We also compare the Envelopes: Subspace Methods for Efficient Estima- proposed method with other order-determination methods 28 CS15 Abstracts

by simulations and in an applied setting. [email protected]

Bing Li Department of Statistics MS8 Penn State High Dimensional Non-Gaussian Bayesian Infer- [email protected] ence with Transport Maps

Wei Luo Characterizing high dimensional posterior distributions in Penn State University the context of nonlinear and non-Gaussian Bayesian in- [email protected] verse problems is a well-known challenging task. A recent approach to this problem seeks a deterministic transport map from a reference distribution to the posterior. Thus MS8 posterior samples can easily be obtained by pushing for- Filtering Unstable Quadratic Dissipative Systems ward reference samples through the map. In this talk, we address the computation of the transport map in high di- Data assimilation refers to the combination of noisy mea- mensions. In particular, we propose a scalable adaptive surements of a physical system with a model of the system algorithm that exploits recent ideas in dimensionality re- in order to infer the state and/or parameters. In the con- duction for Bayesian inverse problems. text of numerical weather prediction the underlying model is typically an unstable dynamical system. Unstable dy- Alessio Spantini,YoussefM.Marzouk namical systems can be stabilized, and hence an estimate Massachusetts Institute of Technology of the solution recovered from noisy data, provided two [email protected], [email protected] conditions hold. First, observe enough of the system: in particular, the unstable modes. Second, weight the ob- served data sufficiently over the model. This talk will il- MS8 lustrate this for the 3DVAR filter applied to three unstable Ensemble Methods for Large-Scale PDE- quadratic dissipative dynamical systems of increasing di- Constrained Bayesian Inverse Problems mension: the Lorenz 1963 model, the Lorenz 1996 model, and the 2D Navier-Stokes equation. Sampling techniques are important for large-scale high di- mensional Bayesian inferences. However, general-purpose Kody Law technique such as Markov chain Monte Carlo is intractable. SRI UQ Center, CEMSE, KAUST We present an ensemble transform algorithm that is rooted [email protected] from the optimal transportation theory. The method trans- forms the prior ensemble to posterior one via a sparse op- Andrew Stuart timization. We develop methods to accelerate the compu- Mathematics Institute, tation of the transformation. Numerical results for large- University of Warwick scale Bayesian inverse problems governed by PDEs will be [email protected] presented.

Daniel Sanz-Alonso Kainan Wang University of Warwick Texas A&M University [email protected] [email protected]

Abhishek Shukla Tan Bui-Thanh Warwick The University of Texas at Austin [email protected] [email protected]

MS8 MS9 Conditions for Successful Data Assimilation in Matrix-Free Interior-Point Method for Large Scale High Dimensions Machine Learning Problems

We show that numerical data assimilation can be successful We present a general interior point method for piecewise only if an effective dimension of the problem is not exces- linear quadratic (PLQ) penalties. These penalties are ubiq- sive. This effective dimension depends on the noise in the uitous in signal processing, inverse problems, and machine model and the data, and can be moderate even when the learning applications; examples include the L2, L1, Huber, number of variables is huge. We analyze several data as- Vapnik, hinge loss, elastic net, and many others. We ex- similation algorithms, including particle filters, and show ploit a conjugate representation of these penalties to design that well-designed particle filters can solve most of those an interior point method for the entire class. The repre- data assimilation problems that can be solved in principle. sentation also gives rise to a calculus that makes it possible to handle compositions, addition, and smoothing of PLQ Matthias Morzfeld penalties, as well as exploit specific problem structure. The Department of Mathematics method is available in an open source package called IP- Lawrence Berkeley National Laboratory solve. Future work focuses on matrix free implementations [email protected] of IPsolve. Joint work with James Burke, Gianluigi Pil- lonetto, and Dominique Orban. Alexandre Chorin Department of Mathematics Aleksandr Aravkin University of California at Berkeley IBM T.J. Watson Research Center CS15 Abstracts 29

[email protected] [email protected]

MS9 MS10 Difference Potentials Method for Parabolic Models Matrix Free Methods for Large-Scale Nonlinear in Irregular Domains Constrained Optimization The Difference Potentials Method (DPM) was originally We present two methods for solving exact penalty subprob- designed as a computationally efficient framework for the lems for nonlinear constrained optimization problems on numerical approximation of the solutions to elliptic prob- product sets that arise when solving large-scale optimiza- lems in irregular domains in 2D and 3D. Additionally, DPM tion problems. The first is a novel iterative re-weighting al- can handle general boundary conditions with equal ease. gorithm (IRWA) that iteratively minimizes quadratic mod- Recently DPM was extended with high-order accuracy to els of relaxed subproblems while automatically updating a parabolic models with variable coefficients and interfaces. relaxation vector. The second approach is based on alter- I will discuss this extension and illustrate the performance nating direction augmented Lagrangian (ADAL) technol- of the approach with several 1D and 2D examples. ogy applied to our setting. The main computational costs of each algorithm are the repeated minimizations of convex Jason Albright quadratic functions which can be performed matrix-free. University of Utah Both algorithms are globally convergent under loose as- Math Department sumptions, and each requires at most O(1/2) iterations to [email protected] reach epsilon-optimality of the objective function. Exper- iments exhibit the ability of both algorithms to efficiently Yekaterina Epshteyn find inexact solutions. However, in certain cases, these ex- Department of mathematics periments indicate that IRWA can be significantly more University of Utah efficient than ADAL. [email protected]

James V. Burke University of Washington MS10 Department of Mathematics Multidimensional Embedded Finite Difference [email protected] Methods which Satisfies Energy Estimates

Abstract not available at time of publication. MS9 Adi Ditkowsky Gauges, Duality, and Phase Retrieval Department of Applied Mathematics Tel Aviv University Gauge functions significantly generalize the notion of a [email protected] norm, and gauge optimization is the class of problems for finding the element of a convex set that is minimal with respect to a gauge. These conceptually simple problems MS10 appear in a remarkable array of applications. I illustrate High Order Cut Finite Elements Methods these ideas in the context of the phase retrieval problem, and show how they lead to new algorithmic approaches for We will present recent work on high order finite element large problems. methods for cut and composite meshes. The common theme is to use Nitsche’s method to enforce conditions on Michael Friedlander boundaries or interfaces, or to solve PDEs on surfaces. The Mathematics Department instabilities that may occur can be resolved in various ways University of California, Davis for example using a mesh-based element-wise association or [email protected] by adding stabilization terms to the variational form. Both theoretical and numerical results will be shown.

MS9 August Johansson Simula School of Research and Innovation Simula Anatomy of a Matrix-Free Interior-Point Solver for Research Lab Convex Optimization Norway [email protected] Recent updates to PDCO (Saunders et al.) implement multiple matrix-free and semi-matrix-free options, includ- Mats G. Larson ing CG with constraint preconditioner, a limited-memory Department of Mathematics LDL factorization preconditioner, and several formulations Umea University of the Newton equations as a system or least-squares prob- [email protected] lem. Most take advantage of regularization. The new object-oriented design lets users select a variant appropri- ate for their problem, and implement new system solvers. MS10 We illustrate the new solvers on large-scale problems. High-Order Accurate Difference Potentials Meth- ods for the Stokes–Darcy Problem Dominique Orban GERAD and Dept. Mathematics and Industrial The Stokes–Darcy problem is a multiphysics model cou- Engineering pling Stokes flow with flow in porous media. In my talk Ecole Polytechnique de Montreal I will present an efficient, high-order accurate numerical 30 CS15 Abstracts

method for this problem. This method, based on the Dif- Hengguang Li ference Potentials Method, uses uniform Cartesian grids Department of Mathematics which do not conform to boundaries or interfaces, and is Wayne State University uniformly high-order accurate. I will present numerical re- [email protected] sults to test the new method. This talk is based on joint work with Y. Epshteyn. Li-yeng Sung Department of Mathematics and CCT Yekaterina Epshteyn Louisiana State University Department of mathematics [email protected] University of Utah [email protected] MS11 Kyle R. Steffen Adaptive Regularization Strategies for Nonlinear University of Utah PDE Department of Mathematics steff[email protected] We will discuss an adaptive regularization strategy for sta- bilizing Newton-like iterations on a coarse mesh, developed in the context of adaptive finite element methods for non- MS11 linear PDE. This methods allows the adaptive algorithm Finite Element Multigrid Framework for Mimetic to start on a coarse mesh where the problem data is badly Finite Difference Discretizations resolved and the linearizations feature indefinite and ill- conditioned Jacobians. Stable configurations of the regu- We are interested in the efficient multigrid method of lin- larized coarse-mesh iterates are used to refine the mesh, ear systems of equations discretized from the mimetic finite leading to sufficient resolution of the data to accurately difference (MFD) schemes which work on general unstruc- approximate the PDE solution. We will discuss the use tured and irregular grids and result in discrete operators of a positive semidefinite penalty term which is adapted that satisfy the exact sequence connecting grad, div and with both mesh refinements and iterations of the nonlinear curl operators on the continuous level. We derive such solver. Numerical examples demonstrate the effectiveness MFD schemes from the standard finite element spaces. of the method and illustrate the distinct phases of the so- Using the finite element framework, we are able to ana- lution process. lyze the convergence of the MFD discretizations and con- struct efficient multigrid methods for the MFD discretiza- Sara Pollock tions of elliptic partial differential equations based on the Texas A&M University local Fourier analysis. Finally, we present several numer- [email protected] ical tests to demonstrate the robustness and efficiency of the proposed multigrid methods. MS11 Francisco Jos´eGaspar Robust Multilevel Preconditioners for Elliptic University of Zaragoza Problems with Discontinuous Coefficients [email protected] We develop robust and efficient multilevel solvers for the Xiaozhe Hu large scale linear systems arising from finite element dis- The Pennsylvania State University cretizations of general second order elliptic equations in [email protected] heterogeneous materials. In this talk, we will discuss the influence of the discontinuous (and possibly anisotropic) coefficients to the overall performance of the multilevel pre- Carmen Rodrigo conditioners. University of Zaragoza [email protected] Yunrong Zhu Department of Mathematics Ludmil Zikatanov University of California at San Diego Department of Mathematics [email protected] The Pennsylvania State University [email protected] MS12 Efficient Eigensolver Algorithm on Accelerator- MS11 Based Architecture New Multigrid Methods for Saddle Point Problems The enormous gap between the high-performance capabil- We have developed new smoothers for the Stokes and linear ities of GPUs and the slow interconnect between them elasticity problems. Using the multigrid Poisson solve, we has made the development of numerical software that is precondition the indefinite system from the finite element scalable across multiple GPUs extremely challenging. We discretization of these saddle point problems. We prove describe a successful methodology on how to address the the resulting multigrid algorithms are contractions with challenges –starting from our algorithm design, kernel opti- the contraction number depending on the regularity of the mization and tuning, to our programming model– in the de- solution but independent of the mesh level. velopment of a scalable high-performance symmetric eigen- value and singular value solver. Susanne Brenner Department of Mathematics Azzam Haidar, Piotr Luszczek Louisiana State University Department of Electrical Engineering and Computer [email protected] Science CS15 Abstracts 31

University of Tennessee, Knoxville [email protected] [email protected], [email protected]

Stanimire Tomov MS12 Innovative Computing Laboratory, Computer Science Towards Materials Design with Extreme-Scale Dept Quantum Simulations University of Tennessee, Knoxville [email protected] With ever improving accuracy of ab initio electronic struc- ture methods, quantum simulations have now become a predictive tool that can be used to search for new mate- MS12 rials with desired properties. For simulations tools to be relevant for such searchers, calculations for individual com- GPGPU Acceleration of the Ams Eigensolver Us- pounds have to be very reliable and optimized to minimize ing Magma the machine and energy footprint, as they have to be re- peated automatically tens or hundreds thousands of times. The automatic multilevel substructuring (AMS) technol- Today, this can be accomplished with clusters that have ogy is a state-of-the-art eigensolver for large-scale eigen- hybrid CPU-GPU nodes. We will discuss the algorithmic value problems and has been frequently used to speed up developments that were necessary to run modern electronic the eigensolution process for finite element models, es- structure codes on such systems. pecially for noise and vibration (N&V) analysis in the automotive industry. To further accelerate the eigenso- Thomas C. Schulthess lution process using the AMS technology, it is essential Swiss National Supercomputing Center to take advantage of high performance GPGPU accelera- [email protected] tors. MAGMA project by University of Tennessee provides various numerical linear algebra subroutines on GPGPU Anton Kozhevnikov and those subroutines have been facilitating the adop- ETH Z¨urich tion of GPGPU acceleration to this technology. Recently, Institut f. Theoretische Physik MAGMA team developed a new high-performance algo- [email protected] rithm for symmetric dense eigenproblems, which has been a performance bottleneck for more than a decade on multi- Solc`a Raffaele core architectures. By adopting this new high-performance ETH algorithm, the performance of the AMS technology can be Eidgen¨ossische Technische Hochschule Z¨urich significantly accelerated. In this paper/talk, we will intro- [email protected] duce the new high-performance MAGMA algorithm and demonstrate the AMS performance benefits using those eigensolution routines. MS14 Opportunities and Challenges in First Principles Mintae Kim Models of Materials SIMULIA Dassault Systemes [email protected] First principles models based on quantum mechanics have provided a significant insight into materials and molecules Luis Crivelli, Michael Wood, Cristian Ianculescu, in recent years, and hold the promise of an ability to de- Vladimir Belsky sign new materials properties one atom at a time. However, SIMULIA-Dassaults systemes these models also raise a number of important challenges. [email protected], [email protected], cris- First, many involve rather ad hoc approximations to the [email protected], [email protected] Schrodinger’s equation. For example, the mathematical basis of widely used exchange and correlation functionals of density functional theory is unclear. Second, many of MS12 these models are extremely computationally demanding, thereby limiting their applicability to relatively small com- High-Performance Computation of Pseudospectra putational cells. However, interesting properties of mate- rials require calculations that are orders of magnitude be- This talk introduces several high-performance variations yond what is currently possible. This talk will give a brief of Van Loan’s triangularization followed by inverse itera- overview of state of the art first principle methods, and pro- tion algorithm which involve parallel reduction to (quasi- vide opinions on opportunities and challenges where math- )triangular or Hessenberg form followed by interleaved Im- ematics and computational sciences can lead to significant plicitly Restarted Arnoldi iterations driven by multi-shift impact. (quasi-)triangular or Hessenberg solves with many right- hand sides. Since multi-shift (quasi-)triangular solves can Kaushik Bhattacharya achieve a very high percentage of peak performance on both Howell N. Tyson Sr. Professor of Mechanics sequential and parallel architectures, such an approach California Institute of Technology both improves the eigenvaluesciency of sequential pseu- [email protected] dospectral computations and provides a high-performance distributed-memory scheme. Results from recent imple- mentations within Elemental (P. et al.) will be pre- MS14 sented for a variety of large dense matrices and practical New Liquid-Crystal Based Models and Technolo- convergence-monitoring schemes will be discussed gies

Jack L. Poulson Research on liquid-crystal based suspensions is rapidly ad- Computational Science and Engineering vancing motivated by applications in materials science as Georgia Institute of Technology well as in biological systems. From proposals for new 32 CS15 Abstracts

display technologies and nanofluidic devices to more fun- cuss is related to wrinkling of thin films and the symmetry damental questions about the mechanisms of clustering breaking in the prestress-to-wrinkle-to-crumple transition, and de-clustering in systems of particles, new experimental where some insight may be gained by simplifying a com- findings call for new modeling and analysis efforts. Efficient plex system in terms of a reduced set of coordinates. The engineering of these systems requires advances to current second class of problems concerns the actuation of thin ne- understanding of isotropic fluid colloids, in that the exis- matic glass sheets. Yet another class of problems relates to tence of structure in the liquid matrix affords new opportu- the interaction of nonlinear pdes and mechanics of materi- nities for flow control, processing, and suspension stability. als in the prediction of static and dynamic microstructure One of the newly observed phenomena is the quadratic de- patterns. pendence of the drift velocity of particles moving in an ionic liquid crystal matrix, on the direction transverse to Marta Lewicka the applied electric field. This property may allow for sig- Department of Mathematics nificant technological applications such as the development University of Pittsburgh of AC- electrophoresis. I will present a survey of the cur- [email protected] rent research status on liquid crystal colloids pointing to challenging mathematical and computational issues, such as in the case of particles of typical size above 50nm. An- MS15 other line of research involving liquid crystal elastomers High Order Semi-Lagrangian Discontinuous is the modeling and development of microdevices, such as Galerkin Schemes for First and Second Order pumps and valves. A basic mechanism is the ability of PDEs the anisotropic elastomer to control the evolution of liquid crystal defects. Devices made of liquid crystal elastomers, High order semi-lagrangian DG schemes are proposed for in addition to exhibiting excellent shape memory, hardly some linear first and second order multi-dimensional time- require any micromachining processes. I will outline some dependant PDEs, based on splitting techniques and one- of the main mathematical issues and their research status. dimensional gaussian quadrature formula. Stability and convergence is proved for the splitting and for variable co- Carme Calderer efficients. Extention to some non-linear PDEs will be also University of Minnesota discussed. [email protected] Olivier Bokanowski Universit´e Paris-Diderot MS14 [email protected] Opportunities in Computational Science: Genomes, Mesoscale and Closing the Loop MS15 High-order Discontinuous Galerkin Methods for Strategies for advancing computational science will be Some Kinetic Models drawn from three concepts now in their infancy: the Materials Genome(1) mesoscale science(2), and closing the In this talk, I will present our recent progress in developing loop among computation, synthesis, characterization and high-order discontinuous Galerkin methods for simulating targeted materials outcomes(3). Each of these strategies some kinetic models, such as Vlasov-Maxwell equations, addresses the fundamental challenge of materials science: some discrete-velocity models in the diffusive limit, and capturing and controlling increasingly complex and the BGK model. Theoretical results will be discussed in functional materials behavior. Examples will be drawn terms of conservation, stability, accuracy, and asymptotic from battery science, composite materials and biology. 1. preserving property, together with some numerical exam- http://www.sciencedirect.com/science/article/pii/S1359028614000060ples. 2. http://science.energy.gov/˜/media/bes/pdf/reports/files/OFMS rpt.pdf 3. http://www.nsf.gov/mps/advisory/mpsac other reports/materialsFengyan Liinstrumentation- final from subcommittee.pdf Rensselaer Polytechnic Institute [email protected] George Crabtree Argonne National Laboratory [email protected] MS15 Convergence of Semi-Discrete Stationary Wigner Equation with Inflow Boundary Conditions MS14 Problems in Pattern Formation, Geometry and De- Making use of the Whittaker-Shannon interpolation for- sign of Materials mula with shifted sampling points, we propose in this paper a well-posed semi-discretization of the stationary Wigner We propose to study some mathematical problems, com- equation with inflow boundary conditions. The conver- bining geometry and analysis, that arise from practical gence of the solutions of the discrete problem to the contin- questions of materials design. Manipulating the micro- uous problem is then analyzed, providing certain regularity structure of a material can radically change its mechan- of the solution of the continuous problem. ical responses. For example, the basic engineering design goal of actuation of nematic glass sheets is to determine Tiao Lu imprinted director distributions in the flat sheet, in order Peking University to achieve particular actuated shapes on exposure to ap- [email protected] propriate stimuli. Another rich source of related analytical questions is provided by the heterogeneous incompatibili- Ruo Li ties of strains, present in bulk and in thin structures, asso- School of Mathematical Science ciated with growth, swelling or shrinkage, plasticity, etc. In Peking University this vein, one class of mathematical problems we will dis- [email protected] CS15 Abstracts 33

Zhangpeng Sun ing the Immersed Boundary Method Peking University [email protected] The lamprey is considered a model organism for neuro- physiology and locomotion studies. Here we present a 2D, integrative, multi-scale model of the lamprey’s anguilliform MS15 (eel-like) swimming driven by neural activation and mus- Self-Organized Hydrodynamics in An Annular Do- cle kinematics coupled to body interactions with fluid sur- main: Modal Analysis and Nonlinear Effects roundings and implemented using the immersed boundary method. Effects on swimming speed and cost (metabolic The self-organized hydrodynamics model of collective be- work) at each scale as well as the role of feedback on per- havior is studied on an annular domain. A modal analysis formance are presented. of the linearized model around a perfectly polarized steady- state is conducted. It shows that the model has only pure Christina Hamlet imaginary modes in countable number and is hence stable. Tulane University Numerical computations of the low-order modes are pro- Department of Mathematics vided. The fully non-linear model is numerically solved and [email protected] nonlinear mode-coupling is then analyzed. Finally, the effi- ciency of the modal decomposition to analyze the complex Eric Tytell features of the nonlinear model is demonstrated. Tufts University Department of Biology Hui Yu [email protected] Universit´e de Toulouse; UPS, INSA, UT1, UTM ; [email protected] Lisa J. Fauci Tulane University MS16 Department of Mathematics [email protected] The Role of Intraclot Transport in the Dynamics of Platelet Deposition and Coagulation Under Flow

We present a spatial-temporal continuum model of blood MS16 clot formation in response to vascular injury that incor- Modeling Escherichia Coli Chemotaxis in a Fluid porates platelet activation, adhesion, and cohesion, treats coagulation reactions comprehensively, and includes the in- The hydrodynamics of Escherichia coli is modeled by cou- fluence of flow and thrombus growth on one another. We pling the chemotaxis equations of a simplified phosphory- focus on transport of platelets and proteins within the clot lation cascade with the method of regularized Stokeslets of itself and how it influences the progression of the coagula- the fluid motion. For a slow enough diffusion rate of the at- tion reactions and thus has profound effects on the growth tractant gradient, simulations have consistently resulted in and ultimate structure of the thrombus. a biased random walk of the majority of cells towards the highest concentration of attractant, chemotactic behavior. Aaron L. Fogelson The results demonstrate how the phosphorylation affects University of Utah the run and tumble mechanism of swimming bacteria. [email protected] Hoa Nguyen Karin Leiderman Trinity University Applied Mathematics [email protected] UC Merced [email protected] MS17 On First Experiments for Nuclear Engineering Ap- MS16 plications on Intel Xeon Phi Modeling Cardiac Electro-Fluid-Mechanical Inter- action Next generation of supercomputers integrate many core computational units and will involve multilevel of paral- Integrative models of the heart that account for the cou- lelism such as Intel Xeon Phi. For nuclear engineering, nu- pling between cardiac mecahnics, fluid dynamics, and elec- merical simulation is based on verified and validated large trophysiology promise to serve as powerful platforms for simulation codes. Moving to these new computing architec- understanding cardiac diseases and for treatment planning tures, will imply deep modifications and all existing codes and optimization. This talk will describe progress towards will not be adapted easily. The subject of this talk is to the development of such electro-fluid-mechanical models of present first experiments on porting existing CEA appli- the heart using the framework of the immersed boundary cations for nuclear engineering on Xeon Phi architecture. (IB) method, with a focus on new image-based model of the heart and work to develop validated high-resolution models of cardiac fluid dynamics. Christophe Calvin Boyce Griffith CEA-Saclay/DEN/DANS/DM2S University of North Carolina at Chapel Hill [email protected] [email protected] MS17 MS16 Opportunities and Challenges in Developing and An Integrative Model of Lamprey Locomotion Us- Using Scientific Libraries on Emerging Architec- 34 CS15 Abstracts

tures fast high-order methods for evaluation of integral operators these algorithms can solve, with high-order accuracy, prob- Scalable manycore and accelerator based systems are be- lems of electromagnetic and acoustic scattering for large coming the norm, and will soon be the dominant platforms and complex three-dimensional geometries. A variety of for very high end systems. In the development of new al- applications will be presented which demonstrate the sig- gorithms and libraries for these systems, common themes nificant improvements the new algorithms can provide over have emerged that, if appreciated and adopted by applica- the accuracy and speed resulting from other approaches. tion and library developers, will improve portability, per- formance and resilience in the future. In this presentation, Oscar P. Bruno we give an overview of some of these themes, and discuss California Institute of Technology strategies for application development efforts today that [email protected] will have lasting value in the future.

Michael Heroux MS18 Sandia National Laboratories Scalable Algorithms for Density Matrix Calcula- [email protected] tions of Cavity Quantum Electrodynamic Systems

MS17 If a coupled quantum systems shows some level of entangle- ment, that system can not simply be described by a single Managing Portability for ASC Applications state. They exist in mixed states. Furthermore, real quan- Large production-quality multi-physics software contains tum systems exhibit dephasing and decoherence, which re- tens of thousands of inner-loop kernels that must run ef- quires a statistical description of the system. This is done fectively on multiple processor architectures and a variety through the density matrix formulation. Density matrices of memory subsystems. We have identified a set of four describe the system as a statistical ensemble of several pure key encapsulation idioms that allow us to manage porta- quantum states.The time dynamics of the density matrix bility in legacy applications while imposing minimal re- are governed by the Lindblad master equation, which has strictions on the way developers write software. We will involves operator multiplication from both the right and discuss our experience integrating these idioms into large left of the density matrix. We study the time dynamics software projects, and present performance behavior for of a system consisting of quantum dots coupled to a sin- select applications. gle plasmon mode. The size of the density matrix grows quickly; a physically reasonable system of 16 quantum dots 16 Jeff Keasler requires a matrix dimension of 50 ∗ 2 . At this size, ex- Lawrence Livermore National Laboratory treme scale computing must be utilized. Aside from the [email protected] novel physics applications, we are currently studying how best to treat this system, through different time stepping Richard Hornung schemes (RK and exponential time integrator) and differ- Lawrence Livermore National Lab ent parallelization algorithms. [email protected] Matthew Otten Department of Physics MS17 Cornell University [email protected] ppOpen-APPL/HEXA: A Framework for Develop- ment of Parallel FEM/FVM Applications on Intel Xeon Phi MS18 ppOpen-HPC is an open source infrastructure for devel- Electromagnetic Power Absorption and Plasmon opment and execution of large-scale scientific applications Resonances on Rough Conducting Surfaces on post-peta-scale supercomputers with automatic tuning (AT). ppOpen-APPL/HEXA is a part of ppOpen-HPC and In this talk we present high-order integral equation meth- a special framework for development of parallel FEM/FVM ods for the evaluation of electromagnetic wave scattering codes with voxel-type hexahedral meshes. In this talk, and absorption by dielectric/conducting bumps and cav- outline of development, optimization and utilization of ities on penetrable half-planes. The numerical far- and ppOpen-APPL/HEXA is described. Moreover, details of near-fields exhibit excellent convergence as discretizations optimization of preconditioned iterative solvers, and ma- are refined –even at and around points where singular fields trix assembling procedures for Intel Xeon Phi processors and infinite currents exist. The methods presented in this are presented. talk are applied to study the absorption of electromagnetic power that results from the presence of defects on flat con- Kengo Nakajima ducting surfaces. The performance of the integral equation The University of Tokyo solvers herein discussed allows for the accurate evaluation Information Technology Center of electromagnetic fields at and around the surface of the [email protected] conducting material where relevant physical phenomena, such as skin-depth effects, occur. Finally we discuss the application of the high-order integral equation methods to MS18 the evaluation electromagnetic fields resulting from excita- Fast Solvers for Wave Propagation and Scattering tion of plamon resonances on rough conducting surfaces. by General Structures We present fast spectral solvers for Partial Differential Carlos A. Perez-Arancibia Equations that address some of the main difficulties as- Computing and Mathematical Sciences sociated with simulation of realistic problems of propaga- California Institute of Technology tion and scattering in the frequency domain. Based on [email protected] CS15 Abstracts 35

Oscar P. Bruno representation with adaptive quadrature nodes, or a con- California Institute of Technology tinuous representation. In general, the positivity of the [email protected] reconstructed density function is not guaranteed with tra- ditional moment methods, and positivity constraints or filtering are required. Here we explore quadrature-based MS18 moment methods that reconstruct the density function on Generalized Combined Sources Integral Equations the unit sphere. The transported moment set is com- for Helmholtz Transmission Problems posed of the trigonometric moments of the spherical an- gles. Compared to quadrature-based reconstruction on the We present a new class of well conditioned integral equa- unit square, the additional constraint of periodicity on the tions for the solution of two and three dimensional scatter- unit sphere requires special considerations. Here we em- ing problems by homogeneous penetrable scatterers. Our ploy Szeg¨o quadrature and an extension of CQMOM on novel boundary integral equations result from representa- the unit circle. The density function is reconstructed using tions of the fields inside and outside the scatterer as com- the extended quadrature method of moments (EQMOM) binations of single and double layer potentials acting on with a von Mises kernel density function. Special attention suitably defined regularizing operators. The regularizing is paid to the hyperbolicity of the moment transport equa- operators are constructed to be approximations of the ad- tions, and to the numerical algorithms to handle realizable mittance operators that map the transmission boundary spatial fluxes, scattering and the diffusion limit. conditions to the exterior and respectively interior Cauchy data on the interface between the media. The latter op- Rodney O. Fox erators can be expressed in terms of Dirichlet-to-Neumann Iowa State University operators. We refer to these regularized boundary inte- Department of Chemical and Biological Engr. gral equations as Generalized Combined Source Integral [email protected] Equations (GCSIE). The ensuing GCSIE are shown to be integral equations of the second kind in the case when the Cory Hauck interface of material discontinuity is a smooth curve in two Oak Ridge National Laboratory dimensions and a smooth surface in three dimensions. [email protected] Catalin Turc Ming Tse P. Laiu Department of Mathematical Sciences Department of Electrical and Computer Engineering New Jersey Institute of Technology University of Maryland - College Park [email protected] [email protected]

MS19 Frederique Laurent Generalized Radiative Transfer: Accounting Accu- Laboratoire EM2C - CNRS UPR 288 rately for Unresolved Variabilities at No Compu- Ecole Centrale Paris tational Cost, Yet Without Homogenization [email protected]

Generalized Radiative Transfer (GRT) is formalized as Marc Massot the integral 1D radiative transfer equation in a uniform Laboratoire EM2C - UPR CNRS 288 medium, but where the exponential functions in the prop- Ecole Centrale Paris agation kernel are replaced with two closely related power [email protected] laws. An adapted Markov chain numerical solution was developed. GRT theory applies to challenging transport problems with highly variable optical properties over a MS19 broad range of scales. Another application is to the effi- Stability of PN Approximations for the Radiative cient and yet accurate computation of broadband spectral Transfer Equation in the Free Streaming Limit responses. Based on a mixed variational framework we will investi- Anthony B. Davis,FengXu gate solvability of the radiative transfer equation in the Jet Propulsion Laboratory free streaming limit. Using this framework we will discuss California Institute of Technology the classical PN approximations and related stability is- [email protected], [email protected] sues. As an alternative we present an equivalent stabilized variational method. MS19 Matthias Schlottbom Quadrature-Based Moment Methods for Radiation Fachbereich Mathematik Transport AG Numerik und Wissenschaftliches Rechnen [email protected] Radiation transport can be described by a kinetic equa- tion with free transport and scattering operators. The high dimensionality of the density function makes the numeri- Herbert Egger cal solution very challenging. Available strategies range Numerical Analysis and Scientific Computing from Monte-Carlo approaches, to collocation such as dis- Darmstadt University of Technology crete ordinate methods, to moment methods. An impor- [email protected] tant aspect of radiation solvers is related to how they rep- resent the phase-space dependence of the density function, which can lead to so-called ray effects where radiation trav- MS19 els along fixed directions in physical space. To overcome On Combining Moment Methods and Discrete- these effects, moment methods can use a delta-function Velocity-Schemes for Solving the Boltzmann Equa- 36 CS15 Abstracts

tion [email protected], [email protected]

Varius methods exit to solve the Boltzmann Equation de- terministically. Moment methods and discrete-velocity- MS20 schemes are two possibilities both using very different ap- One-dimensional Turbulence Simulation: Overview proaches and serving very different purposes. Moment and Application to Soot Formation in Non- methods focus on physical variables and come with build-in premixed Flames conservation properties, Galilean invariance, easy coupling to CFD, etc. Discrete velocity schemes can approximate An overview of one-dimensional turbulence (ODT) simula- very complex distribution functions and are relatively easy tion of turbulent flows is presented along with recent ad- to implement. This talk will discuss the similarities of vances and application to soot formation in nonpremixed both approaches and possible combinations, like the use flames. ODT is a computationally affordable stochastic of physically-adaptive velocity grids. model that resolves a full range of scales and can be ap- plied to flow regimes not available to direct numerical simu- Manuel Torrilhon lation. Soot formation, radiation, and flame emission is an Schinkelstrasse 2 important and challenging multiphysics problem to which RWTH Aachen University we apply ODT for fundamental insight and model valida- [email protected] tion. David O. Lignell,VictoriaLansinger Brigham Young University MS20 [email protected], [email protected] ODTLES: A Multiscale Approach for Highly Tur- bulent Flows John C. Hewson Sandia National Laboratories ODTLES combines the ability of ODT to resolve molecular [email protected] effects with the ability of Large Eddy Simulations (LES) to describe 3D large scale flows. ODTLES is based on an extended LES scale separation ansatz wherein molecular MS20 effects and the turbulent cascade are simulated by ODT Multiphase Turbulent Reacting Flow Simulations while a standard 3D numerical approach time advances Using ODT the 3D large scale flow. Simulation results for highly tur- bulent flows reveal the model and numerical properties of Abstract Results for application of the One-Dimensional ODTLES. Turbulence model to multiphase turbulent combustion of coal is considered. Results are compared to a pilot-scale Christoph Glawe reactor and the ability of the model to capture ignition de- BTU Cottbus lay in this situation is evaluated. Because of its low cost [email protected] relative to DNS and LES, ODT can be used to explore high-fidelity thermochemistry models. We explore several models for heterogeneous and homogeneous reactions and Heiko Schmidt evaluate their ability to reproduce the observed experimen- BTU Cottbus tal data. Mechanical Engineering [email protected] James C. Sutherland Department of Chemical Engineering Alan Kerstein The University of Utah Consultant [email protected] [email protected] Babak Goshayeshi University of Utah MS20 [email protected] Particle-Scalar Field Interactions in One- Dimensional Turbulence MS21 The development of Lagrangian particle models in the con- The most current list of partic- text of one-dimensional turbulence (ODT) allows the study ipating companies is available at of the interactions of particles with various scalar fields in www.siam.org/meetings/cse15/career.php. a novel sense. We describe finite Stokes-number effects of For the most recent list of participating companies visit the relative dispersion of scalars and particles. We also http://www.siam.org/meetings/cse15/career.php show the wide range of interaction time scales associated with particle slip across scalar gradients and with scalar- Bill Kolata field diffusion possible with full ODT resolution of scalar SIAM fields. [email protected] John C. Hewson Sandia National Laboratories MS22 [email protected] Cilia Beating Patterns are not Hydrodynamically Optimal Guangyuan Sun, David O. Lignell Brigham Young University We examine the hydrodynamic performance of two cilia CS15 Abstracts 37

beating patterns reconstructed from experimental data. Karin Leiderman In their respective natural systems, the two beating pat- Applied Mathematics terns correspond to: (A) pumping-specialized cilia, and UC Merced (B) swimming-specialized cilia. We compare the perfor- [email protected] mance of these two cilia beating patterns as a function of the metachronal coordination in the context of two model systems: the swimming of a ciliated cylinder and the fluid MS22 pumping by a ciliated carpet. Three performance mea- Accelerated Boundary Integral Simulations for sures are used for this comparison: (i) average swimming Fluid-Structure Interactions in Periodic Stokes speed/pumping flow rate; (ii) maximum internal moments Flow generated by the cilia; and (iii) swimming/pumping effi- ciencies. We found that, in both models, pattern (B) out- performs pattern (A) in almost all three measures, includ- Boundary integral formulations for Stokes flow involves ing hydrodynamic efficiency. These results challenge the the periodic summation of Green’s functions. The Ewald notion that hydrodynamic efficiency dictates the cilia beat- summation formula for the Stokeslet under triply pe- ing kinematics, and suggest that other biological functions riod boundary conditions is well known (Hasimoto, 1959). and constraints play a role in explaining the wide variety Based on this formula, we have developed a spectrally ac- of cilia beating patterns observed in biological systems. curate FFT based method to speed up the computations. Such methods are also needed for the Stresslet, and for Hanliang Guo systems that are only quasi-periodic. Ewald summation Aerospace and Mechanical Engineering formulas and corresponding FFT based Spectral Ewald University of Southern California methods for such cases will be discussed. Boundary inte- [email protected] gral formulations and simulation results for fluid-structure problems employing Spectral Ewald methods will also be Janna C. Nawroth presented. Harvard School of Engineering [email protected] Anna-Karin Tornberg KTH [email protected] Yang Ding Beijing Computational Science Research Center [email protected] MS23 Eva Kanso Symmetry-Preserving Conservative Lagrangian University of Southern California Scheme for Compressible Euler Equations in Two- [email protected] Dimensional Cylindrical Coordinates In applications such as astrophysics and inertial confine- MS22 ment fusion, there are many three-dimensional cylindrical- A Numerical Method for Doubly-Periodic Stokes symmetric multi-material problems which are usually simu- Flow Near a Wall lated by Lagrangian schemes in the two-dimensional cylin- drical coordinates. For this type of simulation, a critical We present a numerical method for computing doubly- issue for the schemes is to keep spherical symmetry in the periodic Stokes flow in the presence of a wall. By finding cylindrical coordinate system if the original physical prob- fundamental solutions to Stokes equation in Fourier space lem has this symmetry. In the past decades, several La- exactly, in practice only an inverse FFT has to be com- grangian schemes with such symmetry property have been puted. Our algorithm can be used to effectively model developed, but all of them are only first order accurate. arrays of pulmonary or nodal cilia. We match theoretical, In this talk, we develop a second order cell-centered La- numerical and experimental results. grangian scheme for solving compressible Euler equations in cylindrical coordinates, based on the control volume dis- Franz M. Hoffmann cretizations, which is designed to have uniformly second Mathematics Department order accuracy and capability to preserve one-dimensional Tulane University spherical symmetry in a two-dimensional cylindrical geom- fhoff[email protected] etry when computed on an equal-angle-zoned initial grid. The scheme maintains several good properties such as con- servation for mass, momentum and total energy, and the MS22 geometric conservation law. Several two-dimensional nu- Computation of the Regularized Image Systems for merical examples in cylindrical coordinates are presented Doubly-Periodic Brinkman Flow in the Presence of to demonstrate the good performance of the scheme in aWall terms of accuracy, symmetry, non-oscillation and robust- ness. This is a joint work with Chi-Wang Shu. A fast summation method of Ewald type is developed for Brinkman flow due to doubly-periodic arrays of regularized Juan Cheng forces near a plane wall. Method of images is applied to Institute of Applied Physics and Computational find the Brinkman flow due to one regularized force; then Mathematics Poisson summation formula is applied to arrive at the final Beijing, China formula for the doubly-periodic flow. Initial simulation re- cheng [email protected] sults for fluid-cilia interaction problems are also presented.

Hoang-Ngan Nguyen MS23 University of California, Merced [email protected] Superconvergent HDG Methods for Third-Order 38 CS15 Abstracts

Equations in One-Space Dimension merical experiments are shown to demonstrate the theo- retical results. We design and analyze the first hybridizable discontinuous Galerkin methods for third-order linear equations in one- Xiong Meng space dimension. The methods are defined as discrete ver- harbin institute of technology sions of characterizations of the exact solution in terms of University of East Anglia local problems and transmission conditions. They provide [email protected] approximations to the exact solution u and its derivatives q := u and p := u which are piecewise-polynomials of de- gree ku, kq and kp, respectively. We consider the methods MS24 for which the difference between these polynomial degrees A Novel Elliptic Solver Based on RBF-Finite Dif- is at most two. We prove that all these methods have su- ferences for Understanding the Earth’s Electric perconvergence properties which allows us to prove that System their numerical traces converge at the nodes of the parti- tion with order at least 2 k +1,where k is the minimum The Global Electric Circuit (GEC) represents the Earth’s of ku,kq ,kp. This allows us to use an element-by-element electric link between solar, upper and lower atmosphere post-processing to obtain new approximations for u, q and processes, and cloud system dynamics. It is modeled by p converging with order at least 2k + 1 uniformly. an elliptic PDE in 3D spherical-like geometry with highly variable coefficients. Due to the several computational Bo Dong challenges that it presents, a novel radial basis function- University of Massachusetts Dartmouth generated finite differences (RBF-FD) solver has been de- [email protected] veloped. Several features of RBF-FD have proven to be very beneficial. Among all, the ability to easily handle ir- Yanlai Chen regular boundaries such as the Earths topography stands Department of Mathematics out. In this talk, we present this novel RBF-FD elliptic University of Massachusetts Dartmouth solver and the new techniques for handling irregular ge- [email protected] ometries that was motivated by it. Victor Bayona Bernardo Cockburn School of Mathematics National Center for Atmospheric Research (NCAR) University of Minnesota [email protected] [email protected] Natasha Flyer National Center for Atmospheric Research MS23 Institute for Mathematics Applied to Geosciences A Local Discontinuous Galerkin Scheme for the fl[email protected] Patlak-Keller-Segel Chemotaxis Model In this talk, a new local discontinuous Galerkin method is MS24 designed for solving the Patlak-Keller-Segel (PKS) equa- Guidelines to Modeling the Navier-Stokes and Eu- tion. We give the error analysis and also prove the positive- ler Equations with RBF-FD preserving property for the scheme on 1D and 2D struc- tured meshes. Numerical simulations will be presented In applications of radial basis functions (RBFs) for fluid which confirm the predicted convergence rate. modeling, infinitely smooth RBFs have traditionally been used due to the spectral convergence properties. However, Yang Yang fluid flows in nature can exhibit complex features such that Michigan Technological University spectral accuracy cannot be realized on resolutions that [email protected] are observable or practical. A novel approach for mod- eling with RBF-generated finite differences (RBF-FD) is Xingjie Li presented by using polyharmonic spline RBFs (PHS RBF) Brown University together with higher-order polynomials. The approach is xingjie [email protected] tested on nonhydrostatic compressible atmospheric flows in limited area domains. Test cases include flows exhibit- Chi-Wang Shu ing Kelvin-Helmholtz instabilities, turbulence, and bubble Brown University updrafts, simulating cloud entrainment. General guidelines Div of Applied Mathematics are given as to how to choose the parameters involved, such [email protected] as the degree of the PHS RBF, the order of the polynomi- als, stencil size, node layout, etc.

MS23 Natasha Flyer National Center for Atmospheric Research Optimal Error Estimates for Discontinuous Institute for Mathematics Applied to Geosciences Galerkin Methods Based on Upwind Biased fl[email protected] Fluxes for Linear Hyperbolic Equations We analyze discontinuous Galerkin methods using upwind- Louis Wicker biased numerical fluxes for time-dependent linear conser- NOAA, NSSL vation laws. In one dimension, optimal a priori error esti- [email protected] mates of order k + 1 are obtained when piecewise polyno- mials of degree at most k (k ≥ 0) are used. We extend the Gregory Barnett analysis to the multidimensional case on Cartesian meshes Department of Applied Mathematics when piecewise tensor product polynomials are used. Nu- University of Colorado, Boulder CS15 Abstracts 39

[email protected] the tensor contraction operation, which can be viewed as a generalization of matrix-matrix multiplication. The alge- bra associated with tensors in these applications is referred MS24 to as multi-linear algebra, the multi-dimensional analog A High-Order RBF-Based Leray Projection of linear algebra. Problems in this area of research fre- Method for the Incompressible Stokes and Navier- quently require the use of distributed-memory computing Stokes Equations architectures to compute the desired method or operation. One common approach to computing multi-linear opera- We present a novel pressure-free Leray projection method tions acting on tensors on such architectures is to cast the for the solution of the incompressible Stokes and Navier- operation in terms of linear operations acting on matri- Stokes equations in two dimensions. The discrete Leray ces and utilize high-performance linear algebra libraries to projector is constructed via generalized interpolation with compute the result. Unfortunately, the underlying linear divergence-free Radial Basis Functions (RBFs). This RBF- algebra library may incur higher network communication based Leray projection method does not require that one costs than is necessary as some structure of the multi-linear specify boundary conditions for the pressure. Results objects is lost when cast to linear objects. In this work, demonstrate that the RBF-based Leray projection method we introduce a notation for describing distributions of ten- demonstrates high orders of convergence in both time and sor data on processing grids, relate redistributions of data space. to well-studied collective communications, and describe a method to systematically derive and analyze algorithms for Edward Fuselier the tensor contraction operation. High Point University Department of Mathematics and Computer Science Martin D. Schatz [email protected] Department of Computer Sciences The University of Texas at Austin Varun Shankar [email protected] School of Computing University of Utah Tamara G. Kolda [email protected] Sandia National Laboratories [email protected] Grady B. Wright Department of Mathematics Robert A. van de Geijn Boise State University, Boise ID The University of Texas at Austin [email protected] Department of Computer Science [email protected] MS25 Distributed Contraction of Tensors MS25 Tensor Computation for Chemistry and Material Unlike distributed matrix multiplication, which has been Science extensively studied, limited work has been done in characterizing distributed tensor contractions. In this Tensors are ubiquitous in many-body quantum physics that talk, a characterization is presented for a family of supports chemistry and materials science. We will dis- communication-optimal distributed tensor contraction al- cuss the types of tensor structures that arise in numer- gorithms on torus networks. The framework uses ical simulation of many-body physics and the resulting three fundamental communication operators to generate computational challenges. We will also discuss TiledAr- communication-efficient algorithms for arbitrary tensor ray, a modern C++ library for block-sparse tensor com- contractions. Trade-off involving use of additional mem- putation and how it addresses some of these challenges. ory for reduced inter-processor communication is also ad- (see github.com/ValeevGroup/tiledarray for more informa- dressed. Experimental results on a BlueGene/Q system tion). demonstrate good scalability on 256K cores. Justus Calvin P Sadayappan, Samyam Rajbhandari Virginia Tech Ohio State University [email protected] [email protected], [email protected] Edward F. Valeev Sriram Krishnamoorthy Virginia Polytechnic Institute and State University Pacific Northwest National Laboratory [email protected] [email protected]

Pai-Wei Lai MS25 Ohio State University Exploiting Multiple Tensor Symmetries though [email protected] Block Diagonalization Suppose an order-6 tensor A has the property that the MS25 value in entry A(i1,i2,i3,j1,j2,j3) does not change if the A Framework for Distributed Tensor Computa- i-indices are permuted, or if the j-indices are permuted, or tions if the i-indices as a group are swapped with the j-indices as a group. Such a tensor has multiple symmetries and Branches of scientific computing, express data as a tensor if it is smartly unfolded into a matrix A,thenA itself has which can be viewed as a multi-dimensional analog of a interesting structure above and beyond ordinary symmetry. matrix. For instance, chemical methods heavily rely on In the case of the given example, there are permutation 40 CS15 Abstracts

matrices Γ1 and Γ2 (both involving Kronecker products [email protected] T T and perfect shuffles) such that both Γ1AΓ1 and Γ2AΓ2 equal A. We show how to compute a structure-preserving, low-rank approximation to A using LDLT with diagonal MS26 pivoting together with a very cheap block diagonalization Towards Multidomain Modeling of Cardiac Elec- that is performed at the start. The full exploitation of trophysiology structure has ramifications for efficiency and applications. Mathematical models are established tools for studies of cardiac tissue physiology and disease. Previously, we intro- Charles Van Loan duced an approach for multidomain mathematical model- Cornell University ing of tissue electrophysiology (Sachse et al, Ann Biomed Department of Computer Science Eng. 2009;37(5):874-89), which allows us to describe tis- [email protected] sues as a mixture of cells with variable electrophysiological properties and intercellular electrical coupling. Here, we Joseph Vokt provide insights into our methodology to establish a micro- Cornell University structural basis for this and other types of models. The ap- [email protected] proach is based on high-resolution three-dimensional con- focal microscopy and image quantification.

Frank B. Sachse MS26 Cardiovascular Research and Training The Role of Microdomains and Ephaptic Coupling Institute and Bioengineering Department in Cardiac Action Potential Propagation [email protected]

Much of our theoretical understanding of cardiac propaga- Thomas Seidel tion is built on the premise that gap junctional coupling Cardiovascular Research and Training Institute between cells is the primary means of electrical coupling. University of Utah In this talk, I will describe some of the newly discovered [email protected] features of propagation that result from consideration of microdomains and spatially inhomogeneous extracellular Jan Christoph Edelmann potential and in doing so, provide new, indirect evidence Cardiovascular Research and Training Institute for the importance of ephaptic, or field effect, coupling. University of University of Utah James P. Keener [email protected] University of Utah [email protected] Gunnar Seemann Karlsruhe Institute of Technology MS26 Germany [email protected] Strongly Scalable Numerical Approaches for Mod- eling Cardiac Electromechanics at High Spatiotem- poral Resolution MS26 Multi-Scale Modeling of the Failing Heart: from This study explores the feasibility of high resolution models Molecule to Patient of bidirectionally coupled cardiac electro-mechanics which resolve cardiac anatomy at a para-cellular resolution. A Heart failure results in remodeling of the heart at the novel algebraic multigrid method is presented, custom- molecular, cellular, tissue, organ and organ system scales. tailored for non-linear mechanics, which is shown to be Here we describe a new cellular model of the cardiac my- strongly scalable up to 4k cores when using a human whole ocyte and the changes that occur in genetically engineered heart model. Benchmark results demonstrate that a single mouse models of heart failure. We then extend the analysis heart beat can be simulated in about 15 minutes at full to multi-scale models of arrhythmia and finally apply these anatomical and biophysical detail. approaches to patient-specific models of atrial fibrillation and heart failure. Christoph Augustin Medical University of Graz Andrew D. McCulloch Institute of Biophysics Department of Bioengineering [email protected] University of California San Diego [email protected] Aurel Neic University of Graz, Institute for Mathematics Christopher Villongco, Adarsh Krishnamurthy Graz, Austria UC San Diego [email protected] [email protected], [email protected]

Manfred Liebmann, Gundolf Haase David Krummen University of Graz UC San Diego [email protected], [email protected] VA San Diego Medical Center [email protected] Gernot Plank Institute of Biophysics Kevin Vincent Medical University of Graz, Austria UCSD CS15 Abstracts 41

[email protected] University of Minnesota [email protected]

MS27 Overview of the Field and the Community of Fast MS28 Multipole Methods Data Mining and Coarse Graining for Network Evolution Problems At the last SIAM CSE conference, at least four mini sym- posia were devoted to fast algorithms for integral equa- In dynamic problems where what evolves is the struc- tions, and I am sure there will be as much interest in ture/connectivity of a complex network, coarse graining the topic at this conference, or more. It’s been almost requires the identification of a small set of macroscopic ob- 30 years since the fast multipole method (FMM) was in- servables (variables) that hopefully suffice to characterize vented, but the activity in the field is getting hot. The the evolutionary dynamics. Data mining tools (and, in landscape of computer hardware has contributed to this, particular, diffusion maps) can be used to provide such a with multi-core and then many-core architectures placing parametrization of the dynamics, using graph metrics to severe constraints on communication bandwidth. FMM provide the pairwise similarities between ”nearby” graphs. has a uniquely favorable communications pattern, making We illustrate this approach in data sets from different it more attractive as an alternative for various applications. (static as well as dynamically evolving) families of graphs This talk will overview the state of the art and of the com- and use the resulting variables to enhance dynamic mod- munity, as the algorithm matures. eling.

Lorena A. Barba Yannis Kevrikidis Department of Mechanical and Aerospace Engineering Princeton University George Washington University [email protected] [email protected]

MS28 MS27 Data-Driven Modeling of Complex Systems with N-body Methods in Computational Science and Control Engineering Analysis of large-scale datasets generated from complex N-body methods find numerous applications in science and systems with external control is becoming increasingly im- engineering. In this talk, I will outline the evolution of portant for the engineering, applied, and biological sci- the methods since the early methods and the adoption of ences. Here, the development of a new method, which their use in fields ranging from gravitational simulations to extends Dynamic Mode Decomposition (DMD), incorpo- machine learning. rates the effect of control to extract low-order models from high-dimensional, complex systems. The method, called George Biros Dynamic Mode Decomposition with control (DMDc), was University of Texas at Austin developed for the purpose of studying infectious disease [email protected] spread and designing intervention campaigns.

Joshua L. Proctor MS27 Intellectual Ventures Computer Science Aspects of Fast Multipole Meth- [email protected] ods

Abstract not available at time of publication. MS28 Richard Vuduc A Deim Induced Cur Factorization Georgia Institute of Technology [email protected]. edu Abstract not available at time of publication. Danny C. Sorensen MS27 Rice University [email protected] The Geometry of the Fast Multipole Methods

An overview of the geometric aspect of the different kinds MS29 of fast multipole methods. Geometric Methods in Image Processing, Net- Lexing Ying works, and Machine Learning Stanford [email protected] We present new methods for segmentation of large datasets with graph based structure. The method combines ideas from classical nonlinear PDE-based image segmentation MS28 with fast and accessible linear algebra methods for com- Low-Complexity Stochastic Modeling of Turbulent puting information about the spectrum of the graph Lapla- Flows cian. The goal of the algorithms is to solve semi-supervised and unsupervised graph cut optimization problems. I will Abstract not available at time of publication. present results for image processing applications such as image labeling and hyperspectral video segmentation, and Mihailo R. Jovanovic results from machine learning and community detection in Electrical and Computer Engineering social networks, including modularity optimization posed 42 CS15 Abstracts

as a graph total variation minimization problem. xavier.bresson@epfl.ch

Andrea L. Bertozzi UCLA Department of Mathematics MS29 [email protected] A Panoply of Graph-ported PDEs and Processes In fields such as image processing, data analysis and com- munity detection, the data sets are often modeled as a MS29 graph in which the nodes represent the data points and Sampling of Dynamic Graphs and Recovery of the the edges encode some relationship between the nodes, Spectral Properties relevant to the task at hand. In recent years, people have studied classical continuum partial differential equa- Massive networks have become ubiquitous today. To mon- tions PDE models from image analysis, but formulated on itor such very large networks, one must resort to sampling graphs to be applicable to data analysis problems. These these networks: a succinct subset of nodes and associated studies show interesting connections between continuum edges are extracted from the original network. In this results and the analogous problems on graphs. In this talk paper, we present an algorithm to recover the dominant we will explore some of these PDE type problems formu- eigenvectors of a very large graph using different realistic lated on graphs and their connections with both contin- sampling strategies. We evaluate the performance of the uum results and notions from graph theory. Examples in- algorithm on realistic synthetic datasets and real networks. clude threshold dynamics, modularity optimization, Ohta- Kawasaki minimization, and their relation to graph cuts, mean curvature flow, and bootstrap percolation.

Nathan D. Monnig Yves van Gennip Department Applied Mathematics Nottingham University University of Colorado Boulder [email protected] [email protected]

Conrad Hougen MS30 University of Colorado at Boulder Symplectic Model Reduction for Hamiltonian Sys- [email protected] tems

Francois G. Meyer Proper symplectic decomposition (PSD) is introduced as University of Colorado at Boulder a symplectic model reduction technique using the sym- USA plectic Galerkin projection. Our aim is two-folded. First, [email protected] to achieve computational savings for large-scale Hamilto- nian systems. Second, to preserve the symplectic struc- ture of the original system. As an analogy to the classical MS29 POD-Galerkin approach, the PSD is designed to build a symplectic subspace to fit empirical data, while the sym- Consistency of Variational Partitioning of Point plectic Galerkin projection constructs a low-order Hamil- Clouds tonian system on the symplectic subspace. The proposed technique can preserve system energy, volume of flow, and I will discuss variational problems arising in machine learn- stability. Therefore, it can be better suited for model re- ing and their consistency as the number of data points duction of hyperbolic PDEs as compared to the classical goes to infinity. Consider point clouds obtained as random POD-Galerkin approach. The stability, accuracy, and ef- samples of a measure on a Euclidean domain. Graph repre- ficiency of the proposed technique are illustrated through senting the point cloud is obtained by assigning weights to numerical simulations of several linear and nonlinear wave edges based on the distance between the points. Many equations. machine learning algorithms are based on minimizing a functional on this graph. Among them are balanced cuts Kamran Mohseni and spectral methods for clustering. We will discuss under University of Florida, Gainesville, FL what conditions do the minimizers of graph based func- mohseni@ufl.edu tionals converge to a well defined limit. Liqian Peng Nicolas Garcia Trillos, Dejan Slepcev University of Florida Carnegie Mellon University liqianpeng@ufl.edu [email protected], [email protected] MS30 James von Brecht An Adaptive and Efficient Greedy Procedure for University of California, Los Angeles the Optimal Training of Parametric Reduced- [email protected] Order Models

Thomas Laurent An adaptive and efficient approach for constructing para- Loyola Marymount University metrically robust reduced-order models is developed. The [email protected] approach is based on a greedy sampling of the underlying high-dimensional model along with a fast and efficient sur- Xavier Bresson rogate based procedure for exploring the parametric space Swiss Federal Institute of Technology (EPFL) to identify parameters for which the error is likely to be Institute of Electrical Engineering high. The procedure is illustrated on several cases, in- CS15 Abstracts 43

cluding the realistic prediction of the response of a V-hull demonstrate the performance of our algorithms. vehicle to underbody blasts. Tania Bakhos Arthur Paul-Dubois-Taine Institute for Computational and Mathematical Stanford Engineering [email protected] Stanford University [email protected] David Amsallem Stanford University Arvind Saibaba [email protected] Department of Electrical and Computer Engineering Tufts University [email protected] MS30 Error Estimation for Hyper-Reduced Elastovis- Peter K. Kitanidis coplastic Models Dept. of Civil and Environmental Engineering Stanford University [email protected] We propose an a posteriori error indicator related to hyper- reduced predictions of simulation outputs. We restrict our attention to elastoviscoplastic materials having an incre- MS31 mental variational formulation of the constitutive equa- An Iterative Algorithm for Large-Scale Tikhonov tions, when the outputs are extracted by a continuous func- Regularization tion of the displacements. We obtain an upper bound of the approximation error due to the hyper-reduced formu- In this talk, we describe a hybrid iterative approach for lation. We show numerical results on oligocyclic fatigue. computing solutions to large scale inverse problems via Computational speed-ups are preserved while errors are es- Tikhonov regularization. We consider a hybrid LSMR ap- timated. proach, where Tikhonov regularization is used to solve the subproblem of the LSMR approach. One of the benefits of David Ryckelynck the hybrid approach is that semiconvergence behavior can MINES Paristech be avoided. In addition, since the regularization parameter [email protected] can be estimated during the iterative process, the regular- ization parameter does not need to be estimated a priori, making this approach attractive for large scale problems. MS30 We consider various methods for selecting regularization Geometric Methods in Adaptive Model Order Re- parameters in the hybrid LSMR framework and discuss duction stopping criteria for the iterative method. Numerical ex- amples from image processing illustrate the benefits and The first part of this presentation addresses an original potential of the new approach. manifold learning approach to nonlinear flow problems, where geometric information is used to choose adaptively Julianne Chung local prediction neighborhoods for each ROM approxima- Virginia Tech tion. The method provides a sensible tool for detecting [email protected] gaps in the design of experiment and thus for adaptive re- finement. The second part deals with adaptive projection- Katrina Palmer based ROMs. We propose a method for adjusting a projec- Department of Mathematical Sciences tion subspace to a given parameter condition by optimizing Appalachian State University a suitable goal function on the Grassmann manifold. [email protected]

Ralf Zimmermann DLR Braunschweig, Germany MS31 [email protected] The Arnoldi-Tikhonov Framework: Choice of Reg- ularization Parameters and Matrices Thomas Franz Iterative Krylov subspace methods play a central role in the Institute of Aerodynamics and Flow Technology regularization of large-scale inverse problems. We describe DLR, German Aerospace Center some new regularization parameter choice techniques for an [email protected] Arnoldi-Tikhonov method. In addition, we describe how to adaptively choose a regularization matrix by exploiting the previous approximations, and we introduce two new MS31 strategies to approximate regularization terms weighted in Flexible Krylov Subspace Methods for Shifted Sys- a generic norm. The first strategy is exploits adaptive pre- tems with Multiple Right Hand Sides conditioning, and the second strategy is based on a restart- ing procedure. Several PDE-based inverse problems require repeated so- lution to large-scale shifted systems of the form (K + Silvia Gazzola zj M)xj,k = bk for j = ...,nz and k =1,...,ns.Wepro- University of Padova pose a flexible Krylov subspace method that uses multiple [email protected] preconditioners of the form K +τM and discuss extensions to multiple right hand sides using both recycling and block James G. Nagy methods. Numerical experiments using synthetic examples Emory University from a model inverse problem, Hydraulic Tomography, will Department of Math and Computer Science 44 CS15 Abstracts

[email protected] Rensselaer Polytechnic Institute [email protected] Paolo Novatti University of Padova [email protected] MS32 Overcoming the Added Mass Instability for Cou- pling Incompressible Flows and Elastic Beams MS31 Unbiased Predictive Risk and Discrepancy Princi- A new partitioned algorithm for coupling incompressible ples Applied for LSQR Solutions of Ill-posed Least flows with elastic beams is described that overcomes the Squares added-mass instability for light solids. The algorithm re- quires no sub-iterations and is fully second-order accurate. Numerous methods exist for finding regularization param- The new scheme is shown to be stable, even for very light eters when solving ill-posed linear inverse problems using beams, through the analysis of a model problem. The ap- full expansion methods such as the singular value decompo- proach is then applied to the simulation of FSI problems sition (generalized SVD). Interpreting the propagation of involving beams undergoing large deformations using de- noise through the Krylov subspace has limited development forming composite grids. of robust parameter estimators for iterative solutions. We demonstrate the use of unbiased predictive risk estimators Longfei Li and discrepancy principles applied at the subspace level. Department of Mathematical Sciences The work is illustrated for a large scale three dimensional University of Delaware inversion of gravity data. [email protected]

Rosemary A. Renaut Arizona State University MS32 School of Mathematical and Statistical Sciences Partitioned Algorithms for FSI Problems Involving [email protected] Elastic Solids Coupled to Compressible and Incom- pressible Fluids

MS32 New partitioned algorithms for the simulation of elastic Half-Imex Time Integrators for Large Scale Simu- solids coupled to compressible and incompressible fluids lations of Turbulent Incompressible Flows are described. For the compressible case, the coupling uses a interface project based on the solution of a fluid-solid Rie- We develop high order time integrators for the incompress- mann problem, while Robin-Robin coupling conditions are ible Navier-Stokes equations. This system is an index 2 derived for the incompressible case. Both coupling meth- differential-algebraic problem. For the velocity, we consider ods result in stable schemes, without sub-iterations, even an explicit treatment of the nonsymmetric convective term, for FSI problems with large added-mass effects. Numeri- keeping the stiff viscous term implicit. At every stage, a cal results are presented which verify the accuracy of these pressure Poisson problem has to be solved. We combine new added-mass partitioned (AMP) algorithms. the time integration with scalable domain decomposition solvers, and show the efficiency of this approach for large Donald W. Schwendeman core counts (orders of hundreds of thousands). Rensselaer Polytechnic Institute Department of Mathematical Sciences Santiago Badia [email protected] International Center for Numerical Methods in Engineering Universitat Polit`ecnica de Catalunya, Barcelona, Spain MS33 [email protected] An Approach to Big Data in Inverse Problems

Oriol Colomes We develop innovative approaches to address the big data International Center for Numerical Methods in challenge in large-scale inverse problems and UQ governed Engineering by expensive PDEs. Various numerical results will be pre- [email protected] sented to demonstrate the effectiveness of our approaches.

MS32 Ellen B. Le Overview of Added-Mass Partitioned Algorithms UT Austin for FSI Simulations [email protected]

In recent work we have developed some partitioned algo- Aaron Myers rithms for fluid-structure interaction (FSI) problems that UT Austin, ICES couple various combinations of compressible and incom- [email protected] pressible fluids with compressible bulk solids, rigid solids and structural beams. These algorithms overcome the added-mass instability for light solids that has plagued the Tan Bui-Thanh traditional partitioned approach. This talk will give an The University of Texas at Austin overview of these new added-mass-partitioned (AMP) al- [email protected] gorithms along with their implementation using deforming overlapping grids. MS33 William Henshaw Active Subspaces for the Design of Supersonic Low- CS15 Abstracts 45

Boom Aircraft erties of the forward operator. In many problems, changes from the prior to the posterior can be confined to a rel- We apply the active subspace method to a realistic atively low-dimensional subspace. We define and identify simulation-based design problem: the Lockheed N+2 low- such a subspace, called the likelihood-informed subspace boom supersonic passenger jet. The method discovered a (LIS). We show that significant computational savings can low-dimensional linear subspace of inputs that explained be achieved by using this subspace to approximate the pos- a majority of the variability in drag, lift, and sonic-boom. terior distribution. We exploited this subspace to find an optimal design at re- duced computational cost, as well as automatically gener- Tiangang Cui ate deformation modes that yield intuitive interpretations Massachusetts Institute of Technology such as twist and camber. [email protected]

Trent W. Lukaczyk James R. Martin Stanford University University of Texas at Austin [email protected] Institute for Computational Engineering and Sciences [email protected] Juan J. Alonso Department of Aeronautics and Astronautics Youssef M. Marzouk Stanford University Massachusetts Institute of Technology [email protected] [email protected]

Francisco Palacios Antti Solonen Stanford University Lappeenranta University of Technology [email protected] Department of Mathematics and Physics [email protected] MS33 Alessio Spantini Parameter Selection Techniques for Disease Models Massachusetts Institute of Technology [email protected] We discuss parameter selection techniques for nonlinearly parameterized, dynamic, disease models. The objective is to develop techniques to determine the sets of identifiable Luis Tenorio or influential parameters for these models. We compare the Colorado School of Mines performance of Morris screening, Sobol analysis employing [email protected] analysis of variance, Bayesian analysis, and active subspace techniques utilizing singular value decompositions (SVD) and QR factorizations for models with both single and mul- MS34 tiple responses. We also detail the necessity of employing Sparse Grid and Reduced Basis Approximation of such parameter selection techniques before Bayesian model Bayesian Inverse Problems calibration and uncertainty propagation for models having a large number of inputs. We present a computational reduction framework for effi- cient and accurate solution of Bayesian inverse problems on Jared Cook high- or infinite-dimensional parameter spaces that com- Asbury University monly face the curse of dimensionality and large-scale com- [email protected] putation. For the approximation of high or infinite di- mensional integration, we take advantage of sparsity in Nicholas Myers the parametric solution maps in novel dimension-adaptive University of Wisconsin-Milwaukee sparse grid interpolation and quadrature algorithms. For [email protected] large scale problems, we also exploit intrinsic sparsity in the solution map and the high-fidelity approximation and propose a novel, goal-oriented reduced basis method. Nina Ning George Washington University Peng Chen [email protected] ETH Zurich [email protected] Mami Wentworth NC State Christoph Schwab [email protected] ETH Zuerich SAM Ralph C. Smith [email protected] North Carolina State Univ Dept of Mathematics, CRSC [email protected] MS34 Goal-Oriented Model Adaptivity for Inference

MS33 We present a goal-oriented adaptive method for inverse Likelihood-Informed Dimension Reduction for problems based on the use of multiple models. Previous Bayesian Inverse Problems work has addressed the use of goal-oriented grid adaptation in inverse problems, but has been restricted to the single The intrinsic dimensionality of an inverse problem is af- model paradigm. Our method develops estimates for the fected by prior information, the observations, and the prop- error in the prediction quantity of interest due to the use 46 CS15 Abstracts

of a lower fidelity model in the inference process. We also Matrix Completion present numerical experiments illustrating the efficiency of the method. The problem of (stable) robust PCA is to separate a data matrix into low-rank, sparse and noise components. Due to Vikram Garg the cost of standard algorithms, which require full or par- ICES, U Texas, Austin tial SVDs at every step, the problem is extremely compu- [email protected] tationally difficult for large-scale applications. We present a new method that incorporates more information than a Harriet Li traditional first-order method, but without increased cost MIT per iteration, and show very favorable results compared [email protected] to other recent solvers. We also present variants of this algorithm. Lastly, we discuss the specific challenges of a variant of distance matrix completion that is applicable for Karen E. Willcox locating sites on chromosomes. Massachusetts Institute of Technology [email protected] Stephen Becker UC Boulder [email protected] MS34 An Empirical Objective Bayes Method for Large Aleksandr Aravkin Inverse Problems IBM T.J. Watson Research Center [email protected] The Geostatistical Approach is a general, flexible, and com- prehensive formalism for solving underdetermined param- Aurelie Lozano eter estimation problems (inverse problems). The method IBM Research is increasingly used for problems with many unknowns and T. J. Watson Research Center observations. I will review some of the tools, all of which [email protected] exploit the problem structure, to make this approach com- putationally tractable for large problems, including Hierar- chical Matrices and Fast Multipole Method for fast matrix MS35 vector products, compression methods for dimensionality Matrix Free Quadratic-penalty Methods for PDE- reduction, and iterative methods. constrained Optimization

Peter K. Kitanidis The large scale of seismic waveform inversion makes ma- Dept. of Civil and Environmental Engineering trix free implementations essential. We show how to ex- Stanford University ploit the quadratic penalty structure to construct ma- [email protected] trix free reduced-space and full-space algorithms, which have some advantages over the commonly used Lagrangian based methods for PDE-constrained optimization. This in- MS34 cludes the construction of effective and sparse Hessian ap- Applying UQ Approaches to Random Ordinary proximations and reduced sensitivity to the initial guess. A Differential Equations computational bottleneck is the need to solve a large least squares problem with a PDE block. When direct solvers Random Ordinary Differential Equations (RODEs) can of- are not available, we propose a fast matrix free iterative fer an alternative concept for Stochastic Differential Equa- approach with reasonable memory requirements. It takes tions via path-wise solutions of ODEs, avoiding Ito calculus advantage of the structure of the least squares problem and frequently using coloured noise instead of white noise with a combination of preconditioning, low rank decompo- processes for the underlying random effects. We focus on sition and deflation. the numerical solution of RODEs and their connection to UQ techniques to improve computational performance for Bas Peters applications such as earthquake-induced motion of wire- UBC frame buildings. [email protected]

Tobias Neckel Felix J. Herrmann Technische Universit¨at M¨unchen Seismic Laboratory for Imaging and Modeling [email protected] The University of British Columbia [email protected] Hans-Joachim Bungartz Technische Universit¨at M¨unchen, Department of Informatics MS35 Chair of Scientific Computing in Computer Science Compressing Clustered Data using Sparse NMF [email protected] We propose a method for storing clustered data compactly, where each cluster is a collection of many similar datasets Alfredo Parra in matrix form (such as a set of related images). We first Technische Universit¨at M¨unchen compute basis elements for each cluster using low-rank [email protected] SNMF via PDCO. We then use the preprocessing approach of Gillis (2012) to sparsify the full set of (already sparse) basis elements, without significant loss of quality. MS35 Matrix-Free Solvers for Robust PCA and Distance Michael A. Saunders CS15 Abstracts 47

Systems Optimization Laboratory (SOL) curacy is achieved efficiently since only simple Cartesian Dept of Management Sci and Eng, Stanford grids used regardless of the interface shape or boundary. [email protected] The performance of the numerical method is illustrated in several numerical examples in 2D. San Kim ICME, Stanford University Michael Medvinsky [email protected] University of Utah Department of Mathematics [email protected] MS35 Dimensionality Reduction and Uncertainty Quan- Yekaterina Epshteyn tification for Inverse Problems Department of mathematics University of Utah Many inverse problems in science and engineering involve [email protected] multi-experiment data and thus require a large number of forward simulations. Dimensionality reduction tech- Semyon V. Tsynkov niques aim at reducing the number of forward solves by Department of Mathematics (randomly) subsampling the data. In the special case of North Carolina State University non-linear least-squares estimation, we can interpret this [email protected] compression of the data as a (low-rank) approximation of the noise covariance matrix. We shoe that this leads to Eli Turkel different design criteria for the subsampling process. Fur- Tel-Aviv University thermore, the resulting low-rank structure can be exploited [email protected] when designing matrix-free methods for estimating (prop- erties of) the posterior covariance matrix. Finally, we dis- cuss the possibility of estimating the noise covariance ma- MS36 trix itself. A Nitsche Stabilized Fictitious Domain Finite Ele- Tristan van Leeuwen ment Method for the Wave Equation Mathematical Institute We give a weak formulation for solving the wave equation Utrecht University ∇2 [email protected] (¨u = u + f) on a 2-dimensional fictitious domain. In the spatial finite element discretization, boundaries do not conform to element boundaries. Boundary conditions are MS36 enforced weakly by Nitsche’s method. Additional penalty terms ensure a non-stiff temporal system. We give opti- A Fourth Order Accurate Embedded Boundary mal a priori error estimates: second order for u − uh and Method for the Wave Equation in Second Order u˙ − u˙ h and first order for ∇(u − uh), for linear elements Form in L2-norm. Numerical experiments verify the theory. Ex- A fourth-order accurate embedded boundary method for tensions to higher orders are discussed. the scalar wave equation with Dirichlet or Neumann Simon Sticko boundary conditions is described. The method is based on Uppsala University a compact Pade-type discretization of spatial derivatives Department of Information Technology together with a Taylor series method (modified equation) [email protected] in time. A novel approach for enforcing boundary con- ditions is introduced which uses interior boundary points instead of exterior ghost points. This technique removes Gunilla Kreiss the small-cell stiffness problem for both Dirichlet and Neu- Division of Scientific Computing mann boundary conditions, is more accurate and robust Uppsala University than previous methods based on exterior ghost points, and [email protected] guarantees that the solution is single-valued when slender bodies are treated. Numerical experiments are presented to illustrate the stability and accuracy of the method as well MS37 as its application to problems with complex geometries. Cascadic Multilevel for Saddle Point Least-Squares Methods Daniel Appelo University of New Mexico We present a cascadic multilevel method for approximat- [email protected] ing variational formulations of symmetric saddle point sys- tems. The discretization algorithm is based on the avail- ability of families of stable finite element pairs and on fast MS36 and accurate solvers for symmetric positive definite sys- High-Order Numerical Methods for Elliptic Inter- tems. On each fixed level an efficient solver such as the face Problems gradient or the conjugate gradient algorithm for inverting a Schur complement is implemented. As a main application In our talk we consider elliptic equations with piecewise of our approach we define the “saddle point least-squares’ smooth coefficients in irregular domains separated by arbi- method for solving first order systems of PDEs and relate trary shaped interfaces. Our numerical approach for these it with the Bramble-Pasciak’s least-squares approach. We problems is based on generalized Calderon’s operators and apply our saddle point least-squares method to discretizing the Difference Potentials Method. The developed algo- the time harmonic Maxwell equations. The variable of in- rithm easily handles curvilinear boundaries, variable co- terest for the Maxwell equations, the magnetic and electric efficients and general boundary conditions. High-order ac- vector fields, become the constrained variable in the saddle 48 CS15 Abstracts

point least-squares formulation, and bases or stiffness ma- ies on fictitious domain method and full Eulerian phase trices associated with these variables are not needed. The field method for FSI problems will be also introduced. In cascadic saddle point least-squares iterative discretization particular, in terms of ALE method, we developed a non- we build does not involve edge elements or spaces of bubble linear rotational and deformable structural model for FSI functions, and is suitable for preconditioning. for the first time. The technique of master-slave relations is employed to realize the interfacial kinematic condition on Constantin Bacuta the interface of fluid and structure. Velocity is adopted University of Delaware as the principle unknown to reformulate the structural Department of Mathematics model. Our algorithm can also handle a large and irregu- [email protected] lar fluid flow channel in which the rotational structure is immersed with ALE method. We use Newtons method to linearize, and Galerkin/least-square (GLS) and streamline- MS37 upwind/Petrov-Galerkin (SUPG) schemes to stabilize the Multigrid Method for Linear Elasticity with mixed finite element discretization of fluid equations with Weakly Imposed Symmetry ALE approach. Numerical experiments are successfully carried out for a simplified turbine in 2D and a realistic We present a new abstract framework for the convergence turbine in 3D which is deforming as well as spinning around analysis of the subspace correction methods applied to the its rotation of axis cases due to the fluid impact. system of linear algebraic equations associated to the dif- ferential operator arising from the finite element-based dis- Pengtao Sun crete systems of the linear elasticity with weakly imposed University of Nevada Las Vegas, Math. Dept. symmetry. The method is proven to be convergent uni- [email protected] formly with respect to the mesh size and parameters that appear in the equations. A special case of our theory can provide a transparent and improved analysis for the multi- MS38 grid methods developed for the pseudo-stress formulations Algorithms for Hessenberg-Triangular Reduction of Stokes equation. Some sample numerical experiments in Parallel for two dimensional cases are provided to illustrate the the- ory. A recent improvement of the parallel QZ algorithm has made the initial reduction to Hessenberg-Triangular form Young Ju Lee a new bottleneck in the solution of generalized non- Department of Mathematics symmetric matrix eigenvalue problems. We propose a new Rutgers University distributed algorithm for Hessenberg-Triangular reduction [email protected] based on a novel static scheduling technique. Experiments demonstrate that the new algorithm improves on the cur- rent state-of-the-art and also identifies the factors that MS37 limit scalability. The developed code is ScaLAPACK com- Solver for Structure-Preserving Discretization of patible. Incompressible MHD Equations Bj¨orn Adlerborn A uniform solver for a stable structure-preserving finite el- Ume˚aUniversity ement discretization of incompressible MHD equation will Computing Science and HPC2N be introduced. Numerical results are provided to verify [email protected] the structure-preserving property and demonstrate the ef- fectiveness of the solver. Lars Karlsson Ume˚a University, Dept. of Computing Science Yicong Ma [email protected] Department of Mathematics The Pennsylvania State University Bo T. K˚agstr¨om ma [email protected] Ume˚aUniversity Computing Science and HPC2N Xiaozhe Hu [email protected] The Pennsylvania State University [email protected] MS38 Jinchao Xu Avoiding Communication in Distributed-Memory Pennsylvania State University Tridiagonalization [email protected] We discuss theoretical and practical improvements to par- allel symmetric tridiagonalization algorithms, augmenting MS37 existing algorithms with more communication-efficient par- Modeling and Numerical Studies for Fluid- allel QR factorization kernels and multiple steps of band Structure Interactions reduction. Our theoretical analysis suggests that our ap- proach can reduce interprocessor communication and mem- In this talk, I will present our recent study on a dynamic ory bandwidth cost by O(p1/6)onp processors, using some fluid-structure interaction (FSI) problem involving with additional memory. We validate our analysis by imple- a rotational and elastic structure by using the arbitrary menting a three-step approach, which uses our key ideas Lagrangian-Eulerian (ALE) method for fluid model in Eu- to reduce interprocessor communication, albeit by a con- lerian description and the St.Venant-Kirchhoff structural stant factor rather than O(p1/6). model in Lagrangian description, and design its monolithic mixed finite element approximation. In addition, our stud- Grey Ballard CS15 Abstracts 49

Sandia National Laboratories [email protected] [email protected]

James W. Demmel MS40 University of California Integrating Mathematical Modeling and Computer Division of Computer Science Simulation with Experimental Synthesis and Char- [email protected] acterization of Materials

Nicholas Knight To design materials through computational modeling and UC Berkeley simulation requires close collaborations among applied [email protected] mathematicians, materials theorists, and experimentalists. The author will discuss his experiences working with ex- Edgar Solomonik perimental groups in synthesis and characterization of ma- University of California at Berkeley terials and with applied math groups in numerical compu- [email protected] tation. Examples to be discussed include designing domain structures and properties of oxide thin films. The author will share his views on the ideal collaboration mechanisms among applied mathematicians, materials theorists, and MS38 experimentalists. A Parallel Multishift QZ Algorithm with Aggres- sive Early Deflation for Distributed Memory HPC Long-qing Chen Systems Department of Materials Science and Engineering Pennsylvania State University [email protected] Appearing frequently in applications, generalized eigen- value problems represent one of the core NLA problems. We propose a parallelization of the QZ algorithm by Moler MS40 and Stewart that incorporates all modern ingredients of dense eigensolvers, such as multishift and aggressive early Mathematical Challenges in Nonequilibrium Ap- deflation techniques. To deal with (possibly many) infi- proaches to Amorphous Solids: Quantifying Disor- nite eigenvalue, a new parallel deflation strategy is devel- der, Predicting Plasticity, Accelerating Simulation oped. Numerical experiments for random and application examples demonstrate the effectiveness of our algorithm on Amorphous solids, materials that exhibit an absence of distributed memory HPC systems. long range order, exist in every class of materials. Despite their ubiquity few methodologies exist to quantify their structure, predict their response or achieve the simulation Bj¨ornAdlerborn,BoT.K˚agstr¨om time scales necessary to understand their complex behav- Ume˚aUniversity ior. I will review some of the underlying gaps in our math- Computing Science and HPC2N ematical knowledge that make the study of amorphous [email protected], [email protected] solids so demanding. Some of these issues limit progress not only in amorphous solids, but in atomic simulation Daniel Kressner generally. In particular I will discuss the difficulty of quan- EPFL Lausanne tifying disorder in a mathematically rigorous way through Mathicse generalizations of the Frank-Kasper criterion. I will also daniel.kressner@epfl.ch consider the challenges that face modeling the plastic flow of materials that bridge the gap between elastic solids and liquids. Finally I will consider the limitations that atom- MS38 istic simulations face when studying materials that have inherent time scales that may span a broad range from Performance Evaluation of Sparse Matrix-Vector nanoseconds to seconds. Multiplication Using GPU/MIC Cluster Michael Falk Sparse matrix-vector multiplication (SpMV) is an impor- Materials Science and Engineering tant computational kernel for many applications. Recently, Johns Hopkins University the number of computing systems equipped with NVIDIA’s [email protected] GPU and Intel’s Xeon Phi coprocessor based on the MIC architecture has been increasing. In this talk, we present a performance evaluation of parallel SpMV using GPU/MIC MS40 cluster. As shown by the results, the implementation for Structural Optimization and 3D Printing the GPU/MIC cluster attained higher performance than the implementation for the CPU cluster in some matrices. We have known since the 1980’s that some structural op- timization problems call for designs with a high degree Hiroshi Maeda of spatial complexity. However such results were mainly Graduate School of Systems and Information Engineering viewed as theoretical benchmarks, since the manufacture University of Tsukuba of spatially complex designs has been difficult. The devel- [email protected] opment of 3D printing (also known as additive manufactur- ing) calls for re-examination of this area. With 3D printing, Daisuke Takahashi spatially complex structures are relatively easy to manu- Faculty of Engineering, Information and Systems facture. It is natural to ask how this capability can be used University of Tsukuba to good effect. The optimization of 3D printed structures 50 CS15 Abstracts

raises many challenging questions, most of them open. plasma turbulence in two and three space dimensions illus- trate the efficiency of the method. Robert V. Kohn Courant Institute of Mathematical Sciences Kai Schneider New York University Universite de Provence, Aix-Marseille [email protected] Centre de Mathematiques et Informatique [email protected] MS40 DNA-Functionalized Nanoparticle Assembly and MS41 Crystallization High-Order Fourier-Penalty Methods for PDEs on Irregular Domains The selectivity of DNA recognition inspires an elegant protocol for designing versatile nanoparticle (NP) assem- Penalty methods offer an attractive approach for solv- blies. We use molecular dynamics simulations to analyze ing partial differential equations (PDEs) on domains with static and dynamic aspects of the assembly process and curved or moving boundaries. The new penalized PDE is identify key ingredients for the assembly of NP superlat- then attractive to solve since one no longer needs to ac- tices through DNA hybridization. A scale-accurate coarse- tively enforce the boundary conditions. Despite the sim- grained model captures the relevant contributions to the plicity, these methods have suffered from poor convergence kinetics of the DNA hybridization process and is able to rates. I will show how to systematically construct a new recover all experimentally reported to date binary super- class of penalization terms which improve the order of con- lattices of DNA functionalized nanoparticles. Using multi- vergence. I will then demonstrate that the new approach scale modeling we show that through very slow cooling, allows one to devise higher order, stable, Fourier spectral DNA functionalized nanoparticles assemble into superlat- methods to solve the penalized PDE. tices with a specific crystal habit. We reproduce polyhedra growth in silico, and confirm the Wulff shape for the BCC. David Shirokoff Due to defects including twinning and stacking faults in the New Jersey Institute of Technology lattice, the FCC system does not show any uniform shape. david.g.shirokoff@njit.edu Simulated crystal habits of both the BCC and FCC system are consistent with experiments. MS42 Monica Olvera De La Cruz Designing Self-Propelling Microgel Swimmer Northwestern University [email protected] Using dissipative particle dynamics, we design a hydro- gel micro-swimmer that is actuated by a periodically ap- plied stimulus. The gel has an X-shaped geometry and two MS41 bonded layers, one of which is responsive to the stimulus A New Penalization Method for the Shallow Water and the other is passive. When the stimulus is turned on, Equations with Applications to Global Ocean Flow the responsive layer swells and causes the swimmer to de- form. We demonstrate that when such stimulus-induced We propose a new mass and energy conserving Brinkman deformations occur periodically, the gel swimmer effec- boundary condition penalization for the rotating shallow tively propels forward through the viscous fluid. water equations. This penalization does not lead to higher wave speeds in the solid region. The error estimates for the Alexander Alexeev penalization are derived analytically and verified numeri- George W. Woodruff School of Mechanical Engineering cally for linearized one dimensional equations. The penal- Georgia Institute of Technology ization is implemented in a conservative dynamically adap- [email protected] tive wavelet method for the rotating shallow water equa- tions on the sphere with bathymetry and coastline data from NOAA’s ETOPO1 database. This code could form Svetoslav Nikolov, Peter Yeh the dynamical core for a future global ocean model. The Georgia Institute of Technology potential of the dynamically adaptive ocean model is illus- [email protected], [email protected] trated by using it to simulate the 2004 Indonesian tsunami and wind-driven global ocean circulation. MS42 Nicholas Kevlahan The Effect of Curved or Flat Edges Microchan- Department of Mathematics & Statistics nels on Vortex Entrapment of Particles as seen in McMaster University Lattice-Boltzmann Simulations [email protected] Numerical simulations were conducted to investigate if and how curved or flat channel wall surfaces, as part of the sur- MS41 face topography in micro-flow channel walls, would impact Imposing Dirichlet and Neumann Conditions in vortex development and vortex entrapments of uniform- Fourier Pseudospectral Methods Using Volume Pe- size particles in pulsating and non-pulsating flows. This nalization research also demonstrated the sensitivity of the location of particle-trapping vortices to particle concentrations. The volume penalization method for computing confined fluid and plasma flows in complex geometries while us- John Carrola ing Fourier pseudo-spectral discretizations is reviewed. Southwest Research Institute The mathematical principle of this technique is described [email protected] and simple examples for imposing Dirichlet and Neumann boundary conditions are given. Applications for fluid and Hakan Basagaoglu CS15 Abstracts 51

Southwest Research Institute [email protected], [email protected], Mechanical Engineering Division [email protected], [email protected] [email protected] Eric Phipps Sandia National Laboratories MS42 Optimization and Uncertainty Quantification Department Scaffold-free Three-dimensional Hepatocyte As- [email protected] sembly for Liver Tissue Engineering Andrew Salinger We demonstrate a scaffold-free hepatocyte assembly CSRI method, which enables generation of repeating and sym- Sandia National Labs metric cellular structures with high cell-packing density [email protected] and viability. Standing waves established at the airliquid interface are used to pack cells in 3D architecture without scaffolding materials. The pattern of 3D architecture is de- MS43 termined by the topography of standing waves and can be dynamically controlled by vibrational frequency and am- Evaluations of Directive Based Programming plitude of standing waves. Model for GPUs and Extensions for Performance Portability Utkan Demirci Stanford University Recently, the number of heterogeneous supercomputers us- School of Medicine ing accelerators such as GPUs is increasing. These sys- [email protected] tems have been showing remarkable performance on real- world applications such as Computational Fluid Dynamics Pu Chen (CFD). However, porting of legacy CPU-based applications Stanford Medicine to systems with accelerators is still big challenge. One of Department of Radiology the reasons of this problem is low-level programming model [email protected] such as CUDA, which is the most widely used for port- ing of these applications. To solve this problem, existing approach includes high-level programming model such as MS42 OpenACC but it still has a problem about performance Brownian Motion of Arbitrarily Shaped Particles portability between devices which have different perfor- Confined in Two-Dimensions mance characteristics about data layout. To improve the performance portability, we suggest an abstraction of data I will present our studies on Brownian motion of micro- layout. We also implement and evaluate a directive-based fabricated boomerang particles in two-dimensions. We source-to-source (extended OpenACC to OpenACC) trans- show that due to translation-rotation coupling, mean lator that automatically transforms data layout to suitable squared displacements of single particles exhibit a non- form. linear crossover from short time faster to long time slower diffusion, and the mean displacements for fixed initial ori- Tetsuya Hoshino entation are biased. I will also show an analytical model Tokyo Institute of Technology based on Langevin theory to explain how the symmetry of [email protected] particle shape affect Brownian motion. Naoya Maruyama Qi-Huo Wei RIKEN Advanced Institute for Computational Science Kent State University [email protected] Liquid Crystal Institute [email protected] Satoshi Matsuoka Tokyo Insitute of Technology [email protected] MS43 A Kokkos Implementation of Albany: A Perfor- mance Portable Multiphysics Simulation Code MS43 Albany is a C++ object-oriented, parallel, unstructured- Optimization of Preconditioned Iterative Linear grid, implicit finite element code for solving partial differ- Solvers Using Openmp/openacc on Gpu and Mic ential equations (PDEs) in various fields of engineering ap- plications and multiphysics simulations in particular. Such OpenMP is widely used for accelerating programs on CPU complex simulations require to be run on modern Super- and MIC. Also, some people use OpenACC on mainly computers and performance portability across variety of GPU. These parallel programming environment can make HPC architectures has become a critical issue. We have parallel programs easy with similar programming fashion. developed a performance portable implementation of the However, in order to obtain good performance, users may Albany code, based on Kokkos programming model from have to make differ programs in view of target architec- Trilinos. A new Albany-Kokkos implementation is a single tures. In this talk, we show the implementation and per- code base which runs and is performant on diverse HPC formance of ICCG method on OpenMP and OpenACC. architectures, and is expected to be performant on future We compare the obtained performances with each other. architectures that are supported by the Kokkos library. Satoshi Ohshima Irina Demeshko, H. Carter Edwards, Michael Heroux, The University of Tokyo Roger P. Pawlowski Information Technology Center Sandia National Laboratories [email protected] 52 CS15 Abstracts

Masaharu Matsumoto modate plane-wave radiation of arbitrary angle of inci- Information Technology Center dence. In order to achieve this, the governing Helmholtz The University of Tokyo equations subject to quasi-periodic boundary conditions [email protected] are rewritten in terms of periodic unknowns. We construct a spectral element operator to approximate the DtN map, Takahiro Katagiri thus ensuring nonreflecting outgoing waves on the artifi- The University of Tokyo cial boundaries introduced to truncate the computational [email protected] domain. We present an explicit formula that accurately computes the Fourier data involved in the DtN map on the Toshihiro Hanawa spectral element discretization space. Our solutions are Information Technology Center represented by the tensor product basis of one-dimensional The University of Tokyo Legendre-Lagrange interpolation polynomials based on the [email protected] Gauss-Lobatto-Legendre grids. We will demonstrate the scattered field in singly and doubly layered media with smooth and nonsmooth interfaces. Kengo Nakajima The University of Tokyo Ying He Information Technology Center UC Davis [email protected] [email protected]

MS43 MS44 OCCA: An Extensible Portability Layer for Many- Electromagnetic Field Enhancement for Metallic Core Programming Nano-gaps

There are a number of relatively popular APIs for pro- There has been increasing interests in electromagnetic field gramming many-core CPUs, GPUs, and accelerators in- enhancement and extraordinary optical transmission effect cluding OpenMP, pThreads, CUDA, OpenCL, and Ope- through subwavelength apertures in recent years, due to its nACC. This manufacturer driven fragmentation echoes the significant potential applications in biological and chemi- scattershot approach to distributed computing before the cal sensing, spectroscopy, terahertz semiconductor devices, Message Passing Interface standard became the de facto etc. In this talk, I will present a quantitative analysis standard. We have developed OCCA as a manufacturer for the field enhancement when an electromagnetic wave independent runtime library and abstraction layer. OCCA passes through small metallic gaps. We focus on a partic- enables a programmer who is comfortable with the notions ular configuration when there is extreme scale difference of parallel loops and barriers to write parallel threaded between the wavelength of the incident wave, the thickness kernel code that is parsable at runtime as either OpenMP, of metal films, and the size of gap aperture. Based upon pThreads, CUDA, or OpenCL. The OCCA library is eas- a rigorous study of the perfect electrical conductor model, ily extensible and has native interfaces that can be called we show that enormous electric field enhancement occurs from C++, C, F90, Python, Java, or Julia. I will show inside the gap. Furthermore, the enhancement strength is examples drawn from numerical PDEs that indicate some proportional to ratio between the wavelength of the inci- application compute kernels can achieve good performance dent wave and the thickness of the metal film, which could across several platforms while other examples show that exceed 10000 due to the scale difference between the two. more than one kernel implementation may be required to On other hand, there is no significant magnetic field en- achieve best possible performance across platforms. hancement inside the gap. The ongoing work along this research direction will also be discussed. Tim Warburton Rice University Junshan Lin Department of Computational and Applied Auburn University [email protected] [email protected] David Medina Rice University MS44 [email protected] Highly tuned hybrid MPI/OpenACC implementa- tion with GPUDirect communication for electro- Amik St-Cyr magnetic solvers based on spectral element dis- Computation and Modeling, cretization Shell International E&P, Inc. [email protected] I will present a collaborative work on highly tuned hybrid MPI/OpenACC implementation with GPUDirect com- muncation for solving electromagnetic systems based on MS44 high-order spectral element discretizations. The OpenACC An Efficient Spectral Element Helmholtz Solver implementation covers the full solution routines including with an Accurate Treatment for Transparent element-by-element operator evaluation as well as tuned Boundary Condition for Periodic Lossy Media MPI communication kernels to effect the near-neighbor flux exchanges. I will demonstrate performance and analysis on We present a high-order spectral element method for solv- up to 16,384 GPUs on the Cray XK7 supercomputer show- ing layered media scattering problems featuring an opera- ing more than 3x speedup, compared to the MPI-only CPU tor that transparently enforces the far-field boundary con- performance on the same number of nodes (262,144 CPUs) dition. The incorporation of this Dirichlet-to-Neumann for the problem sizes of up to 6.9 billion data points. (DtN) map into the spectral element framework is a novel aspect of this work, and the resulting method can accom- MiSun Min CS15 Abstracts 53

Argonne National Laboratory Lawrence Livermore National Laboratory Mathematics and Computer Science Division [email protected] [email protected]

MS45 MS44 Particle-Particle, Particle-Mesh Methods for Elec- A High Order Perturbation of Surfaces Method for tromagnetic Problems Simulating Surface Plasmons on Periodic Gratings In this talk we revisit the topic of subcell methods inside In this talk we describe a High Order Perturbation of Sur- of traditional particle-in-cell methods. The subcell method faces (HOPS) method for simulating the scattering of elec- proposed in this work is based on using the boundary in- tromagnetic waves by periodic grating structures. The tegral tree code as a subcell model inside of a multidi- method amounts to Nystrom’s method applied to a class mensional PIC code. 1D introduces some some greatly of Integral Equations for the Helmholtz equation on peri- reduces issues associated with numerical heating and pro- odic domains inspired by the recent work of Fokas and col- vides greater accuracy in the calculation. This work inves- laborators on novel solution formulas for boundary value tigates issues of numerical seating and accuracy in a multi- problems. These Integral Equations have a number of ad- D setting. Further potential roadmap is presented for vantages over standard alternatives including: (i.) ease producing heating time domain electromagnetic particle- of implementation (high-order spectral accuracy is real- particle particle-mesh method that is well-suited to the ized without sophisticated quadrature rules), (ii.) seamless simulation of non-relativistic plasmas. enforcement of the quasiperiodic boundary conditions (no periodization of the fundamental solution, e.g. via Ewald Andrew J. Christlieb summation, is required), and (iii.) reduced regularity re- Michigan State Univerity quirements on the interface proles (derivatives of the defor- Department of Mathematics mations do not appear explicitly in the formulation). We [email protected] show how these can be efficiently discretized and utilized in the simulation of surface plasmon excitations on periodic Eric Wolf metal gratings in configurations of engineering interest. Michigan State University [email protected] David P. Nicholls University of Illinois at Chicago [email protected] MS45 Stochastic Galerkin Method for Hamilton-Jacobi Equations with Uncertainty MS45 Performance of Parallel Algorithms for Particle Abstract not available at time of publication. Transport on Massively Parallel Architectures Jingwei Hu We describe algorithms that execute multi-octant discrete- The University of Texas at Austin ordinate transport sweeps in the minimum possible stage [email protected] count for a given partitioning across processors and given work-unit aggregation. We describe automated selection Shi Jin of the best partitioning and aggregation for a given prob- Shanghai Jiao Tong University, China and the lem on a given machine. Spatial grids can be locally un- University of Wisconsin-Madison structured within structured blocks. We present results [email protected] to O(106) parallel processes, including results from nested parallel algorithms in which each MPI process uses multi- Dongbin Xiu ple threads. University of Utah [email protected] Marvin L. Adams, Michael Adams, W. Daryl Hawkins, Timmie Smith Texas A&M University MS45 [email protected], [email protected], Uncertainty Quantification in Kinetic Theory [email protected], [email protected] In this talk we will study generalized polynomial chaos Lawrence Rauchwerger (gPC) approach to transport equation with uncertain Computer Science Department coefficients/inputs and show that they can be made Texas A&M University asymptotic-preserving, in the sense that in the diffusion [email protected] limit the gPC scheme for the transport equation ap- proaches to the gPC scheme for the diffusion equation with Nancy Amato random diffusion coefficient. This allows the implemen- Texas A & M University tion of the gPC method without numerically resolving (by [email protected] space, time, and gPC modes) the small mean free path for transport equation in the diffusive regime. We will also discuss more general hyperbolic equations with (random) Teresa S. Bailey geometric source terms and the relevant stochastic well- LLNL balanced property. [email protected] Shi Jin Robert Falgout Shanghai Jiao Tong University, China and the Center for Applied Scientific Computing University of Wisconsin-Madison 54 CS15 Abstracts

[email protected] ditional stair-step discretization on Cartesian meshes like those used in the block-structured AMR BISICLES code. Dongbin Xiu, Xueyu Zhu Also, the fundamental discontinuous nature of flow across University of Utah the grounding line is respected. [email protected], [email protected] Daniel Martin Lawrence Berkeley National Laboratory MS46 [email protected] Testing the Multilayer Shallow Shelf Approxima- tion Against Higher-order Models Peter O. Schwartz Lawrence Berkeley Laboratory In this talk, I will introduce a new hybrid ice flow model [email protected] (called MSSA) which generalises the Shallow Shelf Approx- imation (SSA) by a Multilayer approach. Advantageously, Esmond G. Ng the MSSA keeps intact the elliptic structure of the SSA Lawrence Berkeley National Laboratory and is mechanically exhaustive (it contains both: mem- [email protected] brane and vertical stresses) while being of 2D complexity. Comparative results will be presented to assess the me- chanical and the computational performances of the MSSA MS46 with respect to classical higher-order models. On the Development and Performance of a First Order Stokes Finite Element Ice Sheet Dynamical Guillaume Jouvet Core Built Using Trilinos Software Components Freie Universit¨at Berlin Institut f¨ur Mathematik This talk describes the new Albany/FELIX parallel, scal- [email protected] able and robust First-Order (FO) Stokes finite element ice sheet code developed using Trilinos libraries. Focus will be on the computational aspects of the code: verification; MS46 multilevel preconditioning to achieve good parallel scalabil- A Finite Element Three-Dimensional Stokes Ice ity for FO systems; homotopy continuation techniques for Sheet Dynamics Model with Enhanced Local Mass robust nonlinear solves; many-core performance portabil- Conservation ity. Coupling of Albany/FELIX to other land ice dycores (CISM, MPAS) for dynamic simulations and global climate In this paper, we present and discuss a new finite ele- runs will also be discussed. ment Stokes ice sheet dynamics model that enforces local element-wise mass conservation by enriching the pressure Irina K. Tezaur finite element space by adding the discontinuous piecewise Sandia National Laboratories constant pressure space to the Taylor-Hood pressure space. [email protected] Through various numerical tests based on manufactured solutions, benchmark test problems, and the Greenland Andrew Salinger ice-sheet, we demonstrate that, for ice-sheet modeling, the CSRI enriched Taylor-Hood finite element model remains highly Sandia National Labs accurate and efficient, and is physically more reliable and [email protected] robust compared to the classic Taylor-Hood finite element model. Mauro Perego Wei Leng CSRI Sandia National Laboratories Chinese Academy of Sciences [email protected] State Key Laboratory of Scientific and Engineering Computing Ray S. Tuminaro [email protected] Sandia National Laboratories Computational Mathematics and Algorithms Lili Ju [email protected] University of South Carolina Department of Mathematics MS47 [email protected] The most current list of partic- ipating companies is available at Max Gunzburger www.siam.org/meetings/cse15/career.php. Florida State University School for Computational Sciences For the most recent list of participating companies visit [email protected] http://www.siam.org/meetings/cse15/career.php

Bill Kolata MS46 SIAM Improving Grounding Line Discretization using an [email protected] Embedded-Boundary Approach in BISICLES

Correctly representing grounding line dynamics is of fun- MS48 damental importance in modeling marine ice sheets. We Application of a Speed Up Fast Direct Solver for have developed a grounding-line discretization based on the Solution of the Lippmann-Schwinger Equation the Chombo embedded-boundary cut-cell framework. This promises better representation of grounding lines vs. a tra- In this work, we applied the HODLR fast solver of Sivaram CS15 Abstracts 55

and Darve on the Lippmann-Schwinger integral equation extension for the localization of fractional powers of uni- for the solution of the Helmholtz problem. We split and formly elliptic operators. In this talk we will develop an discretize the domain by using an adaptive level-restricted approximation theory for weighted Sobolev spaces when tree structure based on its contrast function. To speed up the weight belongs to the Muckenhoupt class Ap,whichis the solver, we use the series representation of the Hankel a class of weights that may degenerate or blow up. This functions to pre-compute tables that can be used with the will provide the tools necessary for an optimal a priori er- tree structure to obtain the far field and local iterations ror analysis of discretizations of such equations. In addi- between the discretizartion points. tion, we will discuss multilevel methods for the solution of such problems and prove their nearly uniform convergence. Carlos C. Borges Finally, we will show how to exploit the structure of the Worcester Polytechnic Institute weight to develop a posteriori error estimators. [email protected] Abner J. Salgado Lise-Marie Imbert-Gerard Department of Mathematics CIMS, New York University University of Tennessee [email protected] [email protected]

Sivaram Ambikasaran MS48 Department of Mathematics Discontinuous Enrichment Method for Problems Courant Institute of Mathematical Sciences with Variable Coefficients [email protected] Abstract not available at time of publication. Leslie Greengard Courant Institute Radek Tezaur, Charbel Farhat New York University Stanford University [email protected] [email protected], [email protected]

Irina K. Tezaur MS48 Sandia National Laboratories Yee Scheme Coupled with Linear Current in Mag- [email protected] netic Plasmas with Varying Coefficients

We analyze the stability of the Yee scheme for non sta- MS49 tionary Maxwell’s equations coupled with a linear current Superconvergence of Discontinuous Galerkin model, with highly varying coefficients. Indeed the usual Methods for Hyperbolic Equations in Two Space procedure is unstable for physical situations that corre- Dimensions spond to strongly magnetized plasmas in X-mode (TE) polarization. We propose to use first order clustered dis- We study the superconvergence of discontinuous Galerkin cretization of the vectorial product that gives back a stable methods for hyperbolic equations in two space dimensions. coupling. Validation is performed with physically based We first consider periodic boundary condition, and will problems. The equivalent time harmonic problem (elliptic prove that with piecewise k-th degree polynomial, the error equation) yields a similar behavior. between the numerical solution and the exact solution at the downwind-biased Radau points are k+2-th order accu- Bruno Despres racy. Moreover, at downwind point, the error is 2k+1-th University Paris VI order accurate. For Dirichlet boundary condition, we have Laboratory LJLL to make a special projection of the exact solution at the [email protected] inflow boundary to obtain similar results. Numerical ex- periments will be given to verify our numerical analysis. Martin Campos Pinto CNRS-LJLL UPMC Waixiang Cao [email protected] Beijing Computational Science Research Center [email protected] St´ephane Heuraux Institut Jean Lamour, UMR 7198 CNRS-University Yang Yang Lorraine Michigan Technological University [email protected] [email protected]

Filipe da Silva Zhimin Zhang Instituto de Plasmas e Fusao Nuclear, Instituto Superior Wayne State University [email protected] Department of Mathematics [email protected]

MS48 Chi-Wang Shu Approximation of Degenerate Elliptic Equations Brown University with Muckenhoupt Coefficients: a priori and a pos- Div of Applied Mathematics teriori Analyses and Efficient Solvers [email protected]

In many problems of interest it is unavoidable to consider elliptic equations with coefficients that either degenerate MS49 or become singular. An example of this is the α-harmonic Runge-Kutta Discontinuous Galerkin Methods for 56 CS15 Abstracts

the Relativistic Vlasov-Maxwell System iters is to obtain high order accuracy and non-oscillatory properties simultaneously. The main novelty of the new The relativistic Vlasov-Maxwell (RVM) system is a ki- HWENO limiter in this talk is to reconstruct the polyno- netic model of plasma to describe the phenomena when mial on the target cell in a least square fashion while the the charged particles move in the relativistiic regime, and simple WENO limiter is to use the entire polynomial of the the collisions of the particles are omitted. In this talk, original DG solutions in the neighboring cells with an addi- we propose several discontinuous Galerkin (DG) methods tion of a constant for conservation. This modification im- with Runge-Kutta time discretizations to solve the RVM proves the robustness in the computation of problems with system. When the DG methods with the standard poly- strong shocks or contact discontinuities, without changing nomial spaces are used, the mass conservation of the sys- the compact stencil of the DG scheme. Numerical results tem is shown both theoretically and numerically. However, for both one and two dimensional equations including Eu- due to the special formulation of the total energy for the ler equations of compressible gas dynamics are provided to RVM system, the energy conservation cannot be obtained. illustrate the viability of this modified limiter. Therefore, we proposed DG methods with non-polynomial spaces to preserve the total energy of the system. We dis- Jun Zhu cuss the conservation properties of both semi-discrete and Nanjing University of Aeronautics and Astronautics fully discrete schemes, the error estimates, and validate [email protected] the theoretical results numerically. Numerical experiments including streaming Weibel instability and wakefield accel- Xinghui Zhong eration are also presented. Michigan State University [email protected] He Yang Rensselaer Polytechnic Institute Chi-Wang Shu Department of Mathematical Sciences Brown University [email protected] Div of Applied Mathematics [email protected] Fengyan Li Rensselaer Polytechnic Institute Jianxian Qiu [email protected] Xiamen University [email protected] MS49 A Simple DG Scheme for Acoustic Wave Equations MS50 with Curved Interfaces and Boundaries Compact Scattered RBF-FD Stencils for PDEs on Consider solving acoustic wave equations with presence Surfaces of curved boundary or interfaces. The conventional high- We present a novel high-order meshfree method for the so- order discontinuous Galerkin scheme on straight-sided el- 3 ements suffers from second order errors due to piece-wise lution of PDEs on smooth surfaces embedded in R ,with segment approximation to the curve. We propose a simple applications in biology and chemistry. The approach is a flux correction to reduce the errors by projecting quadra- combination of local Hermite RBF interpolation and iter- ture points for line integration onto curved interfaces, ated application of the projected gradient, and thus only and evaluating numerical fluxes at projection points. For requires a set of points and the corresponding normal vec- curved interfaces, numerical tests demonstrate that this tors. A diagonally dominant sparse matrix is obtained for simple modification may reduce interface error and non- fourth order discretizations of the Laplace–Beltrami oper- physical diffractions. For curved boundary conditions, with ator, ensuring computational efficiency. the assumption that the exact solution can be smoothly Erik Lehto extended, the local truncation error of the modified DG Department of Mathematics scheme is high order. Accuracy tests will be shown to Royal Institute of Technology demonstrate the effectiveness of this simple correction. [email protected] Xiangxiong Zhang Massachusetts Institute of Technology Varun Shankar Department of Mathematics School of Computing [email protected] University of Utah [email protected]

MS49 Grady B. Wright Runge-Kutta Discontinuous Galerkin Method with Department of Mathematics a Simple and Compact Hermit Weno Limiter Boise State University, Boise ID [email protected] In this talk, we propose a new type of weighted essentially non-oscillatory (WENO) limiter, which belongs to the class of Hermite WENO (HWENO) limiters, for the Runge- MS50 Kutta discontinuous Galerkin (RKDG) methods solving Solving PDEs on the Sphere via Novel Galerkin hyperbolic conservation laws. This new HWENO limiter Method using Highly Localized Kernel Bases is a modification of the simple WENO limiter proposed recently by Zhong and Shu. Both limiters use informa- In this talk we will discuss a novel, kernel-based meshless tion of the DG solutions only from the target cell and its Galerkin method for numerically solving partial differential immediate neighboring cells, thus maintaining the original equations on the sphere. In particular, we will apply this compactness of the DG scheme. The goal of both lim- method to treat a general PDE describing stationary heat CS15 Abstracts 57

conduction in an inhomogeneous, anisotropic medium on [email protected] S2. The Galerkin method used to do this employs spatially well-localized, ”small footprint, ” robust bases for the as- sociated kernel space. The stiffness matrices arising in the MS51 problem have entries decaying exponentially fast away from High-Order Finite Element Methods for Cardiac the diagonal. Discretization is achieved by replacing the Electrophysiology stiffness matrix with one whose entries are computed by a very efficient kernel quadrature formula for the sphere. The Finite element and finite difference methods are widely discretized stiffness matrix retains the exponential decay in used for solving problems in computational cardiac elec- its off diagonal entries. We will present error estimates for trophysiology. However, their computational cost prohibits this problem and give a numerical example illustrating the their direct use in online clinical practice during ablation results obtained. therapy. In this talk we illustrate how high-order finite ele- ment methods and surface representations of the left atrial Francis J. Narcowich chamber can be used to achieve greater accuracy, reduced Department of Mathematics computation times and increased scalability to bring mod- Texas A&M University elling closer to achieving clinical utility. [email protected] Chris Cantwell Joseph Ward Imperial College London Texas A&M University [email protected] Department of Mathematics [email protected] Sergey B. Yakovlev University of Utah Stephen Rowe School of Computing Department of Mathematics [email protected] Texas A&M University [email protected] Rheeda Ali Department of Bioengineering Imperial College London MS50 [email protected] A Least Squares-RBF Approach to Transport Problems on Surfaces Nicholas Peters National Heart and Lung Institute In this this talk, we aim to solve hyperbolic PDEs such as Imperial College London the wave equation on a given manifold S, using interpola- [email protected] tion with Radial Basis Functions (RBFs). Our approach is to use the process of approximating the differential opera- Mike Kirby tor suggested and outlined originally by Wright. We seek University of Utah to address challenges involved in solving hyperbolic prob- School of Computing lems on surfaces. One primary challenge is the need for [email protected] added hyper-viscosity in solving hyperbolic problems. This talk discusses how hyper-viscosity can be implemented and Spencer Sherwin the possibility of using an RBF-Least Squares method for Imperial College London avoiding hyper-viscosity altogether. [email protected] DarylJ.Springer Department of Mathematics MS51 Arizona State University Three-Dimensional Modeling of Ca2+ Signaling in [email protected] Healthy and Failing Cardiomyocytes

Calcium (Ca2+) is an important ion that drives contrac- MS50 tion of muscle cells. In cardiac cells, Ca2+ dependent Quadrature on Spheres and Other Manifolds Based steps of the contractile cycle involve influx of the ion into on Kernels the cytosol from the extracellular membrane (sarcolemma) and sarcoplasmic reticulum (SR), diffusion to the myofib- Quadrature formulas for spheres, the rotation group, and ril where it activates force generation, and uptake at the other compact, homogeneous manifolds are important in sarcolemma and SR. The presence of intracellular struc- a number of applications. The purpose of this talk is to tures including the myofibrils, organelles (SR, mitochon- present coordinate independent quadrature formulas asso- dria), and myriad protein crowders restrict the volume, ciated with certain classes of positive definite and condi- through which Ca2+ diffuses and thus reduces the ions tionally positive definite kernels that are invariant under apparent diffusion rate. Theories that account for the ar- the group action of the homogeneous manifold. In par- rangement and excluded volume of intracellular diffusion ticular these formulas are accurate-optimally so in many obstacles provide accurate estimates of the apparent dif- cases-and stable under anincreasing number of nodes and fusion rate. We extend one of these theories, homogeniza- in the presence of noise, provided the set X of quadrature tion, to explore the impact of diffusional obstacles and non- nodes is quasi-uniform. uniformly distributed Ca2+ fluxes or buffers on Ca2+ sig- naling using realistic cell geometries of from healthy and Joseph Ward failing hearts. Texas A&M University Department of Mathematics Peter Kekenes-Huskey 58 CS15 Abstracts

University of Kentucky [email protected] [email protected]

MS52 MS51 Modeling and Simulation of Multimaterial Com- pressible Flows Assessing the Credibility of Computational Models of Cardiac Electrophysiology Abstract not available at time of publication.

There is a much interest in clinical applications of com- Marianne M. Francois putational models of cardiac electrophysiology, which will Los Alamos National Laboratory require the reliability of model predictions to be thoroughly [email protected] investigated. Rigorous methods for assessing credibility of computational models have been developed within engi- neering and physical sciences (’verification, validation and MS52 uncertainty quantification’). However, applying such tech- Methods for Computing Turbulent Phase Interface niques to evaluate highly complex physiological models Dynamics Across Multiple Scales such as cardiac electrophysiology models is extremely chal- lenging. In this talk we will discuss work bridging this gap. Dynamics of turbulent interfaces, e.g. the primary atom- ization of liquid jets, can span several orders of magni- Pras Pathmanathan tude in scales ranging from centimeter scales of the injec- Department of Computer Science tor down to the sub-micron scale of the smallest drops. University of Oxford Strategies and examples to efficiently couple these scales [email protected] and enable predictive simulations will be discussed, includ- ing coupling Eulerian interface capturing methods to La- Richard Gray grangian drop models and dual-scale approaches to enable U.S. Food and Drug Administration LES-type simulations of the phase interface dynamics in [email protected] turbulent flows. Marcus Herrmann School of Mechanical, Aerospace, Chemical and Materials MS51 Engi Multi-Scale Modeling in Cardiac Electrophysiol- Arizona State University ogy: What Are the Challenges in Front of Us? [email protected]

Mathematical models of cardiac electrophysiology across MS52 many scales, from single ion channels to the whole or- gan, have been developed. However, a multi-scale mod- Direct Numerical Simulations of Multiphase Flow: eling framework, which is key for linking random molec- Now What? ular events to organ functions and diseases, has not been After briefly reviewing the history and current status of di- developed. This talk will focus on what progress we have rect numerical simulations of multiphase flows, two future made, what are the hurdles in front of us, and discuss how challenges for such simulations are discussed. The first is mathematics may help to overcome these challenges. how to use the vast quantity of data now available to im- prove modeling of the large scale or average flow and the Zhilin Qu other is how to efficiently include isolated processes, often University of California due to additional physics, taking place on length and time Dept of Medicine scales much smaller than the dominant flow scale. [email protected] Gretar Tryggvason University of Notre Dame MS52 Department of Aerospace and Mechanical Engineering Conservative and Accurate Geometric Transport [email protected] Methods for Discontinuous Variables in Turbulent Multi-physics Two-phase Flows MS53 Discovering Underlying Nonlinear Dynamics of Simulating multiphase flows presents significant challenges: flow variables exhibit discontinuities across the phase in- Complex Systems from Data terface, complex microscale dynamics arise due to surface Abstract not available at time of publication. tension, and the interface develops highly complex cor- rugations. Fluid turbulence and multi-physics processes Steven Brunton such as electro-hydrodynamics exacerbate these difficulties. University of Washington We will discuss recently advanced geometric techniques [email protected] capable of addressing these challenges conservatively and with second order accuracy. Applications ranging from interface-turbulence interaction in homogeneous flows to MS53 electro-hydrodynamic fuel atomization will be presented. Common Manifold Learning Using Alternating Dif- fusion for Multimodal Signal Processing Olivier Desjardins Cornell University One of the true challenges in signal processing is to dis- Department of Mechanical and Aerospace Engineering tinguish between different sources of variability. In this CS15 Abstracts 59

work, we consider the case of multiple multimodal sensors and organizational networks. Probabilistic linear and non- measuring the same physical phenomenon, such that the linear models for node activity and edge interactions char- properties of the physical phenomenon are manifested as a acterize network activity. PhySense includes algorithms to hidden common source of variability (which we would like post-process the resulting temporal data to generate met- to extract), while each sensor has its own sensor-specific ef- rics such as node-to-node influence, activity-based central- fects. We will address the problem from a manifold learn- ity and transfer entropy. The framework serves as a virtual ing standpoint and show a method based on alternating laboratory for generation and extraction of signatures to products of diffusion operators and local kernels, which ex- understand phenomena in a class of social networks. tracts the common source of variability from multimodal recordings. The generality of the addressed problem sets Vikram Jandhyala the stage for the application of the developed method to University of Washington many real signal processing problems, where different types [email protected] of devices are typically used to measure the same activity. In particular, we will show application to sleep stage assess- Arun Sathanur ment. We demonstrate that through alternating-diffusion, Dept. of Electrical Engineering the sleep information hidden inside multimodal respiratory University of Washington signals can be better captured compared to single-modal [email protected] methods.

Ronald Coifman MS54 Yale University Computational Analysis of Ensemble Neural Data Department of Computer Science Recorded From An Insect Brain [email protected] Methods to simultaneously monitor neural activity across Roy Lederman an ensemble of neurons with fine temporal precisions and Yale University across multiple trials/conditions have become standard [email protected] practices in systems neuroscience. However, analysis of such datasets to reveal the underlying neural representa- Ronen Talmon tion on a trial-by-trial basis has been a challenge. Since, Technion these neural datasets are high dimensional: neurons vs. [email protected] time vs. trials; we present methods that take advantage of this data-structure to extract meaningful response features in these neural datasets. MS53 Debajit Saha, Chao Li Title Not Available at Time of Publication Washington University in St. Louis Abstract not available at time of publication. [email protected], [email protected]

Surya Ganguli Barani Raman Stanford University Biomedical Engineering [email protected] Washington University in St. Louis [email protected]

MS53 Data-Driven Model Reduction to Support Decision MS54 Making in Complex Systems Computational Tools and Methods for Signature Discovery (Session Overview) The next generation of complex engineered systems will be endowed with sensors and computing capabilities that Scientists engaged in signature discovery have developed enable new modes of decision-making. For example, new numerous analytic algorithms for data processing, feature sensing capabilities on aircraft will be exploited to assim- extraction, machine learning, and classification. These al- ilate data on system state, make inferences about system gorithms are written in a wide variety of programming lan- health, and issue predictions on future vehicle behavior— guages and utilize data stored in many types of databases. with quantified uncertainties—to support critical opera- We will discuss analytic tools we developed for signa- tional decisions. Model reduction is one way to achieve ture discovery and a supporting framework that allows re- this challenging task, in particular through data-driven re- searchers to easily use (and reuse) analytic codes, regard- duced models that exploit the synergies of physics-based less of the language in which they were originally written. computational modeling and physical data. Landon H. Sego Karen E. Willcox Pacific Northwest National Laboratory Massachusetts Institute of Technology [email protected] [email protected]

MS54 MS54 Statistics, Learning, and Optimization for Data PhySense: Social and Organizational Network Ac- Analysis and Visualization tivity Simulation for Signature Generation and Ex- traction A variety of technologies in diverse areas such as medi- cal imaging, industrial inspection, and oil and gas share We present PhySense an agent-based temporal event sim- common underlying challenges. Many of these problems ulator that addresses signal propagation in online social lend themselves to statistical methods that entail estima- 60 CS15 Abstracts

tion, learning, or regression. We motivate these ideas from requires fully coupled structural/aerodynamic/thermal some traditional problems in image processing and develop analyses. This effort being computationally very demand- the concepts of nonparametric modeling with applications ing on full order models, reduced order modeling tech- to data analysis and visualization more generally. Applica- niques have been developed for this multidisciplinary prob- tions from simulations, demographics, and industrial pro- lem. Central to these approaches is the selection of appro- cesses will be discussed. priate bases to represent the solutions. This talk focuses on the determination both a-priori and during computa- Ross Whitaker tions of bases to represent the temperature field which are School Of Computing, Scientific Computing and Imaging representative of the multidisciplinary interactions. Inst. University of Utah Andrew Matney [email protected] Arizona State University [email protected] MS55 Marc P. Mignolet Real-Time Data-to-Decision Using Adaptive Sur- Arizona State rogate Modeling Strategies [email protected] This talk presents an approach to achieve a dynamic data- to-decision process in real-time. We use a non-intrusive MS55 adaptive strategy that combines reduced-order modeling and localization techniques. The methodology is demon- Numerical Study of Local Reduced Basis with strated for a self-aware autonomous vehicle that relies on Adaptive Training for Incompressible Navier- the ability to dynamically process sensor data, assess sys- Stokes Flows tem state and capabilities, and make decisions accordingly. We consider the specific case of real-time structural assess- In this work, we combine a set of reduced-order repre- ment in the presence of damage. sentation techniques for simulating incompressible Navier- Stokes flows over a range of physical parameters and il- Laura Mainini lustrate that an adaptive time-integration scheme can effi- Politecnico di Torino ciently accelerate the generation of snapshots as well as the [email protected] simulations with the reduced-order representations. The number of training configurations selected in snapshots is Karen E. Willcox adaptively increased until the norms of residuals are re- Massachusetts Institute of Technology duced below a user-specified tolerance. The reduced-order [email protected] representation is further accelerated by combining the ideas of local bases and hyper-reduction of nonlinear terms. The accuracy and efficiency of the proposed method is illus- MS55 trated on numerical examples with parameter sweeps. An Occam’s Razor Strategy for Field Estimation Yuqi Wu from Wall-Mounted Sensors Department of Applied Mathematics, University of We present a field estimation technique suitable for exper- Washington imental closed-loop control. The method relies on an of- [email protected] fline/online strategy where an approximation basis is learnt using information provided by very few, wall-mounted, sen- Ulrich Hetmaniuk sors. Offline derivation of the basis uses sparsity promo- University of Washington tion techniques and an informative sequence while online Department of Applied Mathematics estimation is achieved by sparse recovery from the sensors [email protected] information only. The method is illustrated with the flow around a cylinder and its performance is compared with POD. MS56 Hierarchical Tensor Approximation of Parameter- Kevin Kasper Dependent PDEs SATIE - ENS Cachan, France [email protected] Parametric PDEs appear in a large number of applications, as e.g. in uncertainty quantification or optimisation. Typ- Lionel Mathelin ically, the amount of data to approximate and represent LIMSI - CNRS the solution scales exponentially in the parameter dimen- [email protected] sion. Therefore, a crucial task is to develop special numer- ical techniques that rely on data-sparsity in order to cope Mohamed Abbas-Turki, Hisham Abou-Kandil even with high parameter dimensions. In this talk, we will SATIE - ENS Cachan, France discuss low-rank tensor techniques that allow to reduce the [email protected], hisham.abou- complexity to a linear dependence on the parameter dimen- [email protected] sion. In particular, our aim is to adaptively construct an approximation of the solution in the hierarchical tensor for- mat from a relatively small set of data samples. Once this MS55 approximation from an offline computation is available, the Thermal Reduced Order Model Adaptation to evaluation of quantities of interest becomes a cheap online Aero-Thermo-Structural Interactions task. Moreover, the explicit tensor representation can be used to compute stochastic properties of the solution in Predicting the behavior of hypersonic vehicles components a straightforward way. The potential of this approach is CS15 Abstracts 61

illustrated by numerical examples. still enabling low order scaling with respect to the dimen- sions. For many high dimensional problems, hard to be Jonas Ballani handled so far, this approach may offer a novel strategy EPF Lausanne to circumvent the curse of dimensionality. For uncertainty jonas.ballani@epfl.ch quantification we cast the original boundary value prob- lem, with uncertain coefficients problem into a high dimen- Lars Grasedyck sional parametric boundary value problem, discretized by Max-Planck-Institute Galerkin method. The high dimensional problem is cast Math in Sciences into an optimization problems, constraint by the restric- [email protected] tion to tensors of prescribed ranks r. This problem could be solved by optimization on manifolds, or more simply by Daniel Kressner alternating least squares. Since the norm of the underlying EPFL Lausanne energy-space is a cross norm, preconditioning is required Mathicse only for the spatial part and e.g. performed by standard daniel.kressner@epfl.ch multi grid approaches, e.g BPX. This leads to a modifica- tion of the orthogonality of the used component tensors. A important task is a posteriori error control, with respect to MS56 the spatial discretization and also w.r.t. the tensor product Tensor Format Representations and Optimal approximation. Model Reduction for Uncertainty Quantification Reinhold Schneider In this talk I will give an introduction to the basic principles Technische Universitat Berlin of tensor format representations with a special focus on [email protected] applications from uncertainty quantification.

Mike Espig MS57 Max Planck Institute for Mathematics in the Sciences Fluid-composit Structure Interaction [email protected] We focus of the interaction between a multi-layered, com- posite structure, and the flow of an incompressible, vis- MS56 cous fluid, giving rise to a fully coupled, nonlinear moving High-Dimensional Tensor Sampling boundary, fluid-multi-structure interaction problem. Ex- amples include arterial walls interacting with blood flow, The hierarchical tensor format allows for the low- and oil platforms interacting with water. We present a parametric representation of tensors even in high dimen- novel stable, modular, loosely coupled scheme for the nu- sions d. On the one hand, this format provides a robust merical simulation of the coupled problem, and prove that framework for approximate arithmetic operations with ten- the scheme converges to a weak solution of the nonlinear, sors based on rank truncations, which can be exploited in fully coupled problem. Our numerical and analytical re- iterative algorithms. On the other hand, it can be used for sults reveal new physical regularizing mechanism: the pres- the direct approximation of high-dimensional data stem- ence of a thin fluid-structure interface with mass regularizes ming, e.g., from the discretisation of multivariate functions. the evolution of the entire FSI solution. In this talk, we discuss several strategies for an adaptive ap- proximation of tensors in the hierarchical format by black Suncica Canic box sampling techniques. Department of Mathematics University of Houston Lars Grasedyck [email protected] Max-Planck-Institute Math in Sciences Martina Bukac [email protected] University of Notre Dame [email protected] Jonas Ballani EPF Lausanne Boris Muha jonas.ballani@epfl.ch University of Zagreb, Croatia [email protected] Melanie Kluge RWTH Aachen [email protected] MS57 Second Order Embedded Boundary Methods for Fluid-Structure Interaction MS56 Novel Tensor-Product Representations for Uncer- This talk presents a second order accurate embedded taintiy Quantification boundary method for fluid-structure interaction. First, a spatially second order accurate embedded boundary Hierarchical Tucker tensor format (HT - Hackbusch ten- method for first order hyperbolic systems is presented. Sec- sors ) and Tensor Trains (TT- Tyrtyshnikov tensors, ond, existing time discretizations for fluid-structure inter- I.Oseledets) have been introduced recently for low rank action are reviewed, with an emphasis on partitioned in- tensor product approximation. Hierarchical tensor decom- tegrators, and then an extension for embedded boundary positions are based on sub space approximation by extend- methods is described. Finally, the framework is verified on ing the Tucker decomposition into a multi-level framework. a set of fluid structure interaction test problems. Therefore they inherit favorable properties of Tucker ten- sors, e.g they offer a stable and robust approximation, but Alex Main, Charbel Farhat 62 CS15 Abstracts

Stanford University Stanford University [email protected], [email protected] [email protected]

Gianluca Iaccarino MS57 Stanford University A Tetrahedral Method for Transient Nonlinear Dy- Mechanical Engineering namics Computations in Solids, Fluids and Cou- [email protected] pled Fluid Structure Problems Johan Larsson A new mixed tetrahedral finite element formulation is pre- University of Maryland sented, aimed at transient dynamic computations of flu- [email protected] ids, solids, and fluid/structure interaction. It utilizes very simple approximation spaces: Piece-wise linear continu- ous functions for displacements and pressures, and dis- MS58 continuous constants for the deviatoric part of the stress Influence of Surface and Subsurface Parameter Un- tensor (if present, as in solids.) A variational multi- certainty and Sensitivity on the Latent Heat Flux scale stabilization eliminates possible pressure checker- Using An Integrated Hydrologic Model board instabilities. Extensive simulations of compressible fluids, nonlinear elastic/visco-elastic/elastic-plastic solids, Integrated hydrologic models simulate surface, subsurface and fluid/structure interaction will conclude the presenta- and land-surface water and energy fluxes and require pa- tion. rameters to characterize land cover, describe hydraulic properties and specify initial and boundary conditions. Un- Guglielmo Scovazzi,XianyiZeng certainty will be propagated through ParFlow, a nonlinear Duke University integrated hydrologic model, using a Monte Carlo simula- [email protected], [email protected] tion approach. Results will then be used to understand pa- rameter sensitivity through an active subspace technique; Brian Carnes, David Hensinger identification of the active subspace will help explain which Sandia National Laboratories parameters result in the greatest model variability. [email protected], [email protected] Jennifer Jefferson Colorado School of Mines MS57 jejeff[email protected] Fractional Modeling of Brain Aneurysms Reed M. Maxwell The arterial wall is typically described using integer-order Department of Geology and Geologic Engineering PDEs. Recently, 1D simulations indicate that fractional- Colorado School of Mines order models is a powerful alternative because they are [email protected] less sensitive to the parameter estimation. We develop nu- merical methods for fractional-order models, and for the first time employ them in 3D fluid-structure interaction MS58 aneurysm simulations. Comparison studies indicate that Dimension Reduction in MCMC using Active Sub- although the 3D models are more sensitive to the frac- spaces tional order compared to 1D cases, they are insensitive to the relaxation parameters. Markov Chain Monte Carlo is a useful tool for sampling from the posterior distribution in Bayesian inverse prob- Yue Yu lems, though it often struggles to converge in high dimen- Brown University sions. We discover and exploit active subspaces—an emerg- [email protected] ing set of tools for dimension reduction—in the misfit term of the likelihood to focus sampling along important direc- George E. Karniadakis tions in the parameter space, which improves mixing and Brown University convergence. We develop the framework and demonstrate Division of Applied Mathematics its capabilities on a 100-dimensional model inverse prob- george [email protected] lem.

Carson Kent MS58 Colorado School of Mines Exploiting Active Subspaces to Quantify Uncer- [email protected] tainty in the Numerical Simulation of the HyShot II Scramjet Paul Constantine Colorado School of Mines We present the computational analysis of the reactive flow Applied Mathematics and Statistics in a hypersonic scramjet engine with emphasis on effects [email protected] of uncertainties in the operating conditions. The active subspaces methodology is used to characterize the effects of the input uncertainty on the scramjet performance. In MS58 addition to discussing the computational cost benefits as- Discovering An Active Subspace in a Single-Diode sociated with this dimension reduction technique, we focus Solar Cell Model on interpretation of the active variable and how it compares to expertise/intuition and sensitivity analysis Single-diode models for solar cells contain several parame- ters, so sensitivity analyses and UQ can be computationally Michael A. Emory expensive. We employ active subspaces for the solar cell’s CS15 Abstracts 63

the maximum power functiona function of the single-diode New York University model parametersto discover a one-dimensional subspace [email protected] that enables us to reduce the dimension for UQ parameter studies. Omar Ghattas The University of Texas at Austin Mark Campanelli [email protected] National Renewable Energy Laboratory [email protected] Noemi Petra University of California, Merced Brian Zaharatos [email protected] Colorado School of Mines [email protected] MS60 MS59 RBF Response Surfaces with Inequality Con- straints Operator Weighted MCMC on Function Spaces In this talk, we describe how to construct RBF interpolants Many inference problems require exploring the posterior that have given function values at some sample points and distribution of high-dimensional parameters, which in prin- satisfy upper and lower bound constraints at other points. ciple can be described as functions. We introduce a family Our approach is based on a constrained quadratic mini- of operator-weighted MCMC samplers that can adapt to mization problem that leads to a unique, parsimonious in- the intrinsically low rank and locally complex structure of terpolant in which RBF centers appear only as they are the posterior distribution while remaining well defined on needed to enforce an equality or inequality constraint. We function space. Posterior sampling in a nonlinear inverse also show that this method always improves the native problem and a conditioned diffusion process are used to space error over an interpolant subject to the equality con- demonstrate the efficiency of these dimension-independent straints alone. operator-weighted samplers. David Bindel Tiangang Cui Cornell University Massachusetts Institute of Technology [email protected] [email protected]

Kody Law MS60 SRI UQ Center, CEMSE, KAUST Miso: Mixed-Integer Surrogate Optimization for [email protected] Computationally Expensive Black-Box Problems

Youssef M. Marzouk We present an algorithm framework that uses surrogate Massachusetts Institute of Technology models for solving mixed-integer global optimization prob- [email protected] lems whose objective function evaluation requires a com- putationally expensive computer simulation, and thus the analytical description and the derivatives are not available MS59 (black-box). Using a range of benchmark problems and Estimation of Parameters of Chaotic Dynamic Sys- two applications arising from groundwater remediation, we tems show that a combination of stochastic and deterministic sampling techniques leads to significantly improved solu- To estimate parameters of chaotic dynamical systems a tions as opposed to using only a single sampling strategy. measure to quantify the likelihood function of chaotic vari- ability (the ’distance’ between different trajectories) is needed. We review problems encountered by previously Juliane Mueller used methods and propose a method related to fractal di- Lawrence Berkeley National Lab mension concepts. The methodology is illustrated using [email protected] classical chaotic examples, the Lorenz 63 and Lorenz 95 systems, as well as higher dimensional fluid systems. MS60 Heikki Haario Parallel Surrogate Global Optimization with Lappeenranta University of Technology Pareto Centers for Single Objective Expensive Department of Mathematics and Physics Functions heikki.haario@lut.fi In single objective optimization with surrogates there are typically two criteria when searching on the surrogate sur- MS59 face for the next x for expensive function evaluation, a) Mapped Stochastic Newton Sampling that s(x), the surrogate surface, is small and b) evaluating f(x) will improve the overall quality of the accuracy of the Different sampling algorithms for inverse UQ problems surrogate approximation. In this new algorithm, a multi- with high-dimensional parameters are reviewed and com- objective optimization method is used to select the next pared. A method that combines ideas from stochastic New- points for multiple parallel processors. Solution accuracy ton MCMC sampling and implicit sampling is proposed is shown to improve. and its efficiency is studied numerically. Christine A. Shoemaker Georg Stadler Cornell University Courant Institute for Mathematical Sciences [email protected] 64 CS15 Abstracts

Tipaluck Krityakierne action calculation. The locally optimal block precondi- Center for Applied Mathematics, Cornell University tioned conjugate gradient (LOBPCG) method is used in [email protected] MFDn to compute a few lowest eigenpairs of the very large, sparse many-body nuclear Hamiltonian matrix. We Taimoor Akhtar present a multi-level strategy that exploits the structure Cornell University of the Hamiltonian matrix and accelerate the convergence [email protected] of the LOBPCG method. Some preliminary results of pre- conditioning are also presented.

MS60 Meiyue Shao Efficient Multi-Start for Global Optimization in Lawrence Berkeley National Laboratory Accelerator Design [email protected] We present a scalable, asynchronous algorithm for locating several/many high-quality local minimizers of expensive computer simulations for which derivatives are unavailable. MS61 Our method adjusts the amount of exploration/refinement Derivative-free Optimization Techniques in ab ini- performed depending on the observed function values and tio Nuclear Structure Calculations user desires. We highlight how our method scales as more computational resources become available. We lastly em- ploy our algorithm on particle accelerator design prob- Many tasks in ab initio nuclear structure calculations lems, performing our computational studies on some of the may rely on search techniques, such as tuning of nucleon- largest supercomputers in the US. nucleon and three-nucleon interactions to fit light nuclei, optimizing of basis functions, and reducing 3-body force Jeffrey M. Larson, Stefan Wild effects by optimizing freedoms in chiral effective-field the- Argonne National Laboratory ory NN interactions. This field is still under-served, how- [email protected], [email protected] ever, by the existing optimization software, mainly due to the complexity of the underlying function evaluations. In this talk, we will first show a flexible framework for in- MS61 terfacing the MFDn package for performing ab initio nu- Symmetry-adapted No-core Shell Model for First clear structure calculations with derivative-free optimiza- Principle Lage Scale Computations of Atomic Nu- tion packages. We demonstrate a few examples of tun- clei ing the interaction parameters and compare results using POUNDeRs and QNSTOP optimization algorithms, and We introduce Symmetry-adapted No-core Shell Model (SA- note on efficient function evaluations when several nuclei NCSM) approach—an emerging tool for first principle are fitted simultaneously. studies of light and medium mass nuclei. We review the pillars of the SA-NCSM framework and discuss techniques Masha Sosonkina and algorithms that facilitate its implementation in form Old Dominion University of a highly scalable computer code for modern petascale [email protected] systems. We also outline future research directions and developments. Tomas Dytrych MS62 Louisiana State University [email protected] Hdg Method for Linear Elasticity

This paper presents a new hybridizable discontinuous MS61 Galerkin (HDG) method for linear elasticity on general Add, Multiply, Divide and Conquer: On-the-fly Al- polyhedral meshes, based on a strong symmetric stress gorithms for Many-body Calculations formulation. The key feature of this new HDG method is the use of a special form of the numerical trace of the Quantum many-body systems can be cast as a large- stresses, which makes the error analysis different from the dimension matrix eigenvalue problem. The dimensional- projection-based error analyzes used for most other HDG ity is not the only challenge; even with very sparse matri- methods. For arbitrary polyhedral elements, we approxi- ces, simply storing the non-zero matrix elements can re- mate the stress by using polynomials of degree k¿=1 and quire terabytes or even petabytes. I discuss how on-the-fly the displacement by using polynomials of degree k+1. In methods can dramatically reduce storage by factorizing the contrast, to approximate the numerical trace of the dis- matrix exactly using additive and multiplicative quantum placement on the faces, we use polynomials of degree k numbers. Any machine, whether a laptop or a supercom- only. This allows for a very efficient implementation of puter, can thus run much larger problems. the method, since the numerical trace of the displacement is the only globally-coupled unknown, but does not de- Calvin W. Johnson grade the convergence properties of the method. Indeed, San Diego State University we prove optimal orders of convergence for both the stresses [email protected] and displacements on the elements. These optimal results are possible thanks to a special superconvergence property MS61 of the numerical traces of the displacement, and thanks to the use of a crucial elementwise Korn’s inequality. Multi-Level LOBPCG Method in MFDn Many Fermion Dynamics for nuclei (MFDn) is a state- Weifeng Qiu of-the-art software package for nuclei configuration inter- City University of Hong Kong CS15 Abstracts 65

[email protected] to be nonsingular under certain reasonable assumptions. A basic Newton method is presented as well two approximate Newton methods based upon Krylov space and generalized MS62 Krylov space projections. The resulting algorithms are ap- HDG Methods for the p-Laplacian plied to a problem from high-resolution image reconstruc- tion that is appropriately modeled by total least squares. We propose a hybridizable discontinuous Galerkin (HDG) method for the p-Laplacian equation. The numerical scheme inherits two distinctive features when the solution Jesse L. Barlow is sufficiently regular. First, when using polynomial of de- Penn State University gree k ≥ 0forh, h and uh, our scheme exhibits optimal Dept of Computer Science & Eng k + 1 order of convergence for all of them in L2, Lp and [email protected] L∞ norm. Second, when k ≥ 1, by applying an element- by-element postprocessing technique, we can obtain a new ∗ Geunseop Lee approximation uh that converges at order k +2 to u.In The Pennsylvania State University addition, we formulate two efficient nonlinear conjugate [email protected] gradient algorithms to solve our HDG methods from the minimization standpoint. We carefully compare these two Haoying Fu algorithms in terms of convergence speed, memory require- Penn State University ment and robustness. To improve the efficiency further, Computer Science & Engineering Department we construct a class of remarkable preconditioners based [email protected] on the unifying hybridization framework. In addition, for the first time, we postprocess the numerical trace uh for constructing a quality initial guess as an implementation MS63 technique. Performance Evaluation of EigenExa Dense Eigen- Bernardo Cockburn, Jiguang Shen solver on the Oakleaf-Fx Supercomputer System School of Mathematics University of Minnesota We have developed a dense eigensolver named EigenExa, [email protected], [email protected] which employs the divide-and-conquer method for a banded matrix (currently penta-diagonal). To capture its current performance in detail, we conducted an evalua- MS62 tion by using the whole supercomputer system Oakleaf- FX, which consists of 4800 nodes and has the almost same Parallel hp-multigrid for HDG architecture as the K computer. In this talk, we present We present a parallel algorithm for hp-adaptive multigrid the results of the evaluation, which shows advantages of for the HDG method. We first coarsen in p, smoothing our eigensolver and issues we face. only on the skeletal system, until we obtain an HDG sys- tem with p = 1. We switch to a linear CG grid at this stage Takeshi Fukaya and continue to coarsen in h. This allows us to create a RIKEN, Japan deep grid hierarchy and obtain optimal multigrid conver- Japan gence. We compare the performance of different smoothers [email protected] and with our recent work on high-order multigrid using a CG discretization. We also present early scalability results Toshiyuki Imamura from a parallel implementation. RIKEN Advance Institute for Computational Science [email protected] Tan Bui University of Texas at Austin [email protected] MS63 Scaling Comparison of Dense Eigensolvers and Pu- Hari Sundar rification Techniques to Large Node Counts Institute for Computational and Engineering Sciences University of Texas at Austin This talk focuses on the case when large parallel resources [email protected] are available for computing the spectral projector of a rela- tively small matrix. This is the case, for example, in quan- tum chemistry where large parallel resources are needed MS63 for computing the Fock matrix, and then all the resources Solving a Parameterized Eigenvalue Problem from are available to diagonalize the Fock matrix. We examine Regularized Total Least Squares the scaling of communication and computation for vari- ous dense eigensolvers, and also for a Newton-Schulz ap- The solution of an ill-conditioned total least squares (TLS) proach for computing the spectral projector which is based problem by a regularization approach of Golub et al. on matrix-matrix multiplications. [SIAM J. Matrix Anal. Appl. 21(1):185-194,1999] is con- sidered. That regularized TLS formulation can be viewed Xing Liu, Edmond Chow as a parameterized eigenvalue problem. The approach School of Computational Science and Engineering given here is a Newton method that iterates for the param- Georgia Institute of Technology eter and the associated parameterized eigenvalue. The two [email protected], [email protected] nonlinear equations are formulated from a standard reg- ularization bound constraint and a spectral function from the parameterized eigenvalue problem. The Jacobian of the MS63 system can be computed inexpensively and can be proven Revisiting SVD(A) through EIG(T) for 66 CS15 Abstracts

Sca/LAPACK [email protected]

It is well known that the SVD of a matrix A, A = T USV , can be obtained from the eigenpairs of the ma- MS64 T T trix CV = A A or CU = AA . Alternatively, the SVD can be obtained from the eigenpairs of the augmented ma- High-Order Gas Evolution Model for Computa- T trix CUV =[0A, A 0]. This presentation focuses on CUV tional Fluid Dynamics in the context of bidiagonal matrices and Sca/LAPACK’s tridiagonal eigensolvers, and discusses accuracy and imple- The foundation of compressible flow solver is based on the mentation issues. first order gas dynamic model, i.e., the Riemann solution of the Euler equations, where the spatial and temporal dis- Osni A. Marques cretizations are decoupled. Here, we will present a high- Lawrence Berkeley National Laboratory order gas evolution model based on the Boltzmann equa- Berkeley, CA tion, and develop the corresponding high-order schemes. In [email protected] the high-order gas-kinetic schemes, the spatial and tempo- ral discretization are fully coupled starting from a piecewise discontinuous high-order initial condition. The necessity to couple spatial and temporal evolution nonlinearly is impor- MS64 tant to construct high order compact schemes. Higher-Order Filtered Methods for Nonlinear Par- tial Differential Equations Kun Xu University of Science & Technology The theory of viscosity solutions has been effective for rep- Hong Kong resenting and approximating weak solutions of nonlinear [email protected] partial differential equations such as Hamilton-Jacobi and second-order elliptic equations. The approximation theory of Barles and Souganidis requires that numerical schemes MS64 be monotone. However, monotone schemes have limited accuracy. We introduce a framework for using monotone An Efficient Spectral Method for the Euler- schemes as the foundation for filtered schemes, which are Lagrange Equations of Minimum Action Methods almost-monotone. This allows us to construct higher-order discretisations that provably converge to the viscosity so- Minimum Action Method is one of the popular approaches lution of the underlying PDE. to study phase transitions of dynamical systems. Accord- ing to the Freidlin-Wentzell theory, at zero temperature Brittany Froese limit, transitions happen along the path which takes min- University of Texas at Austin imum action. Minimum Action Method converts a phase [email protected] transition problem to an optimal control problem. Tradi- tional method to solve the optimal control problem usually Adam M. Oberman first discretize the problem, then use a general purpose op- McGill U. timization package to solve the discretized problem. In [email protected] this talk, we will propose another approach, which first derive the Euler-Lagrange equation of the minimum ac- tion, then solve this high-order partial differential equa- tion directly. By taking advantage of good properties of MS64 the Euler-Lagrange equation, we establish an efficient spec- High Order Methods for Traveltime and Amplitude tral solver. Numerical results for phase transitions of both in Geometrical Optics ODEs and PDEs, gradient and non-gradient systems will be presented. In geometrical optics approximation for the Helmholtz equation, accurate and efficient computation of traveltime Haijun Yu and amplitude is important. We present an approach to re- LSEC solving the source singularities and high order methods to Academy of Mathematics and Systems Science, China compute the traveltime and amplitude efficiently. Numer- [email protected] ical examples are presented to demonstrate the methods. Xiaoliang Wan Louisiana State University Songting Luo Department of Mathematics Department of Mathematics, [email protected] Iowa State University [email protected] MS65 Jianliang Qian Department of Mathematics Title Not Available at Time of Publication Michigan State University [email protected] Abstract not available at time of publication.

Robert Burridge Mary Galvin-Donoghue Department of Mathematics and Statistics National Science Foundation University of New Mexico Div. of Materials Research CS15 Abstracts 67

[email protected] [email protected]

MS65 MS66 Materials from Mathematics A Dispersionless Fourier Method for the Maxwell Equations Using Volume Penalization

We present examples of new materials whose synthesis We develop numerical Fourier methods for solving the time was guided by some essentially mathematical ideas. These dependent boundary value problem for Maxwell’s equa- materials undergo phase transformations from one crystal tions in the vicinity of perfect electric conductors. The structure to another, without diffusion. The underlying high order methods are obtained by analytically modifying mathematical theory was designed to identify alloys that the standard Maxwell equations with a volume penaliza- show exceptional reversibility of the transformation. Some tion term. The absence of strong dispersive effects and the of these alloys convert heat to electricity (without a sepa- efficiency of the fast Fourier transform make this approach rate electrical generator), and provide an interesting pos- potentially well suited for high frequency applications. We sible route to recover the vast amounts of energy stored on demonstrate the approach with several simulations of scat- earth at small temperature difference. The broader lessons tering and wave guide problems (with the inclusion of per- from this research are: 1) mathematics can be used for un- fectly matched layers where appropriate). expected discovery, but nonstandard approaches are help- ful (what if?, rather than what? and why?), 2) an algorith- Ryan Galagusz mic approach (theorems =⇒ algorithms) seems to be use- McGill University ful, 3) a functioning feedback loop with experiment is desir- Department of Electrical Engineering able, 4) a useful development would be to integrate modern [email protected] applied mathematics with the synthesis/characterization tools that play such an essential role in materials science. MS66 Richard James Fourier based PDE Solution on Complex Domains Department of Aerospace Engineering and Mechanics University of Minnesota Fourier continuation/extension (FC) methods allow for [email protected] highly-accurate Fourier representations of non-periodic functions. FFT speed algorithms, including the FC(Gram) algorithm, have been developed for these Fourier approx- MS65 imations and subsequently applied to the solution of par- tial differential equations. In particular, a new analysis Computational Materials Design: Challenges in approach has been utilized to ensure unconditional stabil- Practical Applications ity for some FC alternating direction solvers. A unique character of solutions generated from the Fourier approx- Abstract not available at time of publication. imations is the lack pollution error for wave propagation problems while avoiding many of the limitations of tradi- Sadasivan Shankar tional spectral methods. Various methods for the solution Harvard University of partial differential equations and other applications of [email protected] FC algorithms will be discussed.

Mark Lyon MS65 University of New Hampshire Title Not Available at Time of Publication [email protected]

Abstract not available at time of publication. MS66 Michael S. Vogelius New Active Penalty Methods with Applications to Rutgers University, New Brunswick Fluid Flow [email protected] In this talk I will present a new active penalty method. This method relies on a construction that systematically MS66 improves the amplitude of the boundary layer that results from the penalty term. As a result, convergence rate is Penalty Methods for the Hyperbolic System Mod- improved. I will present a Fourier Spectral 4th order glob- eling the Wall-Plasma Interaction in a Tokamak ally convergent version of this approach for the heat equa- tion with internal non-mesh-conforming Dirichlet bound- One main challenge for producing energy using magnetic ary conditions. I will then extend this to the solution of confinement fusion in a tokamak is the control of wall- incompressible Navier-Stokes equations in the presence of plasma interactions. Thus, numerical tools with efficient solid non-mesh-conforming boundaries. I will finish by dis- implementations of the boundary conditions are needed. cussing convergence rate and stability of the method in This talk presents several penalty methods. A penalization general. method for a non linear hyperbolic problem is provided and analyzed theoretically and numerically: this method does Jean-Christophe Nave not generate any boundary layer and the convergence rate, McGill University when the penalty parameter goes to 0, is optimal. [email protected]

Philippe Angot, Thomas Auphan, Olivier Gu`es Aix-Marseille Universit´e MS67 [email protected], [email protected], The Use of Residual-Based Compact Schemes for 68 CS15 Abstracts

Industrial Les [email protected]

The use of suitable high accurate numerical techniques is of the utmost importance for the simulation of turbulent MS67 flows since they enable capturing flow structures from large Validation of a High-Order Implicit Les Solver to small scales at an acceptable computational cost. In for the Simulation of a Low-Reynolds-Number this sense, compact schemes appears to be particularly at- Vertical-Axis Wind Turbine tractive because of their spectral-like accuracy. Moreover, for industrial aerodynamics computations, robustness and We use a high-order DG scheme for the ILES simulation shock capturing capabilities are also crucial issues. In this of a straight-bladed Vertical Axis Wind Turbine (VAWT). work, we discuss the capabilities of a family of high order We validate the solver by simulating the flow field about residual-based compact (RBC) schemes, characterized by a single static NACA0012 airfoil over a range of angles odd orders of accuracy and a genuinely multidimensional of attack. Using an ALE-scheme in both 2D and 3D, we numerical dissipation, for the implicit large eddy simula- simulate a real-world VAWT configuration at low chord tion (ILES) of compressible turbulent flows in complex con- Reynolds number (about 50,000) for which experimental figurations. data is available, and determine the accuracy for various flow conditions. Paola Cinnella ENSAM, ParisTech Samuel Kanner [email protected] University of California, Berkeley [email protected] C´edric Content Laboratoire DynFluid Per-Olof Persson Arts et M´etiers ParisTech University of California Berkeley [email protected] Dept. of Mathematics [email protected] Luca Sciacovelli Laboratoire DynFluid, Arts et M´etiers Paristech MS67 and Politecnico di Bari [email protected] Applications of the Spectral/hp Element Method to Complex Flow Geometries

As industrial requirements evolve to require both transient MS67 and scale-resolving capabilities, the use of under-resolved The Application of High Order Dgm for Resolved DNS and implicit LES methods is needed to capture the and Wall-Modeled Les of Full Scale Turbomachin- essential flow features. In this talk, we give some examples ery Passages of industrially-relevant simulations, and highlight some of the challenges that arise when performing simulations in complex three-dimensional geometries. Furthermore we Large Eddy Simulations of turbulent flows require highly demonstrate how the spectral/hp element method com- accurate discretisations in order to minimise the impact bined with appropriate stabilisation and discretisations can of discretisation errors for inevitably underresolved com- resolve flow features in these complex domains. putations. Although extremely accurate methods are used in academia, industry relies low order finite volume meth- David Moxey ods, mainly due to their geometric flexibility. The dis- Imperial College London continuous Galerkin Method promises to be an enabler of [email protected] high-resolution LES in an industrial context, as it provides high-accuracy on unstructured meshes and therefore com- Joaquim Peiro plex geometry, but also provides excellent parallel scaling. Dept of Aeronautics It furthermore offers the perspective of adaptive computa- Imperial College London, UK tions. The current contribution describes the development [email protected] of an industrial CFD code for LES, including validation, optimisation and extreme scalability, and concludes with practical examples. Spencer Sherwin Imperial College London [email protected] Koen Hillewaert Cenaero Cenaero MS68 [email protected] Unit and Conquer Algorithms for Large Eigenvalue Problems Corentin Carton de Wiart Cenaero The emerging new multi-level and heterogeneous computer [email protected] architectures, gearing up the road to exascale computing, are requiring numerical algorithmic revisions and their cor- Guillaume Verheylewegen responding implementations to achieve performance scala- Universit´e catholique de Louvain bility. We present unite and conquer approach as a solution [email protected] to achieve this goal. That consists to accelerate the rate of convergence of a restarted method by coupling either Ariane Fr`ere synchronously or asynchronously, several restarted meth- Cenaero ods called also co-methods. Some experiments validating CS15 Abstracts 69

the approach will be presented. of large dense matrices when a small rank perturbation is applied. Here several different practical scenarios are con- Nahid Emad sidered: partial or full spectrum to be computed, interior PRiSM laboratory and Maison de la Simulation, or extreme eigenvalues, etc. University of [email protected] Yousef Saad Department of Computer Science University of Minnesota MS68 [email protected] Performance of Algebraic Multigrid Precondition- ers for Large-Scale Finite Element Simulations Vasilis Kalantzis CEID,SchoolofEngineering Finite element method (FEM) approaches are used for University of Patras, Greece the large-scale, high fidelity simulation of many impor- [email protected] tant physical phenomena, e.g. fluid flow or magnetohy- drodynamics (MHD). Our solution approach for the re- sistive magnetohydrodynamics (MHD) equations employs MS69 an FEM discretization with an algebraic multigrid precon- Augmenting the One-Shot Framework by Addi- ditioned Newton-Krylov method on unstructured meshes. tional Constraints We present scaling results for resistive MHD test cases, in- cluding results on 500,000 cores on an IBM Blue Gene/Q The multi-step Oneshot method for design optimization platform. problems has been successfully implemented for various ap- plications. To this end, a slowly convergent primal fixed Paul Lin point iteration of the state equation is augmented by an ad- Sandia National Laboratories joint iteration and a corresponding preconditioned design [email protected] update. Within this talk we present a modification of the method that allows for additional equality constraints be- John Shadid sides the usual state equation. A retardation analysis and Sandia National Laboratories the local convergence of the method in terms of necessary Albuquerque, NM and sufficient conditions are given, which depend on key [email protected] characteristics of the underlying problem and the quality of the utilized preconditioners.

MS68 Torsten F. Bosse Intelligent Iterative Methods : the Future of Par- Humboldt-Universit¨at zu Berlin, allel and Distributed Runtime Tuned Linear Alge- Institut f¨ur Mathematik bra? [email protected]

We discuss some recent comparisons on clusters of accelera- Andreas Griewank tors between orthogonal, incompletely orthogonal and non- HU Berlin, Germany orthogonal Krylov Basis computing, focusing on communi- [email protected] cations and orthogonality accuracy. Then, we discuss some results for the ERAM method with respect to the restart- ing strategies. We survey some smart-tunning strategies we MS69 proposed and evaluated for some of the Krylov method pa- Fixed-Point Iterations for Simultaneous One-Shot rameters. As a conclusion, we propose auto-tuning strate- Optimization of Unsteady Flows gies for future hybrid methods on future exascale hyper- computers, on the road to intelligent linear algebra meth- The One-shot method has proven to be very efficient in ods mixing both distributed and parallel programming optimization with steady PDEs which are solved by fixed- models. point iterations. We provide a framework that extends the method to unsteady problems that are solved by clas- Serge G. Petiton sical time-marching schemes. The One-shot method is University Lille 1, Science and Technologies - CNRS applied to an optimal control problem with unsteady in- serge.petiton@lifl.fr compressible Navier-Stokes equations. The unsteady fixed- point iteration is further improved applying adaptive time scales. Opportunities and first results on integrating One- MS68 shot optimization into parallel-in-time simulation will be Divide and Conquer Algorithms for Large Hermi- presented. tian Eigenvalue Problems Stefanie G¨unther, Nicolas R. Gauger A number of eigenvalue problems are considered from the RWTH Aachen University point of view of highly parallel distributed environments. [email protected], We first discuss a polynomial filtering technique for ex- [email protected] tracting extreme or interior eigenvalues of large sparse ma- trices. This general approach can be effective in the situa- Qiqi Wang tion when a large number of eigenvalues is sought, as is the Massachusetts Institute of Technology case in electronic structure calculations for example. The [email protected] method presented relies on a combination of the Lanczos algorithm with partial reorthogonalization and polynomial filtering based on least-squares polynomials. We also dis- MS69 cuss the problem of updating eigenvalues and eigenvectors Towards Second Order One-Shot Methods in the 70 CS15 Abstracts

Context of Shape Calculus for kinetic equations in regimes leading to hyperbolic or diffusive systems of conservation laws appearing e. g. in One-shot methods aim at efficient implementation of gra- some models of radiative transfer or fluid-particle interac- dient based optimization methods. Highest efficiency is tions, we apply the projective integration method devel- reached, if second order methods can be employed. This oped by Gear and Kevrekidis in the context of large mul- poses a certain challenge for shape optimization methods, tiscale differential systems appearing in Chemistry. The which employ shape calculus for efficiency reasons. The crucial point of this work is our obtaining high order in challenge lies in the fact that the space of shapes is not time asymptotic preserving schemes. a linear space. This talk proposes the usage of Rieman- nian shape manifolds in order to carry over second order Pauline Lafitte properties to shape optimization problems. Numerical re- Project team SIMPAF, INRIA Lille sults for PDE constrained shape optimization problems are pauline.lafi[email protected] provided. Annelies Lejon, Ward Melis Volker H. Schulz KU Leuven University of Trier [email protected], [email protected] Department of Mathematics [email protected] Giovanni Samaey Department of Computer Science, K. U. Leuven MS69 [email protected] On An Extension of the Augmented Lagrangian Approach for One-Shot Optimization MS70 One-shot approaches for design optimization augment the Effective High-Order Diffusive Moment Closures solution of the state equation with an adjoint solver yield- with the StaRMAP Software ing approximate derivatives to change the design. The co- ordination of these iterative processes is well established StaRMAP is a software to efficiently compute linear mo- when only the state equation serves as equality constraint. ment models of radiative transfer (e.g., PN, SPN, FPN) We propose a modified augmented Lagrangian function for using staggered grid finite difference approximations. We the handling of additional equality constraints. We show present the extension of the method and software to diffu- that this augmented Lagrangian can be used in gradient- sive closures that possess a “viscosity” in the highest re- based optimization to solve the original design task. solved moment. We show how the new term can be incor- porated into the numerical approach without incurring a Andrea Walther reduction in convergence order or a requirement for unde- Universit¨at Paderborn sirably small time steps. Then, using the StaRMAP code, [email protected] the benefits and drawbacks of various diffusive closures are discussed. The StaRMAP code is available for download, Nicolas R. Gauger and the results are easily reproducible. RWTH Aachen University Benjamin Seibold [email protected] Temple University [email protected] MS70 Energy-Conserving Schemes for Vlasov-Type Sys- Martin Frank tems RWTH Aachen University Center for Computational Engineering Science In this talk, we present the discontinuous Galerkin (DG) [email protected] methods to solve the Vlasov-Maxwell system. The scheme employs DG discretizations for both the Vlasov and the Maxwells equations, resulting in a consistent description of MS70 the probability density function and electromagnetic fields. An Asymptotic-preserving Scheme for Linear Ki- We prove that using this description the total particle num- netic Equation with Fractional Diffusion Limit bers are conserved, and the total energy could be preserved upon a suitable choice of numerical flux for the Maxwells We present an asymptotic-preserving scheme for the linear equations and the underlying polynomial spaces on the Boltzmann equation with fractional diffusion limit. The semi-discrete level, if boundary effects can be neglected. equilibrium is a fat tail function, which disables any trun- We further established error estimates based on several flux cation in the velocity space numerically. The stiffness choices. We test the scheme on the Weibel instability and adds more numerical difficulty. Our idea is based on a verify the order and conservation of the method. macro/micro/tail decomposition, where the macro/micro components support on a compact velocity space and de- Yingda Cheng compose the equation following a reshuffled Hilbert expan- Department of Mathematics sion. The tail that collects all the rest information solves Michigan State University a limit equation. [email protected] Li Wang UCLA Mathematics MS70 [email protected] High Order Asymptotic Preserving Projective In- tegration Methods MS71 In order to introduce new asymptotic preserving schemes Multilevel Methods for Forward and Inverse Ice CS15 Abstracts 71

Sheet Modeling [email protected]

We present our work on recovering ice sheet modeling Nathan Martin parameter fields (such as basal slipperiness) from obser- IMT CNRS/INSA/UPS, Toulouse, France. vations, using both deterministic and Bayesian inversion. [email protected] The scalability of our adjoint- and Hessian-based meth- ods is determined by the scalability of two sub-problems: the solution of the state PDEs (Stokes equations of ice MS71 sheet dynamics), and the approximation and precondition- Advances on Ice-Sheet Model Initialization using ing of the parameter-to-observation Hessian. For the for- the First Order Model mer problem, we compare the effectiveness of geometric and algebraic multigrid within the solution of the state Ice sheet initialization is critical for performing reliable for- PDEs; for the latter, we discuss the use of multilevel ap- ward simulations. We propose an adjoint-based optimiza- proximations to improve on Hessian approximation by low- tion algorithm for the ice-sheet initialization, where we in- rank updates. The scalability of our work is tested on full- vert for basal topography and basal friction fields simul- scale models of the Antarctic ice sheet. taneously, minimizing the mismatch between: 1. observed and computed surface velocity data, and 2. surface mass Toby Isaac balance forcing and modeled flux divergence. We show ICES the effectiveness of the initialization on the Greenland ice The University of Texas at Austin sheet. We mention ongoing work on quantifying uncertain- [email protected] ties in the optimized parameters.

Georg Stadler Mauro Perego Courant Institute for Mathematical Sciences CSRI Sandia National Laboratories New York University [email protected] [email protected] Stephen Price Omar Ghattas Los Alamos National Laboratory The University of Texas at Austin [email protected] [email protected] Georg Stadler Courant Institute for Mathematical Sciences MS71 New York University Assessment of Finite Element Schemes for Accu- [email protected] rate Modeling of the Grounding Line MichaelS.Eldred Modeling grounding line dynamics is critical in order to im- Sandia National Laboratories prove the projections of the contribution of the ice sheets Optimization and Uncertainty Quantification Dept. to sea level rise. The most advanced way of modeling the [email protected] grounding line consists of formulating a contact criterion, where the normal stress at the base of the ice is compared to the ocean pressure in the vicinity of the grounding line. Charles Jackson The grounding line is also the location of a sharp change UTIG in boundary condition, which generates a singularity in the University of Texas at Austin pressure field. The contact condition is therefore applied at [email protected] a location where the basal stress is most challenging to cap- ture accurately. Here, we present a new approach for the John D. Jakeman validation of Stokes Free-Surface flow with friction bound- Sandia National Labs ary conditions based on analytical-numerical solutions. We [email protected] then compare the performance of several full-Stokes finite element solvers and show that the solvers currently used in Irina K. Tezaur the glaciological community are not capable of capturing Sandia National Laboratories the pressure field when there is a non-penetration condi- [email protected] tion. These results show that the grounding line cannot be accurately modeled with the current solvers. Finally, we Andrew Salinger propose an algorithm that reaches a precision at the per- CSRI cent level in the pressure field for a typical ice flow regime. Sandia National Labs This work has vast implications for the modeling of ground- [email protected] ing lines and the ice sheets in a warming climate.

Mathieu Morlighem MS71 University of California - Irvine Uncertainty Quantification for Large-Scale [email protected] Bayesian Inverse Problems with Application to Ice Sheet Models Jerome Monnier Mathematics Institute of Toulouse We consider the estimation of the uncertainty in the so- [email protected] lution of large-scale ice sheet inverse problems within the framework of Bayesian inference. The ice flow is modeled Helene Seroussi as a three-dimensional, creeping, viscous, incompressible, Jet Propulsion Laboratory non-Newtonian fluid via the nonlinear Stokes equations. 72 CS15 Abstracts

The observational data come from InSAR satellite mea- [email protected] surements of surface ice flow velocity, and the uncertain parameter field to be inferred is the basal friction param- eter. We show that the work required for applying our MS73 framework–measured in number of forward (and adjoint) A Polarized-Trace Preconditioner for 2D ice sheet model solves–is independent of the state and pa- Helmholtz and Frequency Domain Full-Waveform rameter dimensions. Inversion Noemi Petra Full-waveform inversion, a method for recovering Earth’s University of California, Merced physical parameters by matching seismic observations with [email protected] simulations, can be treated in the frequency domain. A scalable solver for Helmholtz’s equation is necessary to Toby Isaac make feasible imaging in high resolution and in 3D; how- ICES ever, this remains an open problem. We present recent The University of Texas at Austin developments on a domain-decomposition solver for the [email protected] acoustic Helmholtz equation, based on the notion of polar- ization, that demonstrates substantial scalability and per- Georg Stadler formance improvements over the state-of-the-art. Courant Institute for Mathematical Sciences New York University Russell Hewett [email protected] Total [email protected] Omar Ghattas The University of Texas at Austin Leonardo Zepeda-Nunez [email protected] MIT [email protected] MS72 Laurent Demanet The most current list of partic- Professor of Mathematics, MIT ipating companies is available at [email protected] www.siam.org/meetings/cse15/career.php.

For the most recent list of participating companies visit MS73 http://www.siam.org/meetings/cse15/career.php Fast Multipole Method as a Preconditioner for Bill Kolata Finite Discretizations of Elliptic Boundary Value SIAM Problems [email protected] We employ the Fast Multipole Method to precondition sparse iterative solvers. FMM solves certain elliptic PDEs MS73 with O(N) complexity via kernels of high thread unifor- Fast Direct Solver based on the Cyclic Reduction mity, high arithmetic intensity, and relaxed synchroniza- Algorithm and Hierarchical Matrix Arithmetic for tion compared with factorization-based or multilevel ap- the Solution of Variable-coefficient Elliptic PDEs proaches. Combined, these features make FMM an in- teresting preconditioner on future architectures, even on We present a fast direct solver for variable-coefficient el- problems where FMM is not an ”exact” solver. We com- liptic partial differential equations on a Cartesian product pare FMM-preconditioned Krylov solvers with multilevel mesh. We combine the Cyclic Reduction algorithm with and sparse direct solvers on a variety of elliptic problems. Hierarchical Matrix arithmetic to reduce the fill-in blocks, resulting in an O(Nk2 log2 N) flop quasi-linear complexity Huda Ibeid,RioYokota solver. We compare against three techniques exploiting hi- King Abdullah University of Science and Technology erarchical low-rankness in the context of matrix bisection, [email protected], [email protected] nested dissection, and multifrontal ordering. Comparisons highlight algorithmic differences and implementation de- David E. Keyes tails with particular consideration to memory locality. KAUST [email protected] Gustavo Chavez KAUST [email protected] MS73 Generalized Plane Waves Adapted to Varying Co- George M. Turkiyyah efficients American University of Beirut [email protected] This talk will focus on new shape functions adapted to the scalar wave equation with smooth coefficients. It follows Rio Yokota the idea of approximating the solution by basis functions King Abdullah University of Science and Technology that have the appropriate oscillatory behavior. The lo- [email protected] cal design procedure of these generalized plane waves is developped to fit the varying coefficients. High order ap- David E. Keyes proximation is achieved, provided that a sufficient number KAUST of basis functions is used. Both theoretical and numerical CS15 Abstracts 73

aspects will be investigated. approximation and borrows heavily from fast multipole- type ideas for compressing structured linear operators. The Lise-Marie Imbert-G´erard factorization allows us to efficiently apply the matrix and Courant Institute of Mathematical sciences, NYU its inverse (inference), apply the matrix square root (sam- [email protected] pling), and compute the log-determinant (likelihood calcu- lations), among other related capabilities. We anticipate that such fast techniques will have a significant impact on MS74 large-scale inversion. This is joint work with Lexing Ying. Accelerating MCMC with Parallel Local Approxi- mations Kenneth L. Ho Department of Mathematics In many inference problems, the cost of MCMC analy- Stanford University sis is dominated by repeated evaluations of expensive for- [email protected] wardmodels.Wehavepreviouslyshownthatwhenthe model is well behaved, locally-constructed surrogates can Lexing Ying significantly reduce the number of evaluations required by Stanford MCMC while preserving the asymptotic exactness of the [email protected] resulting inference. We extend those results with parallel computing resources and adjoint techniques, demonstrat- ingstrongimprovementsinrun-time on challenging exam- MS74 ple inference problems. Stochastic inadequacy operators with applications Patrick R. Conrad, Youssef M. Marzouk to chemical kinetics Massachusetts Institute of Technology We investigate model form uncertainty for a reaction mech- [email protected], [email protected] anism model in hydrocarbon combustion. In a typi- cal reaction, the complete mechanism is either not well- Natesh Pillai understood, or too complex to effectively use as part of a Statistics larger combustion problem, necessitating a reduced model. Harvard To account for the discrepancy between the full model and [email protected] its reduced version, we propose an additive, linear, prob- abilistic formulation. This representation is encoded in a Aaron Smith random matrix, whose entries are calibrated using a hier- University of Ottawa archical Bayesian scheme. In particular, this formulation [email protected] is designed to respect certain physical constraints, but also be flexible enough to apply to multiple reactions.

MS74 Rebecca Morrison Convex Relaxations of Polynomial Imaging Prob- UT Austin lems [email protected]

Recent work on phase retrieval suggests that quadratic op- Robert D. Moser timization problems can sometimes be solved by lifting into University of Texas at Austin the space of PSD matrices. This approach can be seen as [email protected] a special case of sum-of-squares moment relaxation, which is known in theory to convexify much more general poly- nomial optimization problems. We show that this set of MS75 ideas offers a fresh point of view toward resolving the hard Multilevel Collocation with Radial Basis Functions nonlinearities of inverse wave scattering. Joint work with Augustin Cosse. In this talk, we discuss multilevel radial basis function collocation methods for solving elliptic partial differential Laurent Demanet equations on bounded domains. The approximate solution Professor of Mathematics, MIT is constructed in a multilevel fashion, each level using com- [email protected] pactly supported radial basis functions with smaller sup- port radius on an increasingly fine mesh. A convergence Augustin Cosse theory is given, which builds on recent theoretical advances MIT for multilevel interpolation using compactly supported ra- [email protected] dial basis functions. If time permits, we also discuss the condition numbers of the arising systems as well as the effect of a simple, diagonal preconditioner. MS74 Fast Algorithms for Linear Inverse Problems with Patricio Farrell Gaussian Priors Weierstrass Institute for Applied Analysis and Stochastics [email protected] A common theme in Gaussian process methods for inverse problems is the need to work with dense covariance matri- ces. Standard approaches based on the Cholesky decom- MS75 position have cubic complexity. In this talk, we describe A Reduced Radial Basis Function Method for Par- a method to construct a generalized Cholesky decompo- tial Differential Equations on Irregular Domains sition of many commonly used covariance matrices (e.g., squared exponential, Mat´ern, rational quadratic) in lin- We propose and test the first Reduced Radial Basis Func- ear time. The algorithm is based on hierarchical matrix tion Method (R2BFM) for solving parametric partial dif- 74 CS15 Abstracts

ferential equations on irregular domains. The two ma- Alfa Heryudono jor ingredients are RBF-FD solver and a collocation-based University of Massachusetts Dartmouth model reduction approach that systematically generates a Department of Mathematics reduced-order approximation whose dimension is orders of [email protected] magnitude smaller than the total number of RBF centers. The resulting algorithm is demonstrated through two- and three-dimensional test problems. MS76 Human Fetal Growth Model of Hypoplastic Left Alfa Heryudono Heart Syndrome University of Massachusetts Dartmouth Department of Mathematics [email protected] Abstract not available at time of publication. Adarsh Krishnamurthy Yanlai Chen UC San Diego Department of Mathematics [email protected] University of Massachusetts Dartmouth [email protected] MS76 Sigal Gottlieb Department of Mathematics A Computational Model of Reverse Cardiac University of Massachusetts Dartmouth Growth in Response to Mechanical Stimulus [email protected] Abstract not available at time of publication. Akil Narayan UMass Dartmouth Lik Chuan Lee [email protected] College of Engineering Michigan State University [email protected] MS75 Kernel-based Image Reconstruction from Scat- MS76 tered Radon Data Modeling Growth and Remodeling in Heart Muscle A novel kernel-based algebraic reconstruction method for Tissue image reconstruction from scattered Radon data is pro- posed. The reconstruction relies on generalized Hermite- Abstract not available at time of publication. Birkhoff interpolation by positive definite kernel functions in combination with a well-adapted regularization of the Joakim Sundnes Radon transform. This leads to a very flexible image re- Simula Research Laboratory construction method, which works for arbitrary distribu- [email protected] tions of Radon lines, unlike in classical Fourier-based meth- ods relying on the filtered back projection formula. The good performance of the proposed kernel-based image re- MS76 construction method is supported by numerical examples Finite Element Models of Growth and Remodelling and comparisons. in the Infarct Injured Left Ventricle Armin Iske Abstract not available at time of publication. University of Hamburg Department of Mathematics [email protected] Samuel Wall Simula Research Laboratory Center for Biomedical Computing MS75 [email protected] RBF-Based Partition of Unity Collocation Meth- ods for the Numerical Solution of PDEs MS77 Numerical methods based on radial basis function (RBF) Tribits: Tribal Build, Integrate, and Test System approximation are attractive because they can achieve high-order accuracy and can handle non-trivial geometries. The Tribal Build, Integrate, and Test System (TriBITS) Global RBF methods can be computationally expensive. is a framework built on top of the open-source CMake Therefore, we propose a localized approach where RBFs are tools which is designed to handle large software develop- used in a partition of unity framework. We have shown the- ment projects involving multiple independent development oretically that the resulting method converges spectrally in teams and multiple source repositories. TriBITS also de- thenodedistanceandalgebraicallyinthepatchsize.We fines a complete software development, testing, and deploy- present numerical experiments for elliptic and parabolic ment system consistent with modern agile software devel- PDEs. opment best practices. TriBITS is used by Trilinos, the Ad- vanced Simulation of Light Water Reactors (CASL) VERA Elisabeth Larsson codes, and other projects. Uppsala University, Sweden Department of Information Technology Roscoe Bartlett [email protected] Oak Ridge National Laboratory CS15 Abstracts 75

[email protected] Patrick O’Leary Kitware, Inc., USA [email protected] MS77 Computational Model Builder and ParaView Cat- alyst: Empowering HPC Workflows MS77 Software Quality with the Open Source Tools A key metric for computational scientists is how quickly CMake, CDash, CTest they gain insight into their problem from simulations. Bar- riers include developing complex input models and analyz- CMake has been used on several large projects such as ing results. We discuss how Computational Model Builder KDE, ITK, Hydra, VTK, ParaView, VXL, Trilinos and (CMB) can create simulation input models starting from CMake itself. In addition to building software, CMake the problem geometry. We show multiple CMB configura- provides a testing client (CTest) that integrates with the tions targeting various simulators. Additionally, we discuss web-based CDash testing server. This talk will cover how how to perform in situ analysis and visualization with Par- these tools can be leveraged in the context of an integrated aView Catalyst to reduce the time spent post-processing development environment to properly manage the software simulation results. process. This speeds up development while maintaining a high quality code-base. Andrew Bauer Kitware Inc. Bill Hoffman [email protected] Kitware bill.hoff[email protected] Patrick O’Leary Kitware, Inc., USA [email protected] MS78 Teaching Computing to Engineers Robert O’Bara, Berk Geveci Kitware The term ”computational thinking” became quite popular [email protected], [email protected] some years ago with a viewpoint piece at the CACM by Wang (2006), but the term goes back to Papert 10 years before. Wang explained it as the ability to think algorith- MS77 mically and apply problem-solving computation in other Developing Hydra-TH: A Vertical, VERA- fields. We’ve been talking about teaching computational integrated Application based on the Hydra Toolkit thinking ever since. With an interest in reforming how we teach computing to engineering students, I stumbled onto Hydra is an extensible C++ toolkit that provides a rich an extension of this idea that defines the pedagogical value suite of software components for rapid scientific applica- of computation. With modern tools for interactive com- tion development. Hydra supports multiple discretization puting (e.g. IPython Notebooks), it becomes possible to techniques and many different physics. This talk describes learn by computing, to actually create knowledgesimilar the development of Hydra-TH, a vertical application for to what we do in scientific computing to make discoveries, thermal-hydraulics specifically targeted for direct integra- but in education. I will describe how this thinking has been tion into VERA, the Virtual Environment for Reactor Ap- inspiring several educational initiatives aiming at making plications. Here, attention is given to the unique aspects computing a core pedagogical instrument. of Hydra that enable Hydra-TH (single/multiphase flow physics) to be automatically integrated into VERA. Lorena A. Barba Department of Mechanical and Aerospace Engineering Mark Christon George Washington University Los Alamos National Laboratories [email protected] [email protected]

Jozsef Bakosi MS78 Computational Physics Group Teaching Data Science from a Computer Science Los Alamos National Laboratory Perspective: Experience from a First Mooc [email protected] In Spring 2013 and Summer 2014, we ran a first massively Markus Berndt open online course in Data Science, attracting over 160,000 Los Alamos National Laboratory students. In this talk, Ill describe our motivation for de- [email protected] signing this course, some unique aspects of the curriculum, our results from the first two offerings, and finally some rec- ommendations around how training students to participate Andrew Bauer in data-intensive science has become essentialy to prepare Kitware Inc. them for both research and industry roles. [email protected] Bill Howe Alan Stagg University of Washington Oak Ridge National Laboratory [email protected] [email protected]

Balasubramanya Nadiga MS78 Los Alamos Opportunities and Experiences with Teaching [email protected] Computational Science from the Very Start of Uni- 76 CS15 Abstracts

versity Studies computers. Here, a recent nonlinear FETI-DP method is combined with an approach that allows an inexact solution Over the last 10 years, newcomers to science programs at of the FETI-DP coarse problem. We combine the nonlinear the Univ. of Oslo have been exposed to a tandem of an- FETI-DP domain decomposition method with an algebraic alytical and numerical methods together with computer Multigrid method and obtain a hybrid nonlinear domain programming. The talk will provide examples on how such decomposition/multigrid method. Parallel scalability re- an approach enhances the understanding of mathematical sults for up to 262 144 cores on the MIRA BlueGene/Q concepts and how it enables a new pedagogical approach, supercomputer (Argonne National Laboratory, USA) are more relevant working styles, and a tighter coupling to re- shown for our new implementation. search in traditional science subjects, with physics as pri- mary example. Axel Klawonn Universit¨at Duisburg-Essen, Germany Hans Petter Langtangen [email protected] Center for Biomedical Computing Simula Research Laboratory and University of Oslo [email protected] Martin Lanser Mathematical Institute Universit MS78 [email protected] Teaching Statistical Computing to Undergraduates Oliver Rheinbach We frame the minisymposium in the context of our experi- Technische Universit¨at Bergakademie Freiberg ence teaching computing with data to undergraduates. We [email protected] discuss our recent efforts to automate grading student com- putational work in Python and R. Automating grading can improve pedagogy by making it easier to assign students MS79 more work, reducing latency in providing feedback, and Fluid-Structure-Interaction in Computational enabling TAs to spend more time working directly with Hemodynamcis using Nonlinear Hyperelastic students by freeing them from the ”busy work” of grading. Arterial Wall Models Kenneth J. Millman We consider the fluid-structure-interaction problem in a University of California, Berkeley blood vessel. We follow a monolithic coupling approach [email protected] (P.Crosetto,S.Deparis,G.Fourestey,A.Quarteroni, Parallel algorithms for fluid structure-interaction prob- Philip B. Stark lems in haemodynamics. SISC, 33(4), 1598-1622, 2011), Statistics applying a Convective Explicit approach for the fluid. University of California, Berkeley To obtain an accurate prediction of transmural stresses [email protected] we make use of sophisticated nonlinear material mod- els for the vessel wall. Fortunately, such models have been developed in the past and their parameters have MS79 been adapted to experimental data. Here, we use an Parallel Scalable FETI Methods for Nonlinear anisotropic, polyconvex hyperelastic material model for the Problems structure (D. Balzani, P. Neff, J. Schr¨oder,G.A.Holzapfel, A polyconvex framework for soft biological tissies. Ad- The solution of nonlinear problems requires fast and highly justment to experimental data. IJSS, 43(20), p. 6052– scalable parallel solvers. FETI-DP domain decomposition 6070, 2006). The coupled simulations build on the LifeV (DD) methods are parallel solution methods for implicit software library (LifeV Software Library, www.lifev.org) problems. A common iterative DD approach for nonlin- and FEAP (R.L. Taylor, Finite Element Analysis Pro- ear problems is a Newton-Krylov-DD strategy where the gram,http://www.ce.berkeley.edu/projects/feap/). Ab- nonlinear problem is linearized using a Newton method. sorbing boundary conditions on the outflow are imposed Then, the linear system associated with the tangent stiff- to reduce reflections. ness matrix is solved with a preconditioned Krylov space method. The preconditioner is an efficient and parallel Daniel Balzani scalable domain decomposition method where local sub- Institute of Mechanics domain problems and a sufficiently small global problem Universit have to be solved. The local problems are inherently par- [email protected] allel, the global problem is needed to obtain numerical and parallel scalability. FETI-DP domain decomposition meth- ods have been shown to be scalable for linearized elasticity Simone Deparis problems on up to 65 536 cores of a BlueGene/P super- EcolePolitechniqueFederaledeLausanne computer (JUGENE, JSC, Germany) in 2009. Recently, simone.deparis@epfl.ch nonlinear versions of the well-known FETI-DP methods for linear problems have been introduced. Here, the non- Simon Fausten linear problem is decomposed directly before linearization. Institute of Mechanics The new approaches have the potential to reduce commu- Universit nication and to show a significantly improved performance, [email protected] especially for problems with localized nonlinearities, com- pared to a standard Newton-Krylov-FETI-DP approach. Davide Forti Another new approach can be viewed as a strategy to fur- Chair of Modeling and Scientific Computing, ther localize computational work and to extend the scala- EcolePolitechniqueFederaledeLausanne bility of FETI-DP methods towards extreme-scale super- davide.forti@epfl.ch CS15 Abstracts 77

Alexander Heinlein [email protected] Mathematical Institute Universit [email protected] MS80 A High-order Finite Element Method for Moving Axel Klawonn Boundary Problems Using Universal Meshes Universit¨at Duisburg-Essen, Germany [email protected] Abstract not available at time of publication. Evan Gawlik Alfio Quarteroni Stanford University Ecole Pol. Fed. de Lausanne [email protected] Alfio.Quarteroni@epfl.ch

Oliver Rheinbach MS80 Technische Universit¨at Bergakademie Freiberg Towards a Hybrid Parallelization of Chebyshev Fil- [email protected] tered Subspace Iteration

J¨org Schr¨oder Abstract not available at time of publication. Institute of Mechanics Universit Maria Kranjcevic [email protected] University of Zagreb [email protected]

MS79 MS80 A Scalable Monolithic Solver for the Coupling of Computational Reduction Strategies for Bifurca- a Finite Element and a Finite Volume Method for tion and Stability Problems Fluid-Structure-Interaction Abstract not available at time of publication.

We use two different discretization methods for the fluid Giuseppe Pitton and the structure sub-problems in a monolithic approach, SISSA, Trieste, Italy i.e both sub-problems as well as the coupling conditions [email protected] are assembled into one large algebraic system. Our solver bases on the application of Newtons method using iterative solvers with different multi-level methods. In this talk we MS80 discuss both, the coupling approach of the two different Nonlinear Frequency Response Analysis of Me- discretizations as well as the efficient solution of the arising chanical Vibrations based on Isogeometric Dis- large nonlinear system. cretization and Model Order Reduction

Abstract not available at time of publication. Johannes Steiner University of Lugano Oliver Weeger [email protected] TU Kaiserslautern [email protected] Rolf Krause Institute of Computational Science University of Lugano MS81 [email protected] Low-Rank Adaptive Tensor Approximation

A strategy to mitigate the curse of dimensionality”, which MS79 roughly means that the computational work, needed to ap- proximate a given function within a desired target accu- Adaptive Spectral Deferred Correction Methods racy increases exponentially in the spatial dimension, is to for Cardiac Simulation seek problem dependent dictionaries with respect to which the function pos- sesses sparse approximations. In this talk we highlight some recent developments centering on The electrical excitation of the heart as described by the the adaptive solution of high dimensional elliptic operator monodomain equations exhibits a wide range of temporal equations in terms of linear combinations of particularly and spatial scales. In this talk we will explore the possibili- adapted rank-one tensors. An adaptive iterative coarse- ties of combining spectral deferred correction (SDC) meth- to-fine algorithm is presented that produces near-minimal ods for time stepping with spatial and temporal adaptivity, rank approximation in stable hierarchical tensor formats in particular using optimized DIRK sweeps, interleaving where the adaptive identification of corresponding sub- mesh refinement with SDC iteration, inexact linear solves, spaces and sparse approximations of the low-dimensional and local time stepping. The efficiency of corresponding tensor factors are intertwined. We highlight the main con- adaptive algorithms are illustrated at some numerical ex- ceptual ingredients as well as some essential obstruction amples. due to the fact that the underlying energy spaces are not endowed with cross norms. The theoretical results are il- Martin Weiser lustrated by some numerical tests. Zuse Institute (ZIB) Berlin, Germany Wolfgang Dahmen 78 CS15 Abstracts

RWTH Aachen [email protected] IGPM [email protected] MS82 Title Not Available at Time of Publication MS81 A Theory for Model Verification Abstract not available at time of publication.

Model verification tries to capture the solution u to a para- George Bosilca metric PDE when the parameters that determine u are not University of Tennessee - Knoxville known but other information about u is present. The form [email protected] of this other information is typically (i) a posteriori mea- surements in the form of linear functionals applied to u and (ii) knowledge that u is well approximated by elements of MS82 a known finite dimensional space V . We describe theoret- ically, the best we can approximate u from this knowledge Portable Programming and Runtime Support for and then discuss numerical algorithms which perform near Application-Controlled Resilience in Large-Scale these best bounds. Scientific Applications

Ronald DeVore The Global View Resilience (GVR) system supports Department of Mathematics flexible, scalable, application-controlled resilience with a Texas A&M University portable abstraction versioned, distributed arrays. We [email protected] have evaluated GVRs utility on both a number of mini- apps (miniMD, miniFE), and larger applications (a PCG solver, OpenMC, ddcMD, and Chombo). Our results show MS81 programming effort (code change) is small (< 1% code) High-Order Digital Nets for Parametric and and localized. Studying the same applications, we find Stochastic Operator Equations that GVR version-based resilience can be achieved with low overhead for all of them. We present sparsity theory for direct and inverse problems for PDEs with infinite-dimensional uncertain input param- Andrew A. Chien eters, stemming from parametrization of distributed uncer- The University of Chicago tainty.It reduces the direct and inverse problem to integra- Argonne National Laborator tion problem over infinite-dimensional parameter spaces. [email protected] Based on a holomorphy condition on the parameteric de- pendence in [1], we present regularity estimates for the Hajime Fujita parametric integrand functions and for uniform prior mea- Department of Computer Science sure on the parameter uncertainty in classes of weighted University of Chicago RKHS introduced in [2]. Related recent results (joint with [email protected] J. Dick, F. Kuo, T. LeGhia and D. Nuyens) [3] on dimen- sion independent convergence rates of the deterministic, Zachary Rubenstein higher order QMC quadrature for integrand functions in Department of Computer Science, The University of weighted function spaces will be presented. The density Chicago of the posterior measure in Bayesian inverse problems as [email protected] considered in [5, 4] is shown to belong to the class of ad- missible integrand functions with a hybrid of product and Nan Dun, Aiman Fang sPOD weights. Research supported in part under ERC Department of Computer Science AdG 247277. University of Chicago [email protected], [email protected] Christoph Schwab ETH Zuerich SAM Ziming Zheng [email protected] Department of Computer Science, The University of Chicago [email protected] MS81 ∞ Multivariate Decomposition Methods -Variate MS82 Problems Resilient Programming Models We present the Multivariate Decomposition Method for ap- proximation of functions of infinitely many variables It Today’s leadership computing systems and scalable clus- works for functions that admit a decomposition f = u fu, ters already exhibit significant failure rates that impact where the sum is with respect to finite subsets u of posi- overall results rates and scientific productivity. Current is- tive integers, and for each u =(i1,...,ik) the function fu sues are expected to persist, and new issues to emerge. In depends only on xi1 ,...,xik . For a number of weighted this presentation we discuss several abstract programming spaces of such functions, the complexity of the correspond- models that permit application and algorithm developers ing problem is small. to reason about and develop resilience capabilities. We present the basic models and then discuss specific strate- Grzegorz W. Wasilkowski gies for how to design and implement applications to be University of Kentucky resilient to system failures such as local process loss, silent Department of Computer Science data corruption, and the performance variability that is CS15 Abstracts 79

inherent in aggressive failure detection and correction. [email protected]

Michael Heroux Sandia National Laboratories MS83 [email protected] Unreduced Symmetric KKT Systems Arising from Interior Point Methods

MS82 We consider symmetrized KKT systems arising in the solu- MPI Fault Tolerance: The Good, The Bad, The tion of quadratic programming problems by Interior Point Ugly methods. Two strictly related and well established formu- lations for such systems are studied, with particular em- The MPI forum is currently investigating the inclusion of phasis on their spectral properties and how these are af- fault tolerance as a feature in the MPI specification. This fected by preconditioning. Constraint and augmented pre- issue has raised and continuous to raise some controversy conditioners are considered here. Both a theoretical and about what MPI implementations can reasonably be ex- experimental analysis is conducted in order to assess which pected to provide and what is useful for application devel- of the two formulations should be preferred when solving opers. In this talk I will present the main proposals that large scale problems. are currently on the table, their advantages and the main concerns against them. The goal of this talk is to expand Mattia Tani, Valeria Simoncini the discussion and to gather feedback that will help the Universita’ di Bologna MPI forum to come to a solution that is helpful for the [email protected], [email protected] larger HPC community. Benedetta Morini Martin Schulz Dipartimento di Ingegneria Industriale Lawrence Livermore National Laboratory Universita’ di Firenze [email protected] benedetta.morini@unifi.it

MS83 MS83 Preconditioning for Various Cahn-Hilliard Systems Convergence of Stationary Iteration with Indefinite Preconditioner The Cahn-Hilliard equation models the motion of inter- faces between several phases and has many applications The relationship of diagonal dominance ideas to the con- including materials science and image inpainting. Besides vergence of stationary iterations is well known. There are a their smooth formulations we study the nonsmooth ones multitude of situations where such considerations are used which result in variational inequalities. The focus is on to guarantee convergence when the splitting matrix (the the efficient solution of the arising large and sparse linear preconditioner) is positive definite. In this talk we will de- systems. Further, we study fractional-in-space versions of scribe and prove sufficient conditions for convergence of a Cahn-Hilliard systems. Numerical results illustrate the ef- stationary iteration based on a splitting with an indefinite ficiency of the approaches. preconditioner. Simple examples covered by this theory from Optimization and Economics will be described. Jessica Bosch MPI Magdeburg Andy Wathen [email protected] Oxford University, UK [email protected] Martin Stoll Max Planck Institute, Magdeburg MS84 [email protected] Quantifying Errors in a Probabilistic Solution to Stochastic Inverse Problems for Physics-Based MS83 Models Null-Space Based Preconditioners for Saddle-Point We define a measure-theoretic framework to formulate and Systems solve a stochastic inverse problem for deterministic physics- based models. Computational algorithms are presented We derive a formula for the inverse of a nonsingular and analyzed to solve problems within this framework in- saddle-point matrix whose leading block is maximally rank- volving high dimensional input parameter and output data deficient, which is based on the null-space of that block. We spaces. Sources of statistical and deterministic errors are then use the formula to develop a class of indefinite block identified and full a priori and a posteriori error analyses preconditioners. When a sparse form of the null space is on computed probabilities of events are presented including approximately available, a preconditioned Krylov iterative numerical examples. solver converges rapidly. We give a couple of examples, discuss spectral properties, and present some numerical re- Troy Butler sults that validate the analysis. University of Colorado Denver [email protected] Ron Estrin The University of British Columbia [email protected] MS84 Region of Influence Sensitivty Analysis for Time Chen Greif Dependant Problems Department of Computer Science The University of British Columbia We review existing strategies for implementing adjoint- 80 CS15 Abstracts

based sensitivity analysis on HPC architectures. We focus netic field. Such materials undergo finite deformations and on strategies based on space-time local adjoint problems, the magneto-mechanical coupling requires nonlinear mod- posed in the ”Region of Influence”(RoI), motivated by the els. Incompressible MSMs are then modeled by heuristic application to uncertainty quantification of DNS-scale tur- equations that minimize the elastic and electromagnetic en- bulent combustion. In addition, we discuss ramifications ergy in the form of a coupled free energy. In this talk, we and potential benefits from implementing this approach on focus on modeling and developing finite-element methods potential exascale systems. for incompressible magneto-elasticity, and we present the- oretical results and numerical experiments for such prob- Varis Carey,RobertD.Moser lems. The exterior of the material body is also taken into University of Texas at Austin consideration due to the magnetic field, resulting in a much [email protected], [email protected] bigger discrete system. Even within uncoupled incompress- ible elasticity, many open questions remain about optimal finite-element approximation and these, of course, impact MS84 our choices for the more complicated coupled problems con- Adaptive Measure-Theoretic Inverse Techniques sidered here. for High Dimensional Parameter Domains and Complex Multi-Scale Models James H. Adler, Luis Dorfmann Tufts University The application of uncertainty quantification methodolo- [email protected], [email protected] gies to computationally complex models often involves the exploration of a high-dimensional parameter space. It is Dong Han well known that this endeavor is plagued by the “curse of Tufts University dimensionality.” We explore the scalability of adaptive al- Department of Mathematics gorithms for solving the stochastic inverse problem within [email protected] the context of a measure-theoretic solution framework to with the goal of reducing error in approximating the prob- Scott Maclachlan ability of implicitly defined “rare” events. Department of Mathematics Lindley C. Graham Tufts University University of Austin at Texas [email protected] Institute for Computational Engineering and Sciences (ICES) Chris Paetsch [email protected] Tufts University [email protected] Troy Butler University of Colorado Denver MS85 [email protected] First-Order System Least Squares for Isotropic and Clint Dawson Anisotropic Materials in Hyperelasticity Institute for Computational Engineering and Sciences We present least squares finite element methods based on University of Texas at Austin the conservation of linear momentum and nonlinear consti- [email protected] tutive equations for hyperelastic materials. Our approach is motivated by a well-studied least squares formulation MS84 for linear elasticity. This idea was already generalized to nonlinear elasticity using a special Neo-Hooke model. We Optimizing Quantities of Interest in High Dimen- recall essential theorems and illustrate the performance us- sions to Improve Solutions to Inverse Problems ing adaptive refinement strategies. Additionally we extend this approach to transversely isotropic materials adapting The predictive capabilities of physics-based models are im- the isotropic model and give examples. proved by reliably decreasing the size of the sets defin- ing the uncertain input parameters. These sets are often Benjamin M¨uller inferred by solution to an inverse problem. We explore University of Duisburg-Essen techniques for identifying the optimal quantities of inter- [email protected] est within a high dimensional output data set for use in the inverse problem to improve the predictive capabilities of a model. Numerical results on physically relevant models are Gerhard Starke provided. University of Duisburg-Essen Fakult¨at f¨ur Mathematik Scott Walsh [email protected] University of Colorado Denver [email protected] J¨org Schr¨oder Universit¨at Duisburg-Essen Institut f¨ur Mechanik, Abteilung Bauwissenschaften MS85 [email protected] Modeling Magneto-Mechanical Interactions in De- formable Solids MS85 A new class of ”smart” materials, magneto-sensitive ma- Advanced Finite Element Methods for Chemo- terials (MSMs), is at the frontier of research in mate- Electromechanical Skeletal Muscle Mechanics rial design. The mechanical properties of these materials change dramatically in the presence of an applied mag- Simulating the mechanical behavior of (soft) biological ma- CS15 Abstracts 81

terials is challenging as one does not only need to consider Dimitri Mavriplis a highly nonlinear material behavior within a complex do- Department of Mechanical Engineering main, but also often needs to consider different scales, e.g. University of Wyoming the cellular scales, to accurately model functional aspects, [email protected] e.g. for simulating the chemo-electromechanical behavior of skeletal muscles. Furthermore, due to high uncertainties Jay Sitaraman within material parameters, one needs fast, efficient, and University of Wyoming accurate solution strategies. [email protected] Oliver Rohrle, Thomas Heidlauf, Mylena Mordhorst, Daniel Wirtz MS86 Institute of Applied Mechanics Efficient Approaches for Optimal Active Flow Con- University of Stuttgart, Germany trol [email protected], [email protected] stuttgart-de, [email protected] For efficient optimal active control of unsteady flows, the stuttgart.de, [email protected] use of consistent and robust adjoint approaches is a first essential ingredient. For the generation of discrete adjoint solvers, we discuss the use of Automatic Differentiation MS85 (AD) and its combination with checkpointing techniques. Momentum Balance Accuracy in Finite Element Furthermore, we discuss so-called one-shot methods. Here, Methods for Elastoplasticity one achieves simultaneously convergence of the primal state equation, the adjoint state equation as well as the design First-order system least squares formulations involving equation. stresses and displacement as process variables are inves- tigated for elastoplasticity models. Optimal order conver- Nicolas R. Gauger gence is shown for the stress approximation with respect RWTH Aachen University to the H(div) norm using Raviart-Thomas finite elements [email protected] in the context of von Mises flow with isotropic hardening. In particular, the implications on the accuracy of momen- Anil Nemili, Emre zkaya tum balance and surface forces is studied. Computational TU Kaiserslautern results for a realistic benchmark problem illustrate the ef- [email protected], [email protected] fectiveness of this approach. Stefanie G¨unther Gerhard Starke RWTH Aachen University University of Duisburg-Essen [email protected] Fakult¨at f¨ur Mathematik [email protected] MS86 Aerodynamic Design for Unsteady Flows Using An MS86 Adjoint Approach A Coupled CFD CAA Adjoint Method for Aeroa- coustic Optimization and Error Estimation A discrete adjoint-based design methodology for unsteady turbulent flows on three-dimensional dynamic overset un- Adjoint techniques have played a major role in gradient structured grids is described. The methodology sup- based steady state aerodynamic optimization, especially in ports both compressible and incompressible flows and is 3D, since the full sensitivity vector of a single objective amenable to massively parallel computing environments. function with respect to any number of design variables The approach provides a general framework for performing can be computed with a single adjoint solution, at a cost highly efficient and discretely consistent sensitivity anal- roughly equivalent to a single flow solution. On the con- ysis. Meshes consisting of mixed-element topologies and trary adjoint methods for unsteady problems have received overset component grids are supported, where grids may be less attention, their development having been hindered by static, dynamic, or deforming, including any combination the inherent computational cost and the complexity of the thereof. An overview of a broad range of aerospace applica- associated flow physics. Recently unsteady adjoint tech- tions for which the implementation has been demonstrated niques have been proposed for both two-dimensional and will be shown. three-dimensional problems. In this work we apply the un- steady adjoint method to a two dimensional blade vortex Eric Nielsen interaction noise problem. An Euler near field flow solver NASA Langley is coupled to an FW-H aeroacoustic code to propagate the [email protected] noise to a far field observer. The discrete adjoint solvers for both the flow and the acoustic codes are derived by Boris Diskin exact linearization and transposition of each subroutine in National Institute of Aerospace, Hampton, VA the analysis code and finally coupled together. We apply [email protected] the newly developed adjoint solver to blade vortex interac- tion noise in the context of gradient based optimization, to investigate optimal passive noise minimization technique, MS86 and a posteriori error estimation to improve the accuracy Optimal Wall-Forcing for Compressible Wall- of the coupled aeroacoustic analysis. Bounded Flows Using Adjoint Techniques Enrico Fabiano Adjoint operators are vastly used in many applications, University of Wyoming ranging from linear stability analysis and optimization to [email protected] flow control. Although highly valuable, the derivation of 82 CS15 Abstracts

these operators in the case of compressible and higher-order tion. We will present several examples in nanophotonics solvers is often a tedious task. This is particularly due and turbomachinery to demonstrate the performance of to the complexity of the governing equations and of the the MHDG method. higher-order numerical schemes. In this study, we have adopted a novel technique for the evaluation of the direct Cuong Nguyen and adjoint operators directly from the flow solvers (Fosas Massachusetts Institute of Technology et al., 2012) which requires minimal additional program- [email protected] ming efforts, and automatically takes into account subse- quent modifications in the governing equations and bound- Joel Saa-Seoane ary conditions. This approach is applied to a compressible, M.I.T. staggered and curvilinear framework, allowing higher-order [email protected] interpolation and derivation schemes. The original nonlin- ear solver has been used to perform large-scale turbulent David Moro, Francisco J. Roca, Jaime Peraire flow simulations, and shown to scale well on up to 62K pro- Massachusetts Institute of Technology cessors. The adjoint solver features similar performances. [email protected], [email protected], [email protected] The developed methodology is first validated in the con- text of a three-dimensional compressible boundary layer, by extracting the optimal initial condition, and comparing MS87 the results to that of the linear stability analysis. Finally, this method is used to extract the optimal wall-forcing in A Computational Framework for Target-Based a compressible wall-bounded flow. HP-Adaptation in Compressible Flow Simulation Using HDG Methods Taraneh Sayadi, Peter Schmid Imperial College London We present a conceptual overview of our computational [email protected], [email protected] framework which includes both standard and hybridized DG methods and offers both isotropic and anisotropic hp- adaptation based on adjoints. The framework is designed MS87 in such a way that both discretizations and physical models can be exchanged rapidly by making heavy use of object- Stable and Robust Hybridized Discontinuous orientation and C++ templates. We will show examples Galerkin Methods for High Reynolds Number Flow in a variety of flow regimes. Problems Georg May, Michael Woopen We present an output-based anisotropic hp-adaptive AICES method for high-order hybrid discontinuous Galerkin RWTH Aachen (HDG) discretizations of the Navier-Stokes equations. The [email protected], [email protected] adaptive framework uses a discrete adjoint on refined spaces to compute error estimates. The effectiveness of refinement options is determined by solving local adjoint MS87 problems. We discuss the effects of different stabilization methods on solver robustness and compare the effective- To CG or HDG: Updates on Our Comparative ness of HDG and traditional discontinuous Galerkin (DG) Study methods. Since the inception of discontinuous Galerkin (DG) meth- Krzysztof Fidkowski, Johann Dahm ods for elliptic problems, there has existed a question of University of Michigan whether DG methods can be made more computationally kfi[email protected], [email protected] efficient than continuous Galerkin (CG) methods. Fewer degrees of freedom, approximation properties for elliptic problems together with the number of optimization tech- MS87 niques, such as static condensation, available within the Multiscale Hybridizable Discontinuous Galerkin CG framework made it challenging for DG methods to be Methods competitive until recently. However, with the introduc- tion of a static-condensation-amenable DG method, the We present the recent development of multiscale hybridiz- hybridizable discontinuous Galerkin (HDG) method, it has able discontinuous Galerkin (MHDG) methods for com- become possible to perform a realistic comparison of CG putational electromagnetics and fluid dynamics. The es- and HDG methods when applied to elliptic problems. In sential ingredients are (i) a HDG discretization of the un- this talk, we extend upon an earlier 2D comparative study, derlying PDEs at the subdomain level to parametrize the providing numerical results and discussion of the CG and numerical solution in terms of a Lagrange multiplier; (ii) HDG method performance in three dimensions. The com- a judicious choice of the numerical flux to provide stabil- parison categories covered include steady-state elliptic and ity and consistency; and (iii) a global jump condition that time-dependent parabolic problems, various element types enforces the continuity of the numerical flux across sub- and serial and parallel performance. domain boundaries to arrive at a global weak formulation in terms of the Lagrange multiplier. The MHDG methods Mike Kirby, Sergey B. Yakovlev inherit all the properties of the HDG method and possess University of Utah additional advantages. First, they reduce the globally cou- School of Computing pled unknowns to the approximate trace of the solution on [email protected], [email protected] subdomain boundaries, thereby leading to a significant re- duction in the degrees of freedom. Second, they make use of the similarity of the subdomain structures to efficiently MS88 accommodate very large-scale simulations. And third, the Partitioned Low Rank fast and Efficient Compres- MHDG methods lend themselves efficient for paralleliza- sion of Absorbing Boundary Conditions for the CS15 Abstracts 83

Helmholtz Equation [email protected]

Absorbing layers are sometimes required to be impracti- cally thick to offer an accurate Absorbing Boundary Con- MS88 dition (ABC) for the Helmholtz equation in heterogeneous Microseismic Event Location Via Full Waveform media. In previous work [BR and Demanet, submitted, Inversion 2014], we used matrix probing to compress an ABC from a few exterior Helmholtz solves with random Dirichlet data. The process of hydraulic fracturing involves injecting large We now present an algorithm (nearly linear in the dimen- volumes of water into impermeable rocks such as shale in sion of the matrix) for applying this compressed ABC using an effort to create flow paths for fluids such as oil and Partitioned Low Rank matrices. gas. This process often generates tiny earthquakes (or mi- croseismic events) which in turn can be used as passive Rosalie Belanger-Rioux seismic sources for imaging the subsurface. In this work Massachusetts Institute of Technology we describe estimating the location of these microseismic Department of Mathematics events and the uncertainty inherent in this process. [email protected] Susan E. Minkoff Laurent Demanet University of Texas at Dallas Professor of Mathematics, MIT Dept of Mathematical Sciences [email protected] sminkoff@utdallas.edu

MS88 MS89 Comparison Between DG and Finite Difference Recovering Exponential Accuracy in Spectral Methods for Acoustics with Smooth Coefficients Methods Involving Piecewise Smooth Functions with Unbounded Derivative Singularities This work analyzes the computational efficiency of two types of numerical methods, finite difference (FD) and dis- Techniques will be presented to overcome the Gibbs phe- continuous Galerkin (DG) methods, in the context of 2D nomenon for functions with unbounded derivative singu- acoustic equations in pressure-velocity form with smooth larities, resulting in recovering exponential accuracy in the coefficients. The acoustic equations, which model propa- maximum norm from the knowledge of the first N Fourier gation of sound waves in elastic fluids, are used throughout coefficients or standard collocation point values of such seismic imaging with applications in oil prospecting. The functions. With these post-processing methods, we are ubiquity of smooth trends in real data, and thus in the able to obtain exponential accuracy of spectral methods acoustic coefficients, validates the importance of this novel applied to linear transport equations involving such func- study. Previous work, from the discontinuous coefficient tion. case of a two-layered media, demonstrates the efficiency of Zheng Chen DG over FD methods but does not provide insight for the Iowa State University smooth coefficient case. Running-times and floating point [email protected] operations are compared, relative to a prescribed accuracy, for standard 2-2 and 2-4 staggered grid FD methods, and a standard DG methods MS89 Mario Bencomo Efficient High-Order Algorithms for Solving Drift- Department of Computational and Applied Math Diffusion Systems Rice University I will discuss about recent developments of spectral ele- [email protected] ment method (SEM) for solving drift-diffusion equations, with applications in semi- conductor device simulation, bi- ological ion channels problems, etc. The drift-diffusion sys- MS88 tem is a non-linear system, involving the coupling of two Analysis and Numerical Approximation for Ad- transport equations for the carrier concentrations with the sorption Models Poisson equa- tion for the electric potential. I will present our SEM algorithms, focusing on stable, efficient, and ac- We focus on the structure of an adsorption model as sys- curate time-splitting schemes, properly designed for the tems of conservation laws (multicomponent case for ad- high-order spectral element discretizations. I will demon- sorption), with equilibrium and non-equilibrium type non- strate the computational results for the study of potassium linearities, where the latter are associated with microscale channel in a biological membrane, provided with the vali- diffusion. We also work with an unusual type isotherm dation. called Ideal Adsorbate Solution, which is defined implicitly. For the IAS adsorption system, we show sufficient condi- Ying He tions that render the system hyperbolic. We also construct UC Davis numerical approximations for equilibrium and nonequilib- [email protected] rium models.

Francis P. Medina MS89 Oregon State University Estimating Residual Stresses in Arteries by an In- [email protected] verse Spectral Technique

Malgorzata Peszynska A mathematical model is studied to estimate residual Department of Mathematics stresses in the arterial wall using intravascular ultrasound Oregon State University (IVUS) techniques. A BVP is formulated for the nonlinear, 84 CS15 Abstracts

slightly compressible elastic wall, the boundary of which is [email protected] subjected to a quasi-static blood pressure, and then an idealized model for IVUS is constructed by superimpos- ing small amplitude time harmonic vibrations on large de- MS90 formations. Using the classical theory of inverse Sturm- From Macroscopic to Microscopic Simulations Us- Liouville problems and op- timization techniques, an in- ing Mesord verse spectral algorithm is developed to approximate the residual stresses, given the first few eigenfrequencies of sev- MesoRD simulates both the spatial and stochastic aspects eral induced pressures. of intracellular chemical reactions using a spatially dis- crete and temporally continuous framework. Spatially dis- Sunnie Joshi crete stochastic simulators may give incorrect results for Temple University bi-molecular reactions. We have incorporated a solution [email protected] to this problem into MesoRD. Using these new features of MesoRD we could simulate a number of simple examples where it is shown how strikingly important it is to choose MS89 a correct modelling-framework for the problem at hand. Force-based Blended Atomistic-to-continuum Cou- pling Method for Crystals: Theory and Computa- David Fange tions Uppsala University Department of Molecular Biology We formulate a multiscale method based on blending atom- [email protected] istic and continuum forces. We present a comprehensive error analysis whichis valid in two and three dimensions, for finite many-body interactions, and in the presence of MS90 defects. Based on a precise choice of blending mechanism, E-Cell System Version 4.0: an Integrated Platform the error estimates are considered in terms of degrees of for Single-particle-level Simulations freedom. The numerical experiments confirm and extend the theoretical predictions, and demonstrate a superior ac- Here, we present a novel software for cellular simulations, curacy of our method over other schemes. E-Cell System version 4, which provides an integrated plat- form with a rule-based modeling environment, bioimaging Xingjie Li visualizations and a variety of single-particle level simula- Brown University tion algorithms including an exact event-driven particle al- xingjie [email protected] gorithm, the enhanced Greens Function Reaction Dynam- ics method, and a microscopic lattice-based method, Spa- tiocyte. Moreover, we also introduce the parallelization MS90 techniques for these particle methods toward the whole- On-Lattice and off-Lattice Hybrid Simulation Us- cell-scale simulation on high-performance computers. ing the Smoldyn Software Kazunari Kaizu, Kozo Nishida, Masaki Watabe, Arjunan The Smoldyn simulator is a tool for modeling biochemical Satya, Kazunari Iwamoto, Koichi Takahashi spatial organization on nanometer to micron size scales. RIKEN Quantitative Biology Center, Osaka It represents proteins and other molecules of interest as [email protected], [email protected], [email protected], individual point-like particles that diffuse, react, and in- [email protected], [email protected], [email protected] teract with membranes, all in continuous space. Although effective, this is computationally expensive, so colleagues and I recently added on-lattice capabilities to Smoldyn as MS91 well. Simulated molecules are able to freely diffuse back Multiscale Model Reduction for PDE-Constrained and forth between the two regions of space. Optimization

Steven Andrews In parameter estimation and data fitting problems, reduced Fred Hutchinson Cancer Research Center order models are usually built from the forward map that [email protected] depends on the unknown parameters. This implies that the reduced model is parameter dependent. Typically, this dependence is ignored and the reduced model is either not MS90 updated in the process of the data fitting process or, its MCell/CellBlender: An Environment for Spatially dependency is not considered when computing gradients Realistic Simulation of Cellular Microphysiology and Hessians. The consequences of this approach can lead to inefficient algorithms as well as unacceptable solution. MCell is a simulation kernel for biophysically realistic In this talk we discuss a framework that allow us to the 3D simulations of reaction-diffusion processes occurring in differentiation of the reduced model with respect to the cells. A major stumbling block for new and experienced parameter. We show that this framework can yield robust users of MCell is the effort required to create 3D mod- estimates for some model inverse problems. els. To remedy this situation we have created CellBlender, a complete integrated development environment for creat- Eldad Haber ing and visualizing MCell and SBML/Spatial models. An Department of Mathematics overview of the design of CellBlender will be presented, in- The University of British Columbia cluding the model creation/simulation/visualization pipe- [email protected] line. Lars Ruthotto Thomas M. Bartol Department of Mathematics and Computer Science The Salk Institute Emory University CS15 Abstracts 85

[email protected] people worldwide. We will present an overview of osteo- porosis, describe the bone remodeling process, and high- light the fundamental elements involve in determining bone MS91 strength in vivo. The talk will show why mathematical Model Mis-Specification and Model Reduction - modeling is playing an increasingly relevant role in the re- Connecting the Dots search, diagnosis, and monitoring of osteoporosis. We will illustrate how modeling has been used at Merck in the de- In addressing large-scale inverse problems, great care needs velopment of novel osteoporosis treatments. to be devoted to attainment of appropriate balance of in- exactness throughout the various stages of modeling and Antonio Cabal inversion. Disregard to such objective, either entails re- Merck Research Laboratories dundant computation or impairment of the overall fidelity Quantitative Pharmacology and Pharmacometrics of the inversion process. Model reduction is instrumental [email protected] in trading-off fidelity for computation, yet, in some situa- tions, it is essential to perform the opposite action, and en- hance model fidelity and thereby inversion output. In this MS92 talk, we shall describe the interplay between model reduc- A Simultaneous Approach to Parameter Estima- tion and model mis-specification mitigation and provide a tion with Ode Models: a Case Study with Viral generic infrastructure for model re-specification based upon Dynamics Models a hybrid first principles and data-driven approach. The successful application of mathematical models and ver- Lior Horesh ifying their underlying hypotheses rely critically on our Mathematical Sciences & Analytics ability to estimate their parameters. Parameter estima- IBM TJ Watson Research Center tion is usually performed using a sequential approach: an [email protected] optimization algorithm calls the model independently to evaluate the agreement with data. Here, using an ODE- based viral dynamics model as an example, we explore and MS91 evaluate a simultaneous approach where the model is dis- Inference for Prediction in Nonlinear Systems cretized and explicitly introduced as equality constraints to the optimization algorithm. When only sparse data are available for the calibration of a many-parameter model that will be used to make only Khamir Mehta a few decisions or predictions, not all parts of the poste- Applied Mathematics and Modeling rior parameter space are either informed by the data or Merck & Co, Inc. informative to the output. This talk presents an adap- khamir [email protected] tive sampling method to preserve the posterior predictive distribution without fully exploring the large posterior pa- Junghoon Lee rameter distribution. Merck & Co, Inc Harriet Li jung hoon [email protected] MIT [email protected] MS92 Numerical Solutions of a Partial Differential Equa- MS91 tions in a Pharmacometric Context Model Reduction for Some Inverse Problems in Fi- nance Pharmacometricians develop quantitative models of the ef- ficacy, potency and safety of drug compounds under devel- Implied volatility is a key value in financial mathematics. opment. These models are often constrained to systems of We discuss some of the pros and cons of the standard ways ordinary differential equations (ODEs) because simulation to compute this quantity, i.e. numerical inversion of the and analysis tools are designed to work with ODEs. Emerg- well-known Black-Scholes formula or asymptotic expansion ing models are starting to clash with these constraints. For approximations, and propose a new way to directly calcu- example, so-called age structured partial differential equa- late the implied variance in a local volatility framework tions (PDEs) have potential utility in oncology and safety. based on the solution of a quasilinear degenerate parabolic We discuss these models and how they may be incorporated partial differential equation using POD and DEIM. Numer- into current tools. ical results prove the quality of our approach compared to other methods. Jeffrey Saltzman AstraZeneca Ekkehard W. Sachs, Marina Schneider Research and Development Information Services University of Trier Jeff[email protected] [email protected], [email protected] MS92 MS92 Applications of Modeling and Simulation in Drug Mathematical Modeling at Two Opposite Ends of Discovery and Development the Scale Spectrum with the Same Objective in Mind: Improve Human Health Model based drug discovery has the potential to increase efficiency at various stages of drug discovery and devel- Osteoporosis is a common age related chronic disorder of opment by reducing the cost and time required to make the skeleton. It constitutes a considerable global public go/no-go decisions. Often times, a mathematical model health problem currently affecting more than 200 million is developed based on what is known about a particular 86 CS15 Abstracts

compound, such as its pharmacokinetic and pharmacody- KAUST namic properties. Such models can be used to simulate the [email protected] behavior of a compound under multiple scenarios and un- derstand various properties of the compound such as the parameters that drive efficacy, the efficacy/toxicity trade- MS93 off or the most effective dosing regimen for the compound. Exascale: the Why and the How The insight obtained using such models can be used to guide decisions such as the selection of the most promis- Applications demand scale for resolution, dimension, ing pre-clinical compound or the selection of a dosing reg- multi-physics fidelity, isolation from artificial boundaries, imen in the pre-clinical or clinical space. The modeling parameter inversion, optimal control, uncertainty quan- techniques used in developing these models are usually tai- tification, and the statistics of ensembles. Are extreme- lored to the questions that arise at the different stages of scale systems able to effectively host state-of-art algorithms drug discovery and development. For example, a system for these pursuits, however, or are advances in hardware of ordinary differential equations can be used to represent and algorithms becoming than multiplicative? We exam- the mechanistic model for a particular compound. Such ine this question of with respect to algorithmic premiums a mechanistic model could then be analyzed to identify on uniform-thread concurrency, arithmetic intensity, asyn- the parameters that affect the efficacy of a compound. In chronicity, and fault-tolerance and from the perspective of other cases, a simpler empirical model could be used to recent Gordon Bell prize finalist computations. capture and assess the efficacy/toxicity tradeoff. In this talk I will present a few examples of how various model- David E. Keyes ing techniques can be used to answer important questions KAUST in the pre-clinical and clinical space of drug discovery and [email protected] development. MS93 Chandni Valiathan Merck From Optimal Algorithms to Fast Petascale Solvers [email protected]; Scalability beyond petascale requires algorithms with opti- mal complexity, but optimal algorithms are not automati- MS93 cally fast. The power of current and future supercomputer can only be unleashed, when grid structure, discretization, Extreme Scale Solution of Engineering Applica- solver, parallel implementations are carefully co-designed tions Using Uintah by using predictive performance models exploiting concur- rency on all levels. We will describe the design of FE Solving extreme scale problems using the Uintah compu- solvers for creeping flow solving a trillion degrees of free- tational framework was achieved with the development of dom in around one minute and using up to a million parallel a general runtime system capable of solving a broad class threads. of problems using a graph-based approach. Important as- pects of the solution process, adaptive approach involving Bj¨orn Gmeiner dynamic out-of-order execution of tasks, the strengths and Computer Science 10 - System Simulation weaknesses of this approach are addressed, in particular Friedrich-Alexander-University Erlangen-Nuremberg, with future architectures in mind. Examples of scaling to Germany about 700K cores are shown on Blue Waters and Mira. [email protected] Martin Berzins Scientific Computing and Imaging Institute Holger Stengel University of Utah Erlangen regional Computing Center, Germany [email protected] [email protected]

Christian Waluga MS93 M2 Center of Mathematics GPU for Adaptive Optics on Ground Based As- Technical University of Munich tronomical Telescopes: Simulations and Real-Time [email protected] Control Barbara Wohlmuth The European Extremely Large Telescope project (E-ELT) M2, Centre for Mathematical Sciences, is one of Europe’s highest priorities in ground-based astron- Technische Universit¨at M¨unchen, Germany omy. ELTs are built on top of several highly sensitive and [email protected] critical astronomical instruments. Particularly, Adaptive Optics (AO), used to stabilize image quality, is essential for Ulrich J. Ruede telescope routine operations. Designing and driving AO University of Erlangen-Nuremberg systems requires fast and high fidelity numerical simula- Department of Computer Science (Simulation) tions. We describe the simulation framework and highlight [email protected] the extreme need for petascale computation to maintain real-time processing. MS94 Damien Gratadour, Eric Gendron Affirmative Actions in Education Creating Division Observatoire de Paris and Inefficiency Among Beneficiary Groups in In- [email protected], [email protected] dia Hatem Ltaief The paper discusses the social and economic disparity Extreme Computing Research Center within the group benefitting from affirmative actions in CS15 Abstracts 87

educational sector of India and also tests this hypothesis- processes used for modeling the accumulation of damage to revealing that a major chuck of population is becoming networks or systems experiencing a sequence of attacks or inefficient because of these actions. With the help of math- failures incapacitating random numbers of nodes (e.g. com- ematical tools it identifies negative cycle present in the so- ponents), each with a random weight (e.g. a cost). Each ciety and calculates the economic cost due to this disparity. component has threshold(s) whose crossing indicate the It concludes with a solution to this complex socio-political system entering a critical state. An operational calculus issue regarding affirmative actions. strategy is used to derive probabilistic information about the process within random vicinities of passage times. Aprant Ajay Delhi Techinical University, INDIA Ryan White,J.H.Dshalalow [email protected] Florida Institute of Technology [email protected], eugene@fit.edu

MS94 System Architecture for a Cooperative Fleet of Au- MS94 tonomous Underwater Vehicles (AUVs) Theory and Computation for Bilinear Quadratures

The Eco-Dolphin system of AUVs has been engineered to We present a general framework for constructing numeri- deploy for the acquisition of coastal ecological data. Each cal integration rules over an arbitrary domain in Rd that member of the fleet has its own payload and objective in are exact when the integrand is the product of two func- arriving at a predefined destination. The talk will detail tions belonging to prescribed subspaces. Such integrals the components of each vehicle, their characteristics, and are useful in Galerkin methods, for example. We prove what requirements are needed for the successful launch, that this framework reduces to Gaussian quadrature for maneuver, and recovery within the systems control center. univariate polynomials and trapezoid rule for trigonomet- ric polynomials. We then describe a numerical procedure Stacey Joseph-Ellison,QiZhou for constructing these integration rules and present some Embry-Riddle Aeronautical University numerical results. [email protected], [email protected] Christopher Wong Zhaoyang Fu University of California, Berkeley EmbryRiddle Aeronautical University [email protected] [email protected] MS94 Zakaria Daud Embry-Riddle Aeronautical University Survival Probability of Beneficial Mutations in [email protected] Bacteria Most novel mutations, even if they confer a benefit to the Hong Liu organism, are ultimately lost during the stochastic popula- Department of Mathematics tion growth process. Their survival probability is sensitive Embry-Riddle Aeronautical University to the organism’s life history details and the traits affected [email protected] by the mutation. We develop a continuous time multitype branching process to predict the survival of initially rare beneficial mutations in bacteria. Predicting bacterial adap- MS94 tation rates is critical to public health issues such as the Interfacial Motion by Mean Curvature in Liquid evolution of drug resistance. Crystals Anna Zhu, Lindi M. Wahl Liquid crystals are mesogenic phases of matter between Western University Canada conventional solid and liquid phases. Nematic liquid crys- [email protected], [email protected] tals are anisotropic liquids with directional order. We use the gradient-flow model associated with the Landau-de Gennes free energy to study interfaces in nematic samples MS95 at the nematic-isotropic transition temperature, demon- Asymptotic-Preserving Scheme for the Fokker- strating that they propagate according to mean curvature Planck-Maxwell System in the Quasi-Neutral flow in some asymptotic limits. We numerically compute Regime dynamically metastable nematic configurations in cylinders and study their delicate dependence on initial conditions. Abstract not available at time of publication.

Amy Spicer Stephane Brull University of Bath, UK Institut de Math´ematiques de Bordeaux UMR 5251 [email protected] Universit´e Bordeaux [email protected] Apala Majumdar University of Bath [email protected] MS95 Solving Kinetic Equations to Model the Core- Collapse Supernova Explosion Mechanism MS94 On Strategic Defense in Stochastic Networks Core-collapse supernovae (CCSNe) are the explosive deaths of massive stars. CCSN explosions are driven by energy In this paper, we discuss a particular class of stochastic transfer from neutrinos to the stellar fluid. This neutrino 88 CS15 Abstracts

heating occurs under non-equilibrium conditions, and a ki- Institut de Mathematiques de Bordeaux netic description based on the Boltzmann equation is war- [email protected] ranted. We describe our recent efforts to develop numerical methods to model neutrino transport in CCSNe with dis- continuous Galerkin methods, including ongoing efforts to MS96 model neutrino-matter interactions. Swimming Dynamics of Microorganisms in Vis- coelastic Fluids Near a Wall Eirik Endeve, Cory Hauck Oak Ridge National Laboratory Microorganisms swimming in viscoelastic fluids are ubiq- [email protected], [email protected] uitous in nature; this includes biofilms grown on surfaces, Helicobacter pylori colonizing in the mucus covering the Yulong Xing stomach and spermatozoa swimming through cervical mu- Department of Mathematics cus. Previous studies have focused on the locomotion of Univeristy of Tennessee / Oak Ridge National Lab microorganisms in unbounded viscoelastic fluids. How- [email protected] ever in many situations, microorganisms interact with solid boundaries. In this work, we numerically study the effect Tony Mezzacappa of solid boundaries on the swimming of an archetypal low- ORNL Reynolds number swimmer in viscoelastic fluids. [email protected] Gaojin Li University of Notre Dame MS95 [email protected] Versions of Discontinuous Galerkin Algorithms for Diffusion and for Energy-Conserving Hamiltonian Arezoo Ardekani Dynamics Notre Dame University Department of Aerospace and Mechanical Engineering We present mixed continuous/discontinuous Galerkin [email protected] schemes for solution of a class of kinetic Vlasov-Boltzmann problems in Hamiltonian Poisson-bracket form (plus colli- MS96 sions). These schemes conserve energy, and optionally the L2 norm, exactly. Application to electromagnetic gyroki- Stabilizing the Collective Motion of Micro- netic problems requires novel extension to avoid the Am- swimmers using Confinement pere cancellation problem and significant time step limita- tions. There are subtle properties of commonly used DG Concentrated suspensions of swimming microbes and other schemes for second order derivatives, such as from diffu- forms of active matter are known to display intricate, self- sion, which we compare with a recovery-based approach. organized spatiotemporal patterns on scales larger than those of the individual motile units. The collective dy- namics of swimming microorganisms exhibits a complex Ammar Hakim interplay with the surrounding fluid: the motile cells stir Princeton Plasma Physics Laboratory the fluid, which in turn can reorient and advect them. This [email protected] feedback loop can result in long-range interactions between the cells. We present a computational model that takes into account these cell-fluid interactions and cell-cell forces and Greg Hammett that predicts counterintuitive cellular order driven by long- Princeton Plasma Physics Laboratory range flows. The predictions are confirmed by experiments Princeton University with Bacillus Subtilis bacteria which measure the flagella [email protected] bundle orientation and tracks the cells in the self-organized state. Simulations and experiments show that if the micro- Eric Shi, Ian Abel, Tim Stoltzfus-Dueck swimmers are confined inside thin cylindrical chambers the Princeton University suspension self-organizes into a stable swirling vortex. If [email protected], [email protected], the micro-swimmers are confined in thin racetracks, a per- [email protected] sistent unidirectional stream can be observed. Both these phenomena emerge as a result of the complex interplay between the swimmers, the confining boundaries and the MS95 fluid flow. The study highlights the importance of models Numerical Simulation of the Crookes Radiometer and simulations of micro-swimmers needing to correctly include both steric and hydrodynamic interactions in oder The Crookes radiometer is a small mill enclosed in a glass to capture the dynamics observed in experiments. Collab- bulb containing a partial vacuum. Its vanes rotate when orators: Hugo Wioland and Raymond Goldstein, DAMTP, exposed to light. This is due to the thermal transpiration, University of Cambridge, UK. as explained by the kinetic theory of gases. In this talk, a numerical method to make full 3D simulations of this Enkeleida Lushi radiometer will be presented. It is based on a discretiza- Brown University tion of the Boltzmann equation by a cut-cell approach that enkeleida [email protected] allows to easily handle moving boundaries.

Guillaume Dechrist´e MS96 Institut de Math´ematiques de Bordeaux Dynamics of Micro-Swimmers Inside a Peristaltic [email protected] Pump

Luc Mieussens Peristaltic pumping is a form of fluid transport along the CS15 Abstracts 89

length of a tube containing liquid when the tube undergoes Lori A. Diachin a contractile wave. While much is known about the peri- Lawrence Livermore National Laboratory stalsis of Newtonian liquids, complex ones have received [email protected] limited attention. There are many examples in nature where motile micro-particles or micro-swimmers (such as Patrick M. Knupp bacteria or spermatozoa) are suspended in the fluid inside Sandia National Laboratories a peristaltic micro-pump. We present a simulation method [email protected] that accounts for the coupling of the dynamics of many micro-swimmers with each other, the pump, and the fluid flow. The pump and the fluid flow it drives can affect MS97 the swimmer dynamics in interesting ways. Moreover, the An Array-Based Mesh Topological Representation presence of the swimmers and their collective motion can That Effectively Supports General Mesh Modifica- affect the net transport and mixing in the pump. The effi- tion ciency of mixing the suspension for a variety of parameters will be discussed. A parallel mesh data structure is presented which stores Adam Stinchcombe each part using a few arrays. It is flexible enough to allow University of Michigan constant-time insertion and removal of elements,enabling [email protected] fully general mesh adaptation. Multiple element types de- fined at compile time can co-exist in one mesh. The mem- ory usage is four times less than object-based structures Enkeleida Lushi with the same features. It can also be configured to repre- Brown University sent reduced meshes, and various other adjacency-storage enkeleida [email protected] schemes.

Dan A. Ibanez MS96 Rensselaer Polytechnic Institute Flagellar Activity Influences Self-Organization in SCOREC Confined Microswimmer Suspensions [email protected] Motile microorganisms are often subject to different types of boundary confinement in their natural environment, but Mark S. Shephard the effects of confinement on their dynamics are poorly Rensselaer Polytechnic Institute understood. We consider a model of microswimmers re- Scientific Computation Research Center stricted to move in a 2D Hele-Shaw cell. In an unbounded [email protected] periodic domain, we show that decreasing flagellar activ- ity induces a hydrodynamically triggered transition in con- MS97 fined microswimmers from turbulentlike swimming to ag- gregation and clustering. We then impose two different Efficient Unstructured Mesh Traversal Methods types of boundary confinement: circular and sidewalls con- Based on Array-Based Half Facets finement and study how additional boundaries influence the emergence of global modes. In the case of circular con- Mesh-based discretization methods for solving PDE’s de- finement, the microswimmers can spontaneously organize pend on local mesh traversals for various purposes such into a single vortex, reminiscent to what have been ob- as linear system formation, boundary conditions, etc. served in recent experiments of bacterial suspensions. In We present efficient traversal methods for unstructured the case of sidewalls confinement, the microswimmers form meshes based on an array-based half-facet data structure. density shock, via interaction with the sidewalls and back- The half-facet representation is generalized from the half- ground flow. edge/face representations in 2D/3D with support for non- manifold mixed meshes. We present the main constructs Alan Cheng Hou Tsang,EvaKanso of the data structure and analyze several efficient entity University of Southern California traversal schemes for the discrete operator assembly. n/a, [email protected] Navamita Ray Argonne National Labratory MS97 [email protected] Threading Mesh Optimization Codes Using Trans- actional Memory Xinglin Zhao Stony Brook University As threading becomes a necessity on multi- and many-core [email protected] modern computers, Transactional Memory (TM) has re- ceived much attention as a thread synchronization mech- Vijay Mahadevan anism that promises both coding elegance and efficiency. Argonne National Laboratory We study the effects of TM on mesh optimization algo- [email protected] rithms using the IBM BG/Q and Intel Haswell platforms. Our preliminary results indicate that these iterative meth- Xiangmin Jiao ods are good candidates for TM when the new metric of Stony Brook University ”time-to-convergence” is used instead of simple wall clock [email protected] time.

Barna Bihari Lawrence Livermore National Lab MS97 [email protected] M3D-C1 Adaptive Loop Going from 2D Axisym- 90 CS15 Abstracts

metric to Full 3D Schemes

Tokamak fusion reactors are the experimental approach to We demonstrate the equivalence between Discontinuous study magnetically confined sustainable fusion reactions. Galerkin (DG) schemes, in strong and weak form, and The tokamak is a symmetric torus along the toroidal di- the Energy Stable Flux Reconstruction (ESFR) schemes rection and the fusion material exists as the state of plasma through the application of a generalized filter to the penal- in the torus. M3D-C1 simulates non-linear instabilities of ized flux terms in the DG formulation. While the essence plasmas in the tokamak. The on-going effort and results of of the idea, the filtering of the highest mode of the correc- M3D-C1 adaptive loop in coordination of SCOREC tools tion functions, was given previously, an elegant extension to change the simulation mode from axisymmetric to full to higher dimensional non-constant Jacobian formulations 3D torus are presented. in arbitrary bases is presented here.

E. Seegyoung Seol, Mark S. Shephard Philip Zwanenburg, Siva Nadarajah Rensselaer Polytechnic Institute McGill University Scientific Computation Research Center [email protected], [email protected], [email protected] [email protected]

Fan Zhang MS98 RPI Theoretical Aspects of High-Order Flux Recon- [email protected] struction Schemes

In this talk I will discuss recent theoretical advances in MS98 the area of high-order Flux Reconstruction (FR) schemes. Comparison of Continuous, Discontinuous and Hy- In particular I will discuss the influence of solution point brid Finite Element Methods for Accuracy and Ef- placement on the stability and accuracy of FR schemes, ficiency and I will present a new extended family of energy-stable FR schemes for one-dimensional linear advection problems. We compare and contrast continuous, discontinuous and hybrid (HDG/EDG) finite element methods for the scalar advection-diffusion problem. For each method we examine Peter E. Vincent effectiveness of preconditioners for linear solves, an impor- Department of Aeronautics tant consideration in the efficiency of each method as it Imperial College London will affect both convergence rates and overall run time. We [email protected] also examine accuracy of both discretization and error es- timates, the latter an important factor in the effectiveness of solution adaptation methods. MS99 The Method of Regularized Stokeslets: Motivation Steven R. Allmaras, Marshall Galbraith and Applications Massachusetts Institute of Technology [email protected], [email protected] Since its introduction in 2001, the method of regular- ized Stokeslets has been very useful in the simulation of many small scale fluid flows. Biological applications in- David l. Darmofal clude swimming motions of microorganisms, cell growth, Department of Aeronautics & Astronautics biofilm/fluid interactions, microfiltration for removing par- Massachusetts Institute of Technology ticulate matter, flagellar bundling, sperm motility, peri- [email protected] staltic pumping, ciliary motion, and other microscopic phe- nomena. We will describe the method, its motivation and the flexibility in choosing its components. We will also MS98 show applications to flagellar motion. Goal-Oriented Curved Mesh Optimization for High-Order Finite-Element Methods Ricardo Cortez Tulane University High-order finite element methods generally require curved Mathematics Department geometry representations, and hence curved elements, to [email protected] maintain accuracy. While mesh validity is paramount, we take a further step and present a method for optimizing the shape of the curved elements to improve their approx- MS99 imation capabilities. The method optimizes the reference- Bacteria Association with Ciliated Surfaces to-global high-order mapping and yields curved elements ideally suited for representing a target solution, or for pre- Abstract not available at time of publication. dicting outputs in a goal-oriented setting. Eva Kanso University of Southern California Krzysztof Fidkowski,DevinaSanjaya [email protected] University of Michigan kfi[email protected], [email protected] MS99 MS98 Modeling Sperm Motility Using a Kirchhoff Rod Model Equivalence between the Energy Stable Flux Re- construction and Filtered Discontinuous Galerkin Sperm flagella have been observed to propagate different CS15 Abstracts 91

waves of bending, depending on the fluid environment. Emergent Subgraphs in Social Networks In this talk, we will discuss modeling aspects of the rel- evant fluid environment and chemical concentrations, re- Social media networks, and more specifically Twitter re- lating emergent waveforms and interactions to current ex- tweet networks, are both very large and incredibly noisy. periments. The sperm flagellum is represented as a Kirch- At the same time, analysis of Twitter networks has the po- hoff rod and a regularized Stokes formulation will be used tential to have both a predictive capability and detection of to solve for the local fluid flow. Results will be shown to emergent trends. In this talk, we combine and co-optimize describe emergent waveforms and swimming speeds. visual analytics with statistical graph analysis algorithms for detection and tracking of emergent subgraphs in dy- Sarah D. Olson namic graphs. A case study focused on movie name hash- Worcester Polytechnic Institute tag networks will be discussed. [email protected] Nadya Bliss, Ross Maciejewski Arizona State University MS99 [email protected], [email protected] The Effects of Rotation and Translation on Flagel- lar Synchronization MS100 Many flagellated microswimmers exhibit some form of flag- Epidemic in Time and Space: Modeling Spatial ellar synchronization. For instance, the bundling and un- Outbreak Dynamics bundling of flagella in E. coli is responsible for their run- and-tumble behavior. In this talk, we look in detail at the Most epidemic models represent the progression of the con- mechanisms responsible for phase synchrony in a pair of tagion process by estimating the number of infectious indi- rigid side-by-side helices. Using an “end-pinned’ model, we viduals per time unit. While this is a valid representation, are able to isolate the effects of translation from those of ro- it neglects to include the spatial progression of the epi- tation, finding synchrony in some cases and anti-synchrony demic. This presentation will focus on representing the in others. spatio-temporal progression of an epidemic and highlight some of the factors that will effect the spatial path a disease Jonathan H. Tu outbreak will follow in the derived contact network. UC Berkeley [email protected] Armin Mikler Department of Computer Science & Engineering Murat Arcak University of North Texas University of California-Berkeley [email protected] [email protected] MS100 Michel M. Maharbiz UC Berkeley Spectral Subgraph Detection in Noisy, Uncertain [email protected] Networks Network analysis in practice may involve considering rela- MS100 tionships that must be observed through some noisy mech- anism. This additional stochasticity compounds the un- Analysis and Control of Cascading Failures of certainty due to random connectivity fluctuations of the Power Transmission Systems: a Macro View underlying graph. This presentation discusses various sim- ple mechanisms for noise and uncertainty in network anal- Cascading failures of power systems are complex phenom- ysis and demonstrates their impact on the ability to detect ena that are governed by a combination of existing low-level small anomalous subgraphs using spectral techniques. We control mechanisms, physics, human input and exogenous also demonstrate fusion of multiple noisy datasets to re- factors (such as weather-related factors). In the event of cover performance achievable on the uncorrupted data. a cascading failure, a goal is to arrest the failure with a minimum of demand lost. We describe ongoing research Benjamin A. Miller with a provably good control methodology that relies on MIT Lincoln Laboratory a combinatorial algorithm, augmented with tools derived [email protected] from the SAA (sample average approximation) approach for stochastic optimization. We describe our results in the context of simulations involving several large-scale grids, MS101 in particular the Eastern Interconnect. Fast Computation of Orthonormal Bases for RBF Native Spaces Daniel Bienstock Columbia University IEOR and APAM Departments We proposed in a recent work the so called WSVD basis, IEOR Department which is strictly connected to the eigendecomposition of [email protected] the integral operator (of Mercer’s theorem) and allows one to overcome some problems related to the stability of the Guy Grebla computation of the approximant for a wide class of radial Columbia University kernels. Although effective, this basis is computationally [email protected] expensive to compute. We discuss here a method to im- prove and compute in a fast way the basis using methods related to Krylov subspaces. After reviewing the connec- MS100 tions between the two bases, we concentrate on the prop- Visual Analytics for Detection and Tracking of erties of the new one, describing its behavior by various 92 CS15 Abstracts

numerical tests. sociated schemes are notoriously ill-conditioned and often show strong boundary effects. We discuss a convergence Stefano De Marchi analysis for a wide class of regularized reconstruction pro- University of Padova (Italy) cesses by means of sampling inequalities. In particular, we [email protected] present improved convergence rates if the scattered data points are distributed more densely near the boundary. Gabriele Santin This is based on joint work with Christian Rieger (Univer- University of Padova sity of Bonn). [email protected] Barbara Zwicknagl University of Bonn MS101 [email protected] Meshless Vector Field Approximation with Radial Basis Functions MS102 In this talk we will discuss customized radial basis func- Parallel, Adaptive, Multi Block Methods for Carte- tion kernels for vector-field problems. Using shifts of a sian Grids using ForestClaw single scalar-valued kernel and its derivatives, one can eas- ily construct approximation bases that are analytically We will discuss recent multiblock and parallel capabilities divergence-free (or curl-free). Such bases lead to mesh- in ForestClaw, an adaptive mesh refinement code based less methods that are suitable for problems involving elec- on the patched-based multi-rate Berger-Oliger algorithmic tromagnetic fields, fluid flow, or other applications where strategy coupled with quad/octree mesh refinement. The a divergence-free or curl-free property must be preserved. support for multiblock capabilities now allows for domains Our focus will be on approximations designed to natu- composed of quadrilaterals, (with up to four quads meeting rally ”split” into divergence-free and curl-free components. at a vertex), each of which is refined as a quadtree. One We will present approximation rates of the resulting field- important example of such a domain is the cubed sphere. splittings, briefly consider a few applications, and share We will also show results from parallel computations on the some numerical observations. Blue Gene/Q supercomputer JUQUEEN, based in Julich, Germany. ForestClaw uses the dynamic grid management Edward Fuselier library p4est (C. Burstedde, Univ. of Bonn). High Point University Department of Mathematics and Computer Science Donna Calhoun [email protected] Boise State University [email protected] Grady B. Wright Department of Mathematics Carsten Burstedde Boise State University, Boise ID Universit¨at Bonn [email protected] [email protected]

MS101 MS102 Beyond Quasi-unifomity: Kernel Approximation Using Explicit Filtering and Reconstruction to Im- with a Local Mesh Ratio prove Large-Eddy Simulation of the Atmosphere on Adaptive Grids Many theoretical results in RBF interpolation assume that data is sampled in a quasi-uniform way. This is somewhat Large-eddy simulation (LES) and adaptive mesh refine- supported by empirical evidence – as centers are badly ar- ment reduce the computational cost of turbulence model- ranged, the underlying interpolation matrices become ill- ing by restricting resolved length scales. Combining these conditioned. In this talk we present a relaxed notion of techniques generates errors at grid refinement interfaces. quasi-uniformity by locally controlling the mesh-ratio. Un- This talk explores using the LES formulation to mitigate der this type of assumption, and with the aid of recently these errors. Explicitly filtering the advection term and developed localized bases for RBF approximation, centers the mixed model are compared to implicit filtering and may cluster or form gaps without giving rise to instabil- the eddy viscosity model. Explicitly filtering the advection ity. At the same time, approximation error is controlled term reduces interpolation errors, and the mixed model by a local density parameter, meaning that pointwise error decreases wave reflection. responds to the local distribution of data. Lauren Goodfriend, Fotini Katopodes Chow Thomas C. Hangelbroek UC Berkeley Department of Mathematics [email protected], [email protected] University of Hawaii at Manoa [email protected] Marcos Vanella, Elias Balaras George Washington University [email protected], [email protected] MS101 Oversampling Near the Boundary and Improved Exponential Convergence Rates MS102 Local Time Stepping for Parallel Adaptive Mesh We consider the reconstruction of smooth functions from Refinement Simulation scattered data. If the data are exact, then one theo- retically expects exponential convergence rates for many In this talk we present a linear, multistep approach to local kernel-based reconstruction processes. However, the as- time stepping for parallel, adaptively refined discontinuous CS15 Abstracts 93

Galerkin and multiblock finite difference methods. The software solution which retains performance and platform scheme is efficiently initialized and, following mesh adapta- portability. tion, restarted using a fixed number of Runge-Kutta steps; the number of Runge-Kutta steps is independent of the Chris Cantwell,DavidMoxey number of time levels. The coupled multiphysics problem Imperial College London of earthquake rupture dynamics is used to demonstrate the [email protected], [email protected] efficiency and accuracy of the method. Mike Kirby Jeremy E. Kozdon University of Utah Stanford University School of Computing Geophysics [email protected] [email protected] Spencer Sherwin Lucas Wilcox Imperial College London Department of Applied Mathematics [email protected] Naval Postgraduate School [email protected] MS103 High order DG Methods on Pyramidal Elements MS102 Progress in Parallel Adaptive Methods for Storm High order time-explicit nodal discontinuous Galerkin (dG) Surge Forecasting methods have grown in popularity over the past decade for reasons both mathematical and computational in nature. Today the threat of coastal hazards such as storm surge and Optimized Lagrange interpolation nodes and sharp trace tsunamis has become increasingly critical to the sustain- inequalities with explicit constants allow for explicit ex- ability of coastal infrastructure and communities. Leverag- pressions for optimal CFL and penalty constants. Finally, ing adaptive mesh refinement approaches to these problems the computational structure of dG methods on simplices has proven to be an effective way to tackle these multi-scale and hexahedra allows for efficient implementation on ac- problems, lowering the computational barrier substantially celerators and graphics processing units. In this talk, we in some cases. In this talk progress in parallelizing these present extensions of these aspects of dG methods to high methods will be discussed including recent work on using order pyramidal elements. many-core technologies. Jesse Chan Kyle T. Mandli Rice University University of Texas at Austin [email protected] ICES [email protected] MS103 What Makes Computational Open Source Libraries MS103 Successful? Applying Object-oriented Programming to PDE Solutions While software is the backbone of scientific computing, we rarely publish information on best practices for writing Object-oriented program design is very appealing for de- large-scale, open source scientific software. In this talk, sign of PDE solvers since many of the ideas fit well with we discuss our observations for success for computational top-down design, abstraction from the underlying discreti- libraries. In particular, we talk about the roles of code, sation, and high-level code re-use. However, too much data documentation, community, project management, testing, hiding and encapsulation, commonly espoused for object- and licenses. The talk is based on our experience maintain- oriented methods, leads to memory-use redundancy and ing the finite element library deal.II (see www.dealii.org). inefficient codes. We will examine some lessons learned during application of object-oriented design to a spectral elementFourier NavierStokes solver. Timo Heister Clemson University Hugh Blackburn Mathematical Sciences Department of Mechanical and Aerospace Engineering [email protected] Monash University [email protected] Wolfgang Bangerth Texas A&M University [email protected] MS103 Architecting Spectral/HP Element Codes for Mod- ern Hardware MS104 Distributed Optimization in Directed Graphs: Complex finite element software is necessary to meet the Push-Sum Based Algorithms demands of some of today’s most challenging computa- tional problems. The design of software is therefore more We consider distributed optimization by a collection of important than ever to ensure correctness of the result and nodes, each having access to its own convex function, whose manageability and sustainability of the implementation. collective goal is to minimize the sum of the functions. We illustrate the approach taken within the Nektar++ The communications between nodes are described by a spectral/hp element framework to compartmentalise code time-varying sequence of directed graphs, which is uni- to align with the mathematical description and produce a formly strongly connected. For such communications, as- 94 CS15 Abstracts

suming that every node knows its outdegree, we develop a [email protected] broadcast-based algorithm, termed the subgradient-push, which steers every node to an optimal value under a Asuman Ozdaglar standard assumption of subgradient boundedness. The Massachusetts Institute of Technology subgradient-push requires no knowledge of either the num- [email protected] ber of agents or the graph sequence to implement. Our analysis shows that the subgradient-push algorithm con- verges at a rate of O(ln t/t). The proportionality constant MS104 in the convergence rate depends on the initial values at the Distributed Optimization in Undirected Graphs: nodes, the subgradient norms and, more interestingly, on Gradient and EXTRA Algorithms both the speed of the network information diffusion and the imbalances of influence among the nodes. Decentralized optimization meets the future needs from mobile computing, self-driving cars, cognitive radios, and Angelia Nedich collaborative data mining, just to name a few. It allows Industrial and Enterprise Systems Engineering optimization problems in a self-organizing network to be University of Illinois at Urbana-Champaign solved without a central computer. Compared to standard [email protected] distributed computing with a central controller, a decen- tralized approach tolerates certain failed nodes or links, has Alexander Olshevsky better load balance, and allows each node to keep its data University of Illinois at Urbana-Champaign private during the computation. The setting of this talk is [email protected] the same as the previous talk but assumes an undirected graph, which is more computationally friendly. We analyze existing first-order algorithms and their convergence rates MS104 and solution accuracies. Blessing of Scalability: A Tractable Dual Decom- position l-0 Approach for Large Graph Estimation Wotao Yin Department of Mathematics Estimating the topology of graphical models has been a University of California at Los Angeles critical problem in high-dimensional statistics. In large- [email protected] scale graphs, the prior knowledge can be formulated as a total sparsity budget constraints. This induces a huge non- Qing Ling, Kun Yuan convex/combinatorial optimization problem involving l-0 University of Science and Technology of China constraint. An interesting observation is: as the graph size Department of Automation increases, the associated optimization problem becomes in- [email protected], [email protected] creasingly convex. This motives the use of the distributed dual decomposition method for estimating the graph topol- ogy. By relating the duality gap with certain Kullback- MS105 Leibler divergence associated with the graph estimation Advanced Discretizations And Multigrid Methods problem, we show that the estimator obtained by dual For The Energy Minimization of Liquid Crystal decomposition achieves asymptotically optimal statistical Equilibrium Configurations rate. Abstract not available at time of publication. Mengdi Wang Department of Operations Research and Financial David Emerson Engineering Tufts University Princeton University [email protected] [email protected] MS105 MS104 A Parallel Volume Integral Equation Stokes Solver for Flows in Complex Geometries On the O(1/k) Convergence of Asynchronous Dis- tributed Alternating Direction Method of Multi- Abstract not available at time of publication. pliers Dhairya Malhotra We consider a network of agents that are cooperatively University of Texas at Austin solving a global optimization problem, where the objective [email protected] function is the sum of privately known local objective func- tions of the agents and the decision variables are coupled via linear constraints. Recent literature focused on special MS105 cases of this formulation and studied their distributed solu- Uncertainty Quantification in Control Problems for tion through either subgradient based methods with O(1/ Flocking Models v k) rate of convergence (where k is the iteration number) or Alternating Direction Method of Multipliers (ADMM) Abstract not available at time of publication. based methods, which require a synchronous implementa- tion and a globally known order on the agents. In this Mattia Zanella paper, we present a novel asynchronous ADMM based dis- University of Ferrara tributed method for the general formulation and show that [email protected] it converges at the rate O(1/k).

Ermin Wei MS106 MIT Polynomial Approximation of Random PDEs by CS15 Abstracts 95

Discrete Least Squares Oak Ridge National Laboratory [email protected] We consider global polynomial approximation of the parameter-to-solution map for PDEs with random input Ronald DeVore parameters. The polynomial approximation is obtained by Department of Mathematics a discrete least squares approach based on noise-free point- Texas A&M University wise evaluations of the map. We present results concerning [email protected] the stability and optimality of the method for random as well as low discrepancy sequences of points, and various un- derlying probability measures and show high dimensional MS107 numerical tests supporting the theory. Runtime Systems for Fault Tolerant Computing Fabio Nobile EPFL, Switzerland Since the number of hardware components is expected to fabio.nobile@epfl.ch grow by one or two orders of magnitude and the circuits’ features will also decrease, reliability is expected to be a critical challenge for exascale computing. Specifically, ex- Raul F. Tempone ascale machines are expected to suffer hard faults, i. e., Mathematics, Computational Sciences & Engineering crashes, soft faults, i. e. silent data corruptions, plus per- King Abdullah University of Science and Technology formance slowdowns due to unexpected behavior of some [email protected] hardware components. In this context, a runtime system able to tolerate the latency due to recovery mechanisms Giovanni Migliorati by overlapping them with algorithmic computations is re- CSQI-MATHICSE, EPFL quired. Such system must dynamically adapt the workload giovanni.migliorati@epfl.ch depending on the hardware status and the prevalence of faults. In this talk, we will describe the general features that this kind of runtime software such have. MS106 Combining Sparsity and Smoothness for Function Marc Casas Interpolation Barcelona Supercomputing Center [email protected] Functions of interest are often smooth and sparse in some sense. Classical linear interpolation methods are effective under strong regularity assumptions, but cannot incorpo- MS107 rate nonlinear sparsity structure. At the same time, non- Fenix: A Framework for Online Failure Recovery linear methods such as L1 minimization can reconstruct for Scientific Simulations Towards Exascale sparse functions from very few samples, but do not neces- sarily encourage smoothness. Here we show that weighted In this talk we present Fenix, a framework for enabling re- L1 minimization effectively merges the two approaches, covery from process/node/blade/cabinet failures for MPI- promoting both sparsity and smoothness in reconstruction. based parallel applications in an online and transparent More precisely, we provide specific choices of weights in the manner. Fenix provides mechanisms for transparently cap- L1 objective to achieve rates for functions with coefficient turing failures, fixing failed communicators, restoring ap- sequencesinweightedLpspaces,p<= 1. We consider the plication state, and returning execution control back to implications of these results in particular for the multivari- the application. It relies on application-driven, diskless, ate setting. implicitly coordinated checkpointing. Using the S3D com- bustion simulation we experimentally demonstrate Fenixs Rachel Ward ability to tolerate high failure rates with low overhead. Department of Mathematics University of Texas at Austin Marc Gamell [email protected] NSF Cloud and Autonomic Computing Center, Rutgers Discovery Holger Rauhut Informatics Institute, Rutgers University Aachen University [email protected] [email protected] Daniel Katz MS106 Computation Institute, University of Chicago Argonne National Laboratory, Chicago Quasi-optimal Polynomial Approximation of PDEs [email protected] with Linear and Nonlinear Stochastic Coefficients Abstract not available at time of publication. Keita Teranishi, Hemanth Kolla, Jacqueline Chen Sandia National Laboratories Clayton G. Webster [email protected], [email protected], Oak Ridge National Laboratory [email protected] [email protected] Scott Klasky Hoang A. Tran Oak Ridge National Laboratory Oak Ridge National Laboratory Oak Ridge, TN Computer Science and Mathematics Division [email protected] [email protected] Manish Parashar Guannan Zhang Rutgers Discovery Informatics Institute 96 CS15 Abstracts

Department of Computer Science [email protected] [email protected]

MS108 MS107 The Solution of Lyapunov Equations with Nonnor- DHARMA: Distributed asyncHronous Adaptive mal Coefficients Resilient Management of Applications Applications in control require solution of the Lyapunov T − T DHARMA (Distributed asyncHronous Adaptive Resilient equation AX + XA = BB .WhenA is stable and B Management of Applications) is a new many-task program- has low rank, the singular values of X often decay rapidly. ming model designed with resilience as a primary con- Existing bounds on those singular values predict slow decay cern. It is a data-flow paradigm that emphasizes over- when A is far from normal. In contrast, we show that if decomposition of work and exploits both task- and data- the numerical range of A extends far into the right half parallelism. These qualities enable dynamic and adaptable plane, there must be a large difference between the extreme execution; yet introduce significant bookkeeping challenges singular values of X. to adequately address faults. In this talk we present an Mark Embree overview of DHARMAs runtime, discuss key design deci- Department of Mathematics sions, and present recent empirical results. Virginia Tech [email protected] Hemanth Kolla, Janine C. Bennett, Jeremiah Wilke Sandia National Laboratories [email protected], [email protected], Jonathan Baker [email protected] Department of Computational and Applied Mathematics Rice University [email protected] Nicole Slattengren Sandia National Labs [email protected] John Sabino The Boeing Company [email protected] Keita Teranishi, John Floren Sandia National Laboratories [email protected], jffl[email protected] MS108 Indefinite Preconditioning of the Coupled Stokes- MS107 Darcy System Understanding the Impact of Transient Faults at We propose the use of an indefinite (constraint) precondi- the Application Level in HPC tioner for the iterative solution of the linear system arising from the finite element discretization of coupled Stokes- As new generations of microprocessors are created, soft Darcy flow. We provide spectral and field-of-value bounds error rates increase as a consequence of technology scal- for the preconditioned system which are independent of the ing and reduced energy consumption. Addressing the soft underlying mesh size. We present numerical results show- error problem has been identified as key to achieve exas- ing that the indefinite preconditioner outperforms both cale computing. In this talk, we will present our work on standard block diagonal and block triangular precondition- understanding the resilience problem with an application- ers both with respect to iteration count and CPU times. level perspective: how they affect different components of HPC applications? and what mitigation strategies can be Scott Ladenheim designed to overcome the problem? Temple University [email protected] Ignacio Laguna Lawrence Livermore National Laboratory Prince Chidyagwai [email protected] Loyola University Maryland Department of Mathematics and Statistics [email protected] MS108 Numerical Solution of PDEs Posed on Graphs Daniel B. Szyld Temple University There is currently considerable interest in a class of models Department of Mathematics (known as Quantum Graphs) which can be described in [email protected] terms of PDEs posed on large and possibly complex graphs. Such models have found applications in quantum chemistry and solid state physics. The discretization of PDEs posed MS108 on graphs using finite element methods and implicit time Exploiting Tropical Algebra in the Construction of stepping techniques leads to large, sparse systems of linear Preconditioners equations. This talk will address iterative methods and preconditioning techniques for solving these systems. This Recently it has been shown that tropical algebra can be is joint work with Mario Arioli. usefully applied in numerical linear algebra, for example to approximate eigenvalues and singular values. The value of Michele Benzi tropical algebra is often greater for unstructured matrices Department of Mathematics and Computer Science with entries that vary widely in magnitude, i.e., problems Emory University that are usually considered difficult. In this talk we show CS15 Abstracts 97

how tropical algebra can be used to understand and de- [email protected] sign effective incomplete factorization preconditioners for Krylov subspace methods for solving linear systems. Troy Butler University of Colorado Denver James Hook [email protected] School of Mathematics University of Manchester [email protected] MS109 QuantifyingErrorinAnInadequateModelfor Jennifer Pestana Flow in a Porous Media Mathematical Institute, Oxford University, UK [email protected] High fidelity models are prohibitively expensive to solve. For porous media flow, these are the Navier-Stokes equa- Francoise Tisseur tions at the pore-scale. To avoid the cost, we usually make University of Manchester simplifying assumptions leading to a cheaper inadequate Department of Mathematics model. We first give an overview of a general validation [email protected] framework for these inadequate models. Then we give an explicit formulation of a model inadequacy for a porous me- dia flow problem and explore how this inadequacy affects MS109 posterior uncertainty. Error Decomposition and Adaptivity for Re- Teresa Portone sponse Surface Approximations with Application ICES to Bayesian Inference UT Austin [email protected] We extend our work on error decomposition and adaptive refinement for response surfaces to focus on the develop- ment of a surrogate model for use in Bayesian inference. Damon Mcdougall Estimation and adaptivity are driven by a quantity of in- Institute for Computational Engineering Sciences terest. The desired tolerance in the error of the posterior The University of Texas at Austin distribution is used to establish a threshold for the accuracy [email protected] of the surrogate model. Particular focus is paid to accurate estimation of evidence to facilitate model selection. Todd Oliver PECOS/ICES, The University of Texas at Austin Corey M. Bryant, Serge Prudhomme [email protected] ICES The University of Texas at Austin Robert D. Moser [email protected], [email protected] University of Texas at Austin [email protected] Todd Oliver PECOS/ICES, The University of Texas at Austin [email protected] MS109 A Scalable Computational Framework for Estimat- Tim Wildey ing Model Discrepancy Optimization and Uncertainty Quantification Dept. Sandia National Laboratories In this talk we will focus on devising a scalable computa- [email protected] tional framework for the estimation of model discrepancies in uncertainty quantification problems. We will answer questions like how do we include the choice of model selec- MS109 tion in our parameter space, how does our data influence model selection, etc. We will answer this in the context of A Scalable Measure-Theoretic Approach to the a measure theoretic framework for stochastic inverse prob- Stochastic Inverse Problem for Groundwater Con- lems. tamination Nishant Panda We compute approximate solutions to inverse problems Colorado State University for determining parameters in groundwater contaminant [email protected] transport models with stochastic data on output quanti- ties. We utilize a measure-theoretic inverse framework to perform uncertainty quantification and estimation for these MS110 parameters. The inverse of the map from parameters to Nested Iteration and Adaptive Finite Elements for data defines a type of generalized contour map. Adjoint Ice Sheet Models problems which are useful in determining a posteriori error estimates are developed and solved numerically. This talk describes a First-order System Least-squares (FOSLS) formulation of the nonlinear Stokes flow used to Steven Mattis model glaciers and ice sheets. A Nested Iteration (NI), University of Texas at Austin Newton-FOSLS-AMG approach is used in which the ma- [email protected] jority of the work is done on coarse grids. A reformula- tion is described that avoids the difficulty of infinite viscos- Clint Dawson ity in regions where ice is undergoing small deformations. Institute for Computational Engineering and Sciences Numerical tests are presented demonstrating good per- University of Texas at Austin formance of the NI-Newton-FOSLS-AMG approach with 98 CS15 Abstracts

adaptive mesh refinement. [email protected]

Jeffery M. Allen John Ruge University of Colorado at Boulder University of Colorado at Boulder jeff[email protected] [email protected]

Thomas Manteuffel Chad Westphal University of Colorado Wabash College [email protected] [email protected]

Harihar Rajaram University of Colorado MS110 Dept. Civil Engineering A Least Squares Finite Element Method for Cou- [email protected] pled Surface/Subsurface Flows

A coupled surface/subsurface flow is presented in this talk. MS110 The surface flow is modeled by shallow water equations Parametric Mixed Finite Elements for Two-Phase and the subsurface flow by a generalized Darcy’s law for Flow Interface Problems the variably saturated case. Coupling is done along an interface and continuity of pressure and continuity of flux Optimal order convergence of a first-order system least is enforced. A least squares finite element method for the squares method using lowest-order Raviart-Thomas ele- spatial discretization is utilized and numerical experiments ments is presented for domains with curved boundaries. using adaptive refinement strategies will be examined. Parametric Raviart-Thomas elements are introduced in or- der to retain the optimal order of convergence in the higher- Steffen M¨unzenmaier order case. In particular, an estimate for the normal flux of Gottfried Wilhelm Leibniz University of Hannover the Raviart-Thomas elements on interpolated boundaries steff[email protected] is derived. As an application, boundary values of forces are estimated in the Stokes problem. MS111 Fleurianne Bertrand Least Squares Shadowing for Adjoint Calculation University of Duisburg-Essen of Chaotic and Turbulent Pdes fl[email protected] The adjoint method is an invaluable tool for scientific re- Gerhard Starke search and engineering design. However, it has been shown University of Duisburg-Essen that the traditional adjoint method diverges and produces Fakult¨at f¨ur Mathematik the wrong gradient for chaotic and turbulent PDEs. For [email protected] these cases, a new approach, Least Squares Shadowing (LSS) has shown promising results. This talk discusses the method and its properties, including sources of error and Steffen M¨unzenmaier convergence rates of the adjoint field. Applications includ- Gottfried Wilhelm Leibniz University of Hannover ing isotropic homogeneous turbulence are also presented. steff[email protected]

Patrick Blonigan MS110 MIT Hybrid FOSLS/ll* for Nonlinear Systems of PDEs [email protected]

∗ This talk presents the extension of Hybrid FOSLS/LL to Qiqi Wang nonlinear systems of PDEs. Hybrid FOSLS/LL∗ combines ∗ Massachusetts Institute of Technology the best features of FOSLS and FOSLL . It controls both [email protected] the Operator Norm and the L2 norm, approximately min- imizing the Graph Norm of the error. It retains a locally sharp and asymptotically accurate a posterior error esti- MS111 mator that can be used with nested iteration and adaptive Actuator and Sensor Placement for Controlling mesh refinement. The efficacy of this method is demon- High-Speed Jet Noise strated on Navier/Stokes equation and Stokes equation with nonlinear viscosity, as used in ice sheet modeling. The loudest source of high-speed jet noise, such as found on naval tactical fighters, appears to be unsteady wavepack- Thomas Manteuffel ets that are acoustically efficient but relatively weak com- University of Colorado pared to the main jet turbulence. These wavepackets can [email protected] be usefully described by linear dynamics and connected to transient growth mechanisms. Through a component-wise Kuo Liu structural sensitivity analysis of the turbulent jet base- Department of Applied Mathematics flow, using both the equilibrium and time-average fields, University of Colorado at Boulder estimates are given as to what location and kind of actu- [email protected] ators and sensors are most effective, in a linear feedback context, to control the wavepackets to reduce their noise. Lei Tang Low and high frequency approaches are examined where Department of Applied Mathematics the controlling mechanisms differ: the low-frequency con- University of Colorado-Boulder trol indirectly targets the slow variation of the mean on CS15 Abstracts 99

which the wavepackets propagate while the high-frequency [email protected], [email protected] control targets the wavepackets themselves. The predicted control strategy is evaluated using direct numerical simu- lations on a series of Mach 1.5 turbulent jets. MS112 Software Productivity Community Input: Con- Mahesh Natarajan, Daniel J. Bodony cerns and Priorities University of Illinois at Urbana-Champaign Department of Aerospace Engineering This session will start with an overview and history of the [email protected], [email protected] software productivity activities across the scientific com- puting community, followed by an open discussion of re- quirements, forums, and opportunities for further engage- MS111 ment. Using Imperfect Outputs and Derivatives in Large- Jeffrey C. Carver scale Optimization Department of Computer Science University of Alabama The outputs of interest in many engineering systems are [email protected] time averages of chaotic solutions. Relevant examples in- clude the lift and drag on aerodynamic bodies, the energy Michael Heroux produced by a fusion reactor, and the (phase-averaged) Sandia National Laboratories pressure in an internal-combustion engine. In practice, [email protected] these outputs must be approximated over a finite integra- tion period, which leads to noise-like errors in the param- eter space. In addition, gradients of these outputs must MS112 be approximated using ensemble averages or other regu- Overview: Software Productivity Challenges for larizations. Thus, both the outputs and their derivatives Extreme Scale Science contain errors: they are “imperfect.” In this talk we dis- cuss a novel sampling strategy for gradient-based surrogate The Department of Energy has initiated research in soft- models that aims to address large-scale optimization prob- ware productivity for application development and soft- lems in the context of imperfect data from computationally ware infrastructure for extreme-scale scientific computing. expensive simulations. The eventual goal is to enable grand challenge science simulations that can survive and even leverage disruptive Jason E. Hicken changes in extreme-scale computer architectures, and thus Rensselaer Polytechnic Institute enable new frontiers in modeling, simulation, and analysis Assistant Professor of complex multiscale and multiphysics phenomena. This [email protected] session will give an overview of DOE activities, including workshops, participating communities, and pilot projects.

MS111 Lois Curfman McInnes Parallel Bayesian Optimization of Massively Paral- Mathematics and Computer Science Division lel Turbulent Flow Simulations Argonne National Laboratory [email protected] Abstract not available at time of publication. Hans Johansen Chaitanya Talnikar Lawrence Berkeley National Laboratory MIT Computational Research Division [email protected] [email protected]

Michael Heroux MS112 Sandia National Laboratories [email protected] Software Productivity Application: Integrated Modeling for Fusion Energy MS112 Integrated modeling of plasmas is a key scientific capability Software Productivity Challenges in Environmen- for the development of fusion as a power source. We will tal Applications present our experience developing the Integrated Plasma Simulator (IPS), an environment which enables plasma Predictive simulations of environmental applications pose physicists to be highly productive in developing and car- significant challenges for multiscale multiphysics frame- rying out a broad range of coupled simulations, while im- works. Problem complexity requires flexibility to compare proving supercomputer resource utilization. The design different models or model features, to add new models, and implementation of the IPS is quite general, and it is and to explore model coupling. We will present our expe- also being used in other domains. rience in addressing these issues in two open-source codes, Amanzi and the Arctic Terrestrial Simulator. We will dis- David E. Bernholdt cuss the importance and challenge of leveraging existing Oak Ridge National Laboratory frameworks and libraries as well as components of estab- Computer Science and Mathematics Division lished codes. [email protected] David Moulton Wael R. Elwasif, Donald B. Batchelor Los Alamos National Laboratory Oak Ridge National Laboratory Applied Mathematics and Plasma Physics 100 CS15 Abstracts

[email protected] Dept of Mathematical Sciences [email protected] Ethan T. Coon Los Alamos National Laboratory [email protected] MS113 Taming Targeted Drug Delivery: a Mathemati- Carl Steefel cal Model of Triggered Drug Delivery Across the Lawrence Berkeley National Laboratory Blood-Brain Barrier [email protected] The blood-brain barrier is necessary to protect the brain from microscopic pathogens and toxic molecules. How- MS113 ever, this protective mechanism also poses a challenge to Modeling the Effects of Flow on Anticoagulant the delivery of pharmaceutical agents to the brain. Sono- Therapy sensitive nanoparticles containing drug show promise as a way to overcome this challenge. Here we propose a sched- Warfarin is a common anticoagulant used to treat blood ule for the treatment of disorders of the brain based on clots. The success of anticoagulation treatment depends a mathematical model of the circulation, triggered release on in vivo dynamics that cannot be captured clinically. and transport of encapsulated drugs. We combine computational models of warfarin dynamics and injury-initiated coagulation to determine the impact Ami Radunskaya of blood flow and platelet dynamics on therapeutic out- Pomona College comes. We highlight the differences between clinical as- Mathematics Department sessment and in vivo measures of warfarin effectiveness. [email protected] Results indicate that blood flow is a significant determi- nant of treatment success. MS113 Erica J. Graham Cooperative Swimming in Viscous Environments North Carolina State University Department of Mathematics Flagellated organisms exhibit different swimming behav- [email protected] iors, depending on their local environment. We consider the cooperative nature of swimming in populations in vis- Lisette dePillis cous environments, in an effort to understand sperm trans- Harvey Mudd College port. Our approach is a numerical model that relies upon [email protected] the method of regularized Stokeslets and is robust to three- dimensional effects. We investigate surface interactions as well as measures of cooperativity to elucidate why sperm Kaitlyn Hood have such a large variation in behavior across species. UCLA [email protected] Julie Simons,LisaJ.Fauci Tulane University Yanping Ma Department of Mathematics Loyola Marymount University [email protected], [email protected] [email protected] Ricardo Cortez Julie Simons Tulane University Tulane University Mathematics Department Department of Mathematics [email protected] [email protected]

Ami Radunskaya MS114 Pomona College A Study of the Entanglement in Polymer Melts Mathematics Department [email protected] Polymer melts are dense systems of macromolecules. In such dense systems the conformational freedom and mo- tion of a chain is significantly affected by entanglement MS113 with other chains which generates obstacles of topological Navier Slip Condition for Viscous Fluids on a origin to its movement. In this talk we will discuss meth- Rough Boundary ods by which one may quantify and extract entanglement information from a polymer melt configuration using tools We study the effect of surface roughness on fluid flow over from knot theory. A classical measure of entanglement is a solid surface. We are able to derive asymptotically an the Gauss linking integral which is an integer topological effective slip boundary condition (Navier slip condition) as invariant in the case of pairs of disjoint oriented closed a corrector to the no-slip condition on the surface. chains in 3-space. For pairs of open chains, we will see that the Gauss linking integral can be applied to calculate Silvia Jimenez Bolanos an average linking number. In order to measure the en- Department of Mathematics tanglement between two oriented closed or open chains in Colgate University a system with three-dimensional periodic boundary condi- [email protected] tions (PBC) we use the Gauss linking number to define the periodic linking number. Using this measure of linking to Bogdan M. Vernescu assess the extend of entanglement in a polymer melt we Worcester Polytechnic Inst study the effect of CReTA (Contour Reduction Topolog- CS15 Abstracts 101

ical Analysis) algorithm on the entanglement of polyethy- is recovered by performing defect-correction subiterations. lene chains. Our results show that the new linking measure is consistent for the original and reduced systems. Yue Yu Eleni Panagiotou Brown University University of California Santa Barbara [email protected] [email protected]

MS115 MS114 Reaction-diffusion and Electrical Signaling in Neu- A Fast Explicit Operator Splitting Method for a rons (Rdesigneur): a System for Multiscale Mod- Multi-scale Underground Oil Recovery Model eling in MOOSE

In this talk, we propose a fast splitting method to solve a MOOSE, the Multiscale Object-Oriented Simulation En- Multi-scale underground oil recovery model which includes vironment, and Rdesigneur support coupled stochastic a third order mixed derivatives term resulting from the reaction-diffusion signaling embedded in electrical neuronal dynamic effects in the pressure difference between the two models. Rdesigneur coordinates loading of electrical and phases. The method splits the original equation into two chemical models using standards like NeuroML and SBML. equations, one with flux term and one with diffusion term It then populates the complex neuronal geometry with the so that the classical numerical methods can be applied im- chemical models, and defines the interfaces between the mediately. Two different spatial discretizations, second- electrical and chemical signaling. A set of modular, in- order Godunov-type central-upwind scheme and WENO5 terchangeable numerical engines plug in to the system to scheme, are used to demonstrate that higher order method carry out computations at the chosen level of detail. provides more accurate approximation of solutions. The various numerical examples in both one and two dimen- Upinder Bhalla sions show that the solutions may have many different satu- National Center for Biological Sciences (NCBS), ration profiles depending on the initial conditions, diffusion Bangalore parameter, and the third-order mixed derivatives parame- [email protected] ter. The results are consistant with the study of traveling wave solutions and their bifurcation diagram. This is joint work with C.-Y. Kao, A. Kurganov, Z.-L. Qu. MS115 Ying Wang Interactive, Distributed Spatial Stochastic Simula- University of Oklahoma tion with PyURDME and MOLNs [email protected] Computational experiments have lead to new biological in- sights, but the complexity of managing the required dis- MS114 tributed computation environments presents a barrier to Computational Study of Dynamics and Transport the adoption. To address this need, we present MOLNs, in Vortex-Dipole Flows a cloud computing appliance for distributed simulation of stochastic reaction-diffusion models. The appliance is A finite number of dipole interactions in free space are based on IPython and a newly developed, spatial model- studied numerically in order to see how they give rise to ing and simulation package, PyURDME. MOLNs provides a collective fluid flow pattern that is widely seen in ocean an interactive programming platform for development of currents and clouds. The classical Lamb Dipole is used sharable and reproducible distributed parallel computa- as our vortex unit. The computation is validated by com- tional experiments. paring results with analytic solutions of a free-translating Lamb Dipole. The results have two ingredients. First, Brian Drawert the intra- and inner-dipole kinematic pressure fields show University of California Santa Barbara distinct features and they relate the phenomenon of no [email protected] mass exchange in dipoles interactions. Second, a general rule of the ultimate vortical flow pattern is observed based MS115 on dipoles interactions in three setups : head on collision, head-end marching, parallel marching. Gepetto/OpenWorm Ling Xu Abstract not available at time of publication. Georgia State University [email protected] Stephen Larson OpenWorm.org, MetaCell [email protected] MS114 A Stabilized Explicit Scheme for Coupling Fluid- structure Interactions MS115 Stochastic Simulation at Your Service We develop a new stabilized explicit coupling partitioned scheme for the fluid-structure interaction problem, where We present StochSS: Stochastic Simulation as-a-Service, the pressure and velocity are decoupled. Proper penalty an integrated development environment for simulation of terms are applied to control the variations at the interface. biological systems with models ranging from ODE to spa- Using energy stability analysis, we show that the scheme is tial stochastic, where a user can build a simple model on a stable independent of the fluid-structure density ratio. Nu- laptop and scale it up to increasing levels of complexity, de- merical examples are provided to show that although the ploying computing resources from the cloud with the push penalty terms degrade the time accuracy, optimal accuracy of a button when they are needed. StochSS is available for 102 CS15 Abstracts

download at www.stochss.org. problems constrained by dynamical systems with high- dimensional state and parameter spaces. To accelerate Linda R. Petzold the inversion, model order reduction can be employed to University of California, Santa Barbara restrict the optimization to the dominant parameter sub- [email protected] space and the evaluation of the model to the dominant state subspace. With this combined state and parame- ter reduction of the underlying model, the inversion be- MS116 comes less computationally costly. Two distinct methods Convergence of Inverse Problems using Reduced for the combined reduction of states and parameters are Order Models presented. First, a gramian-based approach, which uses empirical gramians to reduce the state and parameter di- Inversion requires the repeated solution of expensive for- mension based upon the associated controllability and ob- ward problems and the computation of Jacobians. In re- servability. Second, an optimization-based approach that cent work, we have successfully used reduced order models uses a data-driven greedy approach to assemble the reduced to make nonlinear inversion cheaper. Our approach works order model. Both methods are tested and compared on a well in practice but does not guarantee convergence. I will dynamic causal model of a neuronal network. discuss the solution of a tomography problem using model reduction and an approach to guarantee convergence. Christian Himpe Institute for Computational und Applied Mathematics Eric De Sturler Universtiy of Muenster Virginia Tech [email protected] [email protected] Mario Ohlberger MS116 Universit¨at M¨unster From Data to Prediction Via Reduced Parameter- Institut f¨ur Numerische und Angewandte Mathematik to-Observable Maps: Applications to Antarctic Ice [email protected] Sheet Flow

Here we consider the following question: given a large-scale MS117 model containing uncertain parameters, (possibly) noisy Imaging Biomarkers in Biopharmaceutical Indus- observational data, and a prediction quantity of interest, try how do we construct efficient and scalable algorithms to (1) infer the model parameters from the data, (2) quantify the Increasingly biopharmaceutical industry is using imaging uncertainty in the inferred parameters, and (3) propagate for understanding disease and for assessment of therapeutic the resulting uncertain parameters through the model to effects in all stages of drug development. Different imag- issue predictions with quantified uncertainties? We present ing modalities can visualize tissue or organ characteristics efficient and scalable algorithms for this end-to-end, data- modulated by disease progression and/or therapy. Imaging to-prediction process under the Gaussian approximation enables development of predictive disease-based biomark- and in the context of modeling the flow of the Antarctic ers that are translatable between preclinical and clinical ice sheet. We demonstrate that the work required is inde- stages of drug development by extracting and mining rel- pendent of the parameter and data dimensions. The key to evant quantitative information from qualitative imaging achieving this is to exploit the fact that, despite their large data in reliable, efficient and objective manner. size, the observational data typically provide only sparse information on model parameters. Belma Dogdas Merck Omar Ghattas [email protected] The University of Texas at Austin [email protected] MS117 Toby Isaac ICES Simulation-Based Analysis of Complex Decision The University of Texas at Austin Options in Pharmaceutical Research and Develop- [email protected] ment

Noemi Petra I will present a multi-method modeling and simulation University of California, Merced framework for decision analysis in dynamic resource- [email protected] constrained situations under uncertainty. The framework was developed for, and applied to, nonlinear problems of strategic planning, portfolio management, asset valuation, Georg Stadler process optimization, and what-if scenario analysis in the Courant Institute for Mathematical Sciences context of pharmaceutical research and development, and New York University can be applied to a broader class of real world problems. [email protected] Otto Ritter MS116 Independent Consultant [email protected] Combined State and Parameter Reduction for the Inversion of Functional Neuroimaging Data

The evaluation of functional neuroimaging data such as MS117 EEG and fMRI requires the solution of large-scale inverse Imaging Genomics for Pharmaceutical Applica- CS15 Abstracts 103

tions We will present methods to integrate simulation into the medical treatment process covering the workflow from CT Imaging Genomics is an emerging field that integrates or MRI based imaging through simulation to visualization. imaging and genomic data for identifying high-confidence genesets that relate to a phenotypic response measured from imaging. This talk will explore the use of Imaging Michael Resch genomics for improved diagnosis, patient stratification and HLRS, University of Stuttgart, Germany assessment of therapeutic response in oncology. Analysis [email protected] techniques described will encompass the areas of machine learning, image processing, and statistics to extract mean- Ralf Schneider ingful information from high-dimensional, multi-modality HLRS data for applications in drug discovery and development. [email protected] Sangeetha Somayajula, Chandni Valiathan Merck [email protected], [email protected]; MS118 What Are the Priorities Beyond Petascale Com- puting? MS118 Petascale Simulations of Cloud Cavitation Collapse Much of the focus in supercomputing has been on floating- point performance since maximizing FLOP/s and GF/W We present our work on scaling workhorse computational means minimizing time and energy to solution of simula- fluid dynamics kernels and complex applications to the tions. However, does this apply to low-density problems petascale domain. We show that by extreme algorithmic and what are the right metrics for these problems? We and code re-engineering we are able to increase sustained discuss a detailed study of energy and time to solution performance of CFD codes from the traditional single digit performed on COSMO; a regional model used for climate regime to a LINPACK like 74%. We employed our codes weather forecasting, and derive effective parameters that to study cloud cavitation collapse to unprecedented levels should be considered in performance optimization. of fidelity. Thomas C. Schulthess Costas Bekas Swiss National Supercomputing Center IBM Research - Zurich [email protected] [email protected]

MS118 MS119 Petascale Simulation of Hurricane Sandy Using Analysis of a Heterogeneous Multiscale Method for WRF Weather Model on Cray XE6 Blue Waters Poroelasticity

The National Center for Atmospheric Research (NCAR) In this paper, we develop a highly parallelizable numeri- Weather Research and Forecasting (WRF) model has been cal method to solve the heterogeneous linear poroelastic- employed on the largest yet storm prediction model using ity equations in multiple dimensions via operator splitting real data of over 4 billion points to simulate the landfall and a finite-volume based heterogeneous multiscale method of Hurricane Sandy. Using an unprecedented 13,680 nodes for the linear elasticity and reaction diffusion equations. (437,760 cores) of the Cray XE6 Blue Waters at NCSA at We demonstrate convergence both analytically and numer- the University of Illinois, researchers achieved a sustained ically, and analyze its computational complexity on high rate of 285 Tflops while simulating an 18-hour forecast. performance computers.

Pete Johnsen Paul M. Delgado Cray Inc. UTEP [email protected] [email protected]

Mark Starka Vinod Kumar, Son Young Yi NCSA University of Texas at El Paso [email protected] [email protected], [email protected]

Melvyn Shapiro, Alan Norton, Thomas Galarneau NCAR MS119 [email protected], [email protected], [email protected] Experimental Analysis of the Performance of Geo- Claw, AnuGA and SurfWB-UC Numerical Models MS118 for the Simulation of Tsunami Inundation Phenom- Petascale Medical Simulations ena

We will present the usage of high performance computing In this study we test and show the performance of three systems for medical applications. The two examples pre- numerical codes for modeling tsunami inundation phenom- sented are: ena (GeoClaw, AnuGA and SurfWB-UC), by experimen- • tally analyzing the numerical convergence to exact analyti- Flow of blood in large arteries with a focus on abdom- cal solutions of the non-linear shallow water equations, and inal aortic aneurysms also, the speed-up and efficiency of their parallel implemen- • Modelling and simulation of bone tissue using direct tation. This, in order to highlight the complexity of repre- numerical simulation senting tsunami wave inundation in the presence of dry-wet 104 CS15 Abstracts

interfaces and shock-waves under variable bathymetry. [email protected]

Jos´e Galaz MS119 Pontificia Universidad Catolica de Chile, CHILE [email protected] Incompressible Flow and (Stabilised) Mixed Finite Element Methods on Highly Stretched Meshes

Rodrigo Cienfuegos Anisotropic refinement is an interesting concept to resolve Hydraulic and Environmental Engineeering Department local features of solutions. Unfortunately, the stability of Pontificia Universidad Catolica de Chile a mixed finite element method may depend on the aspect [email protected] ratio and other mesh properties caused by the refinement. We show which part of the pressure space is responsible for the deterioration of stability. By imposing a minimal MS119 amount of constraints on the pressure, two mixed methods circumventing the behaviour arise. Numerical experiments Stabilization in Relation to Wavenumber in HDG confirm their stability. Methods Andreas Wachtel We study the Hybrid Discontinuous Galerkin (HDG) University of Strathclyde, UK method for complex wavenumber cases in acoustics and [email protected] electromagnetics and show how the HDG stabilization pa- rameter must be chosen in relation to the wavenumber. We Mark Ainsworth show that the commonly chosen HDG stabilization param- Brown University eter values are not appropriate for all complex wavenum- [email protected] bers, then discover a constraint on the stabilization pa- rameter, dependent on the wavenumber, that guarantees GabrielR.Barrenechea unique solvability of both the global and the local HDG University of Strathclyde problems. We also perform a dispersion analysis for the [email protected] Helmholtz case.

Nicole Olivares MS119 Portland State University Sublinear Preconditioners for the 2D Helmholtz [email protected] Equation We present a new preconditioner for 2D Helmholtz equa- Jay Gopalakrishnan tion in the high frequency regime based on domain de- Portland state university composition, integral operators and fast algorithms. The [email protected] preconditioner is designed to be seamlessly integrated in a high performance computing environment. The algorithm Liang Li separates the computation in two parts, one expensive, but University of Electronic Science and Technology of China highly parallel, and a second one, sequential but with sub- plum [email protected] linear complexity; keeping a sub-linear overhead of commu- nication per solve. We will discuss the new algorithm the Ronan Perrussel supporting mathematics and prove that the new method Universit´e de Toulouse; CNRS;INPT, UPS; has sub-linear complexity. Finally, we will demonstrate the Laboratoire Plasma et Conversion d’Energie (LAPLACE) sub-linear complexity numerically on examples from geo- [email protected] physics.

Leonardo Zepeda-N˜nez Massachusetts Institute of Technology MS119 [email protected] Solving the Heat Equation with Wavelets Laurent Demanet The numerical solution of parabolic time evolution prob- Professor of Mathematics, MIT lems such as the heat equation is required in numerous [email protected] applictions. Solving this problem using the boundary ele- ment method (BEM) is an attractive alternative to tradi- MS120 tional methods, such as Finite Elements combined with a time-stepping scheme. Using BEM generally leads to full A Fast Conservative Spectral Solver for the Non- systems, so we combine it with a wavelet method. This linear Boltzmann Collision Operator leads to sparse system matrices that can be solved in lin- We present a conservative spectral method for the fully ear complexity. nonlinear Boltzmann collision operator based on the weighted convolution structure in Fourier space developed Anne Reinarz by Gamba and Tharkabhushnanam. The novelty of this University of Reading, UK approach consists of factorizing the convolution weight [email protected] on quadrature points by exploiting the symmetric na- ture of the particle interaction law. This procedure re- Alexey Chernov duces the computational cost and storage of the method University of Bonn to O(M 2N 4logN)fromtheO(N 6) complexity of the origi- Hausdorff Center for Mathematics nal spectral method, where N is the number of velocity grid CS15 Abstracts 105

points in each velocity dimension and M is the number of Coulomb Collisions quadrature points in the factorization. We will present nu- merical results that exhibit the efficiency of this approach. In this work we propose a novel negative particle method for the general bilinear collision operators in the spatial Jeffrey Haack homogeneous case and apply it to the Coulomb collisions. University of Texas at Austin This new method successfully reduces the growth of parti- [email protected] cle numbers from the numerical time scale to the physical time scale for the Coulomb collisions. We also propose a Jingwei Hu particle resampling method to reduce the particle number The University of Texas at Austin to further improve the efficiency. Various numerical sim- [email protected] ulations are performed to demonstrate the high accuracy and efficiency.

Irene M. Gamba Bokai Yan Department of Mathematics and ICES Department of Mathematics University of Texas UCLA [email protected] [email protected]

MS120 Russel Caflisch Department of Mathematics Kinetic Equation in a Bounded Domain University of California, Los Angeles Half-space problem is known as the key to understand the cafl[email protected] boundary layers for kinetic equations (Boltzmann equa- tion, neutron transport equation etc.) in a bounded do- MS121 main, where sharp transitions from kinetic to fluid regime present. In this talk, I will present a damping-recovery OCC-Based Meshing for RGG Applications Using scheme to obtain the solution in a general setting: the MeshKit equation is modified by a damping term, and a recovery processisproposed.Thedampedequationisprovedtobe High fidelity simulations of physical phenomena described well-posed, and a spectral method is designed to solve it. on complex geometries involve efficient generation of opti- mally resolved computational meshes. We present a com- Qin Li pletely open-source end-to-end workflow focused on nuclear Computing and Mathematical Sciences engineering problems that provide components to describe CalTech the geometry representation, parallel mesh generation and [email protected] in-situ visualization. This is made possible with a OCC- based geometry engine used in combination with a wide ar- ray of mesh generation algorithms implemented in MeshKit MS120 exposed through a GUI from Kitware called RGGNuclear. High-Order Semi-Lagrangian Discontinuous Rajeev Jain Galerkin Methods for Kinetic Plasma Models Argonne National Laboratory [email protected] We present a high-order operator split discontuous Galerkin (DG) method for solving the Vlasov-Poisson sys- tem. Our hybrid method relaxes strict CFL limitation by Jacob Becker using semi-Lagrangian techniques, and we permit compli- Kitware cated geometries in configuration space with unstructured [email protected] grids. We present 2D-2V results including the formation of a plasma sheath in the proximity of a cylindrical Langmuir Vijay Mahadevan probe, as well as the simulation of a single-species charged Argonne National Laboratory particle beam in a particle accelerator. [email protected]

David C. Seal Patrick Shriwise Department of Mathematics University of Wisconsin, Madison Michigan State University [email protected] [email protected] Robert O’Bara James A. Rossmanith Kitware Iowa State University [email protected] Deparment of Mathematics [email protected] Iulian Grindeanu Argonne National Laboratory Andrew J. Christlieb [email protected] Michigan State Univerity Department of Mathematics [email protected] MS121 High-Order Surface Reconstruction with Appli- cations in Parallel Meshing and Finite Element MS120 Solvers A Monte Carlo Method with Negative Particles for General Binary Collisions and Application to We present a method for reconstructing high-order surfaces 106 CS15 Abstracts

from a given unstructured surface mesh, based on weighted Mark Beall least squares polynomial fitting. The method can achieve Simmetrix, Inc. third and even higher order accuracy. We present the the- [email protected] oretical framework and compare it with existing methods. We also present its applications in mesh refinement and fi- Rocco Nastasia nite element methods, and show that the meshes adapted Simmetrix Inc. or refined using the proposed method preserve the order of [email protected] convergence of numerical discretizations.

Xiangmin Jiao Mark S. Shephard Stony Brook University Rensselaer Polytechnic Institute [email protected] Scientific Computation Research Center [email protected] Navamita Ray Argonne National Labratory MS122 [email protected] Modeling Active Flows and Stress Generation in Cao Lu, Xinglin Zhao Microtubule-Motor Networks Stony Brook University [email protected], [email protected] We describe a multi-scale theory for biologically-inspired soft active materials composed of microtubules crosslinked by molecular motors. Brownian dynamics simulations of MS121 microtubules with motile crosslinks reveal that activity- Parallel Mesh Curving and Adaptation with High- generated extensile stresses arise from both polarity sorting Order Surface Continuity for High-Order Finite El- and crosslink relaxation. These simulations yield polarity- ement Simulations dependent active stress coefficients for a Doi-Onsager ki- netic theory that captures activity-induced hydrodynamic This talk presents work on developing parallel curved flows. The model exhibits turbulent-like dynamics, and meshing techniques for unstructured meshes where high- the continuous generation and annihilation of disclination order surface continuity is maintained for the triangular el- defects associated with coherent flow structures. ement faces representing the curved domain surfaces. Op- timal nodal placement methods are studied and applied Robert Blackwell, Meredith Betterton, Matthew Glaser to minimize interpolation error. Mesh modification opera- University of Colorado tions are extended to deal with the complexities involved [email protected], with adapting high-order curved meshes. Benefits of us- [email protected], ing curved meshes with high-order continuity are demon- [email protected] strated in a set of CFD applications. Qiukai Lu Michael J. Shelley Rensselaer Polytechnic Institute New York University [email protected] Courant Inst of Math Sciences [email protected] Dan A. Ibanez Rensselaer Polytechnic Institute Tony Gao SCOREC Courant Institute of Mathematical Sciences [email protected] New York University [email protected] Mark S. Shephard Rensselaer Polytechnic Institute Scientific Computation Research Center MS122 [email protected] Computational Models of Cilia and Flagella in a Brinkman Fluid MS121 The interaction between dynamic elastic structures and Parallel Meshing Technologies for Large Scale their surrounding fluid is important for sperm navigation Adaptive Simulations and cilia beating within airways. We study a generalized Euler elastica immersed in a Brinkman fluid, a viscous fluid Scalable parallel simulation workflows require mesh gen- filled with a network of proteins. Regularized Greens func- eration and adaptation components to operate in paral- tions for Brinkman flow are used to investigate emergent lel and interact with the analysis code using in-memory dynamics with preferred kinematics. Results are presented interfaces. Recent developments include improvements in for swimming speeds, synchronization, and efficiency of scalability, and the ability to adapt anisotropic boundary flagella with planar waveforms in a Brinkman fluid. layer elements in both tangential and normal directions. A procedure to distribute the geometric model to avoid maintaining the entire geometry on each process has been Karin Leiderman developed. Specific examples of in-memory interfaces with Applied Mathematics analysis codes will be presented. UC Merced [email protected] Saurabh Tendulkar Simmetrix Inc. Sarah D. Olson [email protected] Worcester Polytechnic Institute CS15 Abstracts 107

[email protected] Stanford University [email protected]

MS122 Fluid Coupling in Continuum Modeling of Micro- MS123 tubule Gliding Assays Spectral Difference Method for Large Eddy Simu- lation Using Non-Conforming and Sliding Meshes Active networks are suspensions of actuated filaments ob- tained by mixing cytoskeletal filaments and motor protein Recently, we have developed a simple, efficient, and high- complexes. We focus on gliding assays, where the molec- order accurate sliding-mesh interface approach to the spec- ular motors are anchored to a bottom plate. We present tral difference method for 2D CFD simulations. The ex- a continuum macroscopic model including the evolution of tension of the sliding interface spectral difference (SSD) rigid filaments density, bound and free motors densities method to solving unsteady turbulent flows requires care- and fluid velocity. We focus on cumulative hydrodynamic ful verification and validation studies. This abstract re- effects and our numerical simulations show the emergence flects two aspects of our research. On the aspect of numer- of ordered subregions. ical methods, we report the development of the spectral difference method for a parallel solver of turbulent com- Tamar Shinar pressible flows on non-conforming and sliding meshes with Computer Sciences all hexahedral elements. On the aspect of verification and UC Riverside validation, we report Large Eddy Simulation results of a [email protected] turbulent Taylor Couette flow and compare to published Direct Numerical Simulation data. Steven Cook UC Riverside Bin Zhang, Chunlei Liang [email protected] George Washington University [email protected], [email protected] Christel Hohenegger University of Utah Department of Mathematics MS123 [email protected] High-Order Methods for Turbulent Flow Simula- tions on Deforming Domains

MS122 We present new high-order accurate methods for moving Accurate Simulations of Complex Fluid Flow in domains with large deformations. Unstructured moving Domains with Smooth Boundaries Using Fft-Based meshes are generated by a sequence of entirely local op- Spectral Methods erations. This produces high-quality meshes throughout the simulation, and provides a simple description of the We present a method for simulating complex fluid flow in mesh changes between each timestep. Using this informa- domains with smooth boundaries using simple FFT-based tion we can construct efficient numerical schemes, and we spectral methods to advance the stress evolution equation. consider both space-time formulations and ALE/projection Dirichlet conditions for the velocity are imposed by solv- based methods. We demonstrate our methods on a range ing Stokes’ equations using a novel high-order saddle-point of problems involving complex domain deformations. method. Our numerical scheme automatically generates a smooth extension for the velocity field over the non- Per-Olof Persson physical regions of the computational domain, allowing for University of California Berkeley straightforward coupling with the stress equation. We in- Dept. of Mathematics vestigate the convergence of channel flow for an Oldroyd-B [email protected] fluid to the analytical solution in the limit of vanishing artificial stress-diffusion. MS123 David Stein On the Utility of High-Order Methods for Unstruc- University of California Davis tured Grids: A Comparison Between PyFR and [email protected] Industry Standard Tools

Becca Thomases Conventional unstructured computational fluid dynamics University of California at Davis solvers used by industry typically employ second-order ac- [email protected] curate spatial discretizations on CPUs. In this work we assess the potential accuracy and efficiency benefits of high- order unstructured schemes implemented on GPUs, when MS123 compared to such industry standard tools. We compare Further Developments in the Flux Reconstruction accuracy and efficiency between the two methods for tur- Method bulent flow computations performed via direct numerical simulation and large eddy simulation. While the Flux Reconstruction method can recover the nodal DG method, it also allows a wide number of al- Brian C. Vermeire ternatives by different choices of the correction function. Imperial College London The presentation will discuss some alternatives optimized [email protected] to improve accuracy or to reduce complexity. Freddie Witherden, Peter E. Vincent Antony Jameson Department of Aeronautics Professor, Department of Aeronautics & Astronautics Imperial College London 108 CS15 Abstracts

[email protected], growths accompanying movement and rotation are simu- [email protected] lated by the GPU accelerated phase-field lattice Boltzmann scheme.

MS124 Tomohiro Takaki Massively Parallel Phase-Field Simulations using Kyoto Institute of Technology HPC Framework waLBerla Mechanical and System Engineering [email protected] We present a massively parallel phasefield code, based on the HPC framework waLBerla, for simulating solidification Roberto Rojas processes of ternary eutectic systems. Various code opti- Graduate School of Science and Technology mizations are shown, including buffering strategies, vector- Kyoto Institute of Technology ization and load balancing techniques. To reduce the ef- rcrmroberto [email protected] fective domain size, a windowing mechanism is developed, such that only the region around the solidification front has Takashi Shimokawabe to be simulated. Our simulations are run on SuperMUC, a Global Scientific Information and Computing Center supercomputer ranked number 12 in the Top500 list, using Tokyo Institute of Technology up to 32768 cores. [email protected] Martin Bauer University of Erlangen-Nuremberg Takayuki Aoki Department of Computer Science Tokyo Institute of Technology [email protected] [email protected]

Harald Koestler University Erlangen-N¨urnberg MS124 [email protected] Large-scale Multi-Phase-Field Simulation of Ab- normal Polycrystalline Grain Growth using TSUB- Ulrich J. Ruede AME2.5 GPU-Supercomputer University of Erlangen-Nuremberg Department of Computer Science (Simulation) The multi-phase-field method has attracted attention as [email protected] a very promising tool for simulating microstructure evo- lutions in polycrystalline materials. We developed a multiple-GPU computing technique that facilitate efficient MS124 3D simulations. Using the technique developed, we per- Large Scale and Massive Parallel Phase-field Simu- formed large scale 3D multi-phase-field simulations of ab- lations of Pattern Formations in Ternary Eutectic normal polycrystalline grain growth on a GPU-cluster and Systems on the TSUBAME2.5 supercomputer at the Tokyo Insti- tute of Technology. Different patterns are forming during directional solidifica- tion of ternary eutectics, depending on the physical param- Akinori Yamanaka eters, with significant influence on the mechanical proper- Tokyo Institute of Technology ties of the material. These patterns are studied with a Graduate School of Science and Engineering thermodynamic consistent phase-field model based on the [email protected] minimization of the grand potential difference, using the massive parallel framework waLBerla. We show structure Masashi Okamoto formation on large scale domains, which give rise to spi- Tokyo University of Agriculture and Technology ral growth and compare them to experiments as well as [email protected] analytic solutions. Takashi Shimokawabe Johannes H¨otzer, Marcus Jainta, Philipp Steinmetz, Global Scientific Information and Computing Center Britta Nestler Tokyo Institute of Technology Karlsruhe Institute of Technology (KIT) [email protected] Institute of Applied Materials (IAM-ZBS) [email protected], [email protected], [email protected], [email protected] Takayuki Aoki Tokyo Institute of Technology [email protected] MS124 Multi-Gpu Phase-Field Lattice Boltzmann Simula- MS125 tions for Growth and Moving of Binary Alloy Den- drite Discussion on Future Directions of Noisy Networks

Solidification microstructures are of great significance in The organizers will lead a discussion, with participation materials science and engineering. The melt convection al- from the other speakers and attendees, on the current state ways occurs in casting and greatly affects the solidification of research on analysis of networks with noise and uncer- microstructures. Meanwhile, the dendrite growth simula- tainty, and possible future directions. The discussion will tion in melt convection needs much computational cost. In focus on the implications of network noise from a theoret- this study, we accelerate the simulation by employing the ical perspective, and its impact in different applications, phase-field lattice Boltzmann method and multiple graph- including the ones presented. A key point will be the inter- ics processing unit computational scheme. The dendrite play between theory and practice in this emerging subfield CS15 Abstracts 109

of network science. [email protected], fi[email protected], [email protected], [email protected] Sanjukta Bhowmick Department of Computer Science Avanti Athreya University of Nebraska, Omaha Johns Hopkins University [email protected] Department of Applied Mathematics and Statistics [email protected] Benjamin A. Miller MIT Lincoln Laboratory [email protected] MS125 Pockets of Instability in Network Centrality Met- rics MS125 Using Consensus to Inform Stochastic Graph Ag- We discuss how the sensitivity of centrality metrics alter as gregation increasingly higher percentage of edges are altered in the network. Ideally the metric should change commensurately Learning an appropriate graph representation from noisy, with the change in network. However, we see that instead multi-source data is an area of increasing interest. We of a monotonic change, there are certain pockets of vertices present a consensus-based framework to improve the stabil- where the centrality values are stable and other pockets ity and quality of graph representations learned by stochas- where they change significantly. We also discuss how the tic graph aggregation techniques. Furthermore, we use structure of the network leads to the formation of these metrics of stability to quantify our confidence on which pockets. edges represent noise versus structure. We demonstrate the effectiveness of our framework using the Locally Boosted Vladimir Ufimtsev Graph Aggregation algorithm on a variety of synthetic and University of Nebraska, Omaha real datasets. vufi[email protected]

Layla Oesper Sanjukta Bhowmick Brown University Department of Computer Science layla [email protected] University of Nebraska, Omaha [email protected] Rajmonda Caceres Lincoln Laboratory Massachusetts Institute of Technology MS126 [email protected] Kernel-Based Image Reconstruction

In image reconstruction a central problem is the approxi- MS125 mate inversion of certain integral transforms like the Radon Statistical Inference on Errorfully Observed transform, the spherical mean transforms, or in a more gen- Graphs eral setting the Funk transform. Popular techniques for the approximate reconstruction are kernel-based interpolation For statistical inference on graphs, the existence of edges methods. This methods are easy to implement and fast is frequently based on imperfect assessment. Instead of algorithms are in many cases available. Nevertheless, the observing a graph, for each potential edge we observe a mathematical analysis of such methods is quite involved. “edge feature’ which is used to assess the presence of an We will discuss several problems regarding these proce- edge. Moreover, we face a quantity/quality trade-off: the dures and compare some kernel-based methods for image proportion of assessed potential edges decreases with the reconstruction from spherical mean value data. edge features quality. For the stochastic blockmodel, we derive the optimal quantity/quality operating point for a Frank Filbir specific inference task. Institute of Biomathematics and Biometry Helmholtz Center Munich Carey Priebe fi[email protected] Johns Hopkins University [email protected] MS126 Daniel L. Sussman A Numerical Study of the Accuracy of Divergence- Harvard University Free Kernel Approximations [email protected] We present a numerical study of the accuracy of divergence-free radial basis function interpolants in 2D and Minh Tang 3D and preliminary numerical results indicating a poly- Johns Hopkins University nomial flat limit (ε → 0). When compared to standard [email protected] interpolants, our results indicate that using a divergence- free basis improves accuracy of the derivatives in certain Joshua Vogelstein directions. In this talk, we explore strategies for improving Duke University approximations in these directions and compare accuracy [email protected] of methods based on radial kernels and multivariate poly- nomials. Vince Lyzinski, Donniell Fishkind, Nam Lee, Youngser Park Arthur Mitrano Johns Hopkins University Arizona State University 110 CS15 Abstracts

[email protected] The University of Texas at Austin [email protected]

MS126 Omar Ghattas Meshfree Computations with SPH and Vortex The University of Texas at Austin Methods [email protected]

We will provide a broad overview of Smoothed Particle Donna Calhoun Hydrodynamics (SPH) and Vortex Methods. This is fol- Boise State University lowed by a brief discussion on some of the software tools [email protected] that are being developed in our group. We will then look at recent comparisons of the vortex method and the SPH for incompressible fluid flow. This is followed by results MS127 from recent work on using SPH for gas dynamics, flood An Implicit, High-Order Accurate, Incompressible simulation, explosions, non-Newtonian fluids and Kelvin- Navier-Stokes Solver on Overlapping Grids Helmholtz instabilities. This talk describes an implicit, high-order accurate method Prabhu Ramachandran for incompressible flow combining compact spatial dis- Department of Aerospace Engineering cretizations with approximate factorization schemes and Indian Institute of Technology, Bombay geometric multigrid on overlapping grids. Efficient implicit [email protected] time discretization is achieved via a second order accu- rate approximately factored Crank-Nicolson method that MS126 incorporates the compact spatial approximations into a se- quence of fast banded solves. When used with Overture’s Reproducing Kernels in Parametric Partial Differ- high-order accurate matrix-free multigrid for the pressure ential Equations equation, our method provides an efficient high-resolution solver for LES applications. In this talk, we address the problem of approximating the solution of a parametric partial differential equation. The Kyle Chand number of parameters in the differential equation deter- Lawrence Livermore National Laboratory mines the dimensionality of the reconstruction problem. [email protected] Without any further information such problems suffer from the curse of dimensionality. The physical model expressed in the partial differential equation, however, allows in many MS127 practical situations to identity a smaller set of important Exploring Astrophysical Flows with High-fidelity parameters. The identification of these important param- Large-scale Simulations eters build also the basis for many algorithms from ma- chine learning. We will outline this connection in a spe- We present a systematic study of compressible flow prob- cific situation using problem adapted reproducing kernels. lems found in many astrophysical environments using high- Further, we will use sampling inequalities to show deter- fidelity, large-scale and multiphysics numerical simulations. ministic a priori (often exponential) convergence rates of It covers topics like developing numerical models, designing a rather large class of regularized reconstruction schemes. simulation strategies according to the code scalability, and This is partly based on joint work with M. Griebel and B. evaluating simulation results in comparisons with observa- Zwicknagl (both Bonn University). tion results. We will share our user experiences in using codes on DOE’s and NSF’s leading supercomputers and Christian Rieger our interests in improving the efficiency of parallelization Universit¨at Bonn and memory usage. Collaborative Research Centre 1060 [email protected] Min Long Department of Physics Boise State University MS127 [email protected] Recent Developments in Forest-of-octrees AMR

Forest-of-octrees AMR offers both geometric flexibility and MS127 parallel scalability and has been used in various finite ele- Runtimes and Autotuning and Hybrid, Oh My! ment codes for the numerical solution of partial differential Chombo Navigates the Waters of Exascale equations. Low and high order discretizations alike are en- abled by parallel node numbering algorithms that encapsu- Adaptive Mesh Refinement (AMR) applications require a late the semantics of sharing node values between proces- long-term sustained investment in software infrastructure sors. More general applications, such as semi-Lagrangian to create scalable solvers that are capable of utilizing the and patch-based methods, require additional AMR func- full capabilities of the largest available HPC platforms. tionalities. In this talk, we present algorithmic concepts The scalable AMR framework Chombo provides an envi- essential for recently developed adaptive simulations. ronment for rapidly assembling portable, high-performance AMR applications for a broad variety of scientific disci- Carsten Burstedde plines. In this talk, we present several levels of parallelism Universit¨at Bonn that can be exploited by Chombo to achieve scaling be- [email protected] yond petascale. These levels include threading the load handled sequentually by each MPI rank, fine-grain paral- Toby Isaac lelism within the dimensional loops, and instruction-level ICES parallelism models to make use of vector processing within CS15 Abstracts 111

a larger threading model. [email protected]

Brian Van Straalen Lawrence Berkeley National Laboratory MS128 Compuational Research Division H-to-P Efficiently: a Nektar++ Update on Com- [email protected] parisons of Cg and Hdg Since the inception of discontinuous Galerkin (DG) meth- MS128 ods for elliptic problems, there has existed a question of whether DG methods can be made more computationally Nek5000: An Environment for Scalable Algorithm efficient than continuous Galerkin (CG) methods. Fewer Development and Production Simulations degrees of freedom, approximation properties for elliptic problems together with the number of optimization tech- Nek5000 is an open source spectral element code for fluid niques, such as static condensation, available within the flow and heat transfer. As Nekton 2.0, it was the first com- CG framework made it challenging for DG methods to be mercially available software for distributed memory com- competitive until recently. However, with the introduc- puters and, with excellent strong scaling (to beyond a mil- tion of a static-condensation-amenable DG method, the lion processes) it is being used by hundreds of researchers hybridizable discontinuous Galerkin (HDG) method, it has in a variety of applications such as combustion, vascular become possible to perform a realistic comparison of CG flow modeling, stability analysis, and MHD. We discuss and HDG methods when applied to elliptic problems. In extensibility, scalability, and performance of Nek5000 in this talk, we focus on embedded manifolds, which are con- this context. sidered a valid approximation for many scientific problems ranging from the shallow water equations to geophysics. Paul F. Fischer We describe a comparison between a CG and an HDG Argonne National Laboratory numerical discretiztion in 2D, 3D and of an embedded fi[email protected] two-dimensional manifold using high-order spectral/hp el- ements.

Mike Kirby MS128 University of Utah Anisotropic Mesh Adaptation for the Many-core School of Computing Era [email protected]

Computing hardware is currently undergoing a rapid trans- formation from the historical trend of increasingly com- MS128 plex single processing units operating at ever increasing Heterogeneous Computing with a Homogeneous clock frequency, towards high numbers of low power pro- Codebase cessing units where computing throughput is achieved by increasing concurrency. The consequence for models is that It is likely that finite element codes of the future will need their constituent algorithms must be amenable to paral- to support a variety of hardware platformsincluding both lelization, otherwise the (quasi-)serial section will quickly conventional CPUs and accelerators such as GPUs. How- become the dominant computational cost. In short, algo- ever, existing implementation strategies often result in fea- rithms without a high degree of parallelism are potentially ture disparity and quickly succumb to bit-rot. In this talk facing extinction as the computational environment shifts. I will explain the approach we have taken in PyFR that Many algorithms that are important for the finite element promotes feature and performance parity across platforms method, such as matrix-vector multiply, are readily paral- with an emphasis on sustainability. lelizable on many levels and lots of effort is going into opti- Freddie Witherden, Peter E. Vincent mal strategies on a range of different types of architectures. Department of Aeronautics However, other important algorithms, such as mesh adap- Imperial College London tation, have complex data interdependencies and irregular [email protected], data access patterns. In such cases the overhead associ- [email protected] ated with parallelization can easily outweigh the gains. In this talk we describe the challenges, and solutions, for par- allelizing anisotropic mesh adaptation. Previous work in MS129 this field has mostly been limited to domain decomposi- A Comparative Analysis of of Asynchronous Many tion methods implemented using MPI. As more finite ele- Task Programming Models for Next Generation ment codes are capable of running in a mixed MPI-thread Platforms parallel mode, mesh it is necessary for mesh adaptation to also exploit thread level parallelism. We find that domain Next generation platform architectures will require a fun- decomposition methods are not particularly successful for damental shift in programming models due to a combina- thread parallelism for this class of problem. Instead, a tion of factors including extreme parallelism, data locality boarder range of parallelization strategies specifically de- issues (for managing both performance and energy usage), signed for irregular computation must be adopted. Per- and resilience. The asynchronous, many-task programming formance analysis shows that fast scalable performance is model is emerging as a leading new paradigm to address achieved but there are still room for improvement. We will these issues, with many variants of this new model being consider what novel trends in parallel programming models proposed. This talk surveys some of the leading proposed and hardware might create new opportunities runtimes, highlighting their key design decisions, strengths, and weaknesses. Gerard J Gorman Department of Earth Science and Engineering Janine C. Bennett Imperial College London Sandia National Laboratories 112 CS15 Abstracts

[email protected] Abhishek Bagusetty Chemical Engineering H. Kolla University of Utah SNL [email protected] [email protected]

Jeremiah Wilke, Keita Teranishi MS130 Sandia National Laboratories Weno Finite Volume Methods for Embedded [email protected], [email protected] Boundary Grids

Nicole Slattengren We discuss the discretization of hyperbolic conservation Sandia National Labs laws on Cartesian grids with embedded boundaries. For [email protected] the regular part of the mesh (i.e., away from the cut cells), we use a high order accurate WENO finite volume method Greg Sjaardema, Samuel Knight with Runge-Kutta time stepping. The cut cells are up- Sandia National Laboratories dated using an appropriate version of the h-box method. [email protected], [email protected] Christiane Helzel Department of Mathematics MS129 Ruhr-University-Bochum Structured Dagger: Supporting Asynchrony with [email protected] Clarity

Abstract not available at time of publication. MS130 DiffusionMRIonaCartesianGridwithImmersed Jonathan Lifflander Interfaces University of Illinois jliff[email protected] Diffusion MRI measures the diffusion of water in biological tissue. To simulate the diffusion MRI signal, it is impor- MS129 tant to accurately describe the geometry of the biological cells and cell membranes. We discretize this problem on Using Multiple Dags to Ensure Portability and a Cartesian grid and model cell membranes by interfaces Scalability in Large Scale Computations Using Uin- that are not necessarily aligned with the computational tah grid. This results in a method that correctly accounts for Computational modeling of the hazards posed by thou- the interface surface area, which has a strong influence on sands of explosive devices during a Deflagration to Deto- simulation results. nation Transition (DDT),requires petascale computing re- sources to resolve the spatial and temporal scales present. Khieu Van Nguyen The resulting scalable software is now capable of determin- Neurospin, CEA, Saclay, France ing how the boosters, which should have just deflagrated, [email protected] interacted to detonate. Preliminary results of the full scale simulation are shown and the broader scalability lessons Jing-Rebecca Li for codes at this scale are discussed. INRIA Saclay [email protected] John A. Schmidt SCI Institute Luisa Ciobanu University of Utah Neurospin, CEA, Saclay, France [email protected] [email protected]

MS129 MS130 A DAG Approach to Tame Complexity in Multi- physics Software on Heterogeneous Architectures High-Order Quadrature on Implicitly Defined Do- mains with Application to a High-Order Embed- Abstract Directed acyclic graphs (DAGs) provide an ef- ded Boundary Discontinuous Galerkin Method for fective abstraction to effectively handle complexity arising Evolving Interface Problems from both hardware as well as physics. This talk addresses our usage of DAGs to dynamically assemble algorithms for We present a high-order accurate (order 2p) numerical highly complex, multiphysics problems. We also discuss quadrature algorithm for evaluating integrals on implicitly- how we are using DAGs to deploy these complex simula- defined domains - suitable for, e.g., cut-cell finite element tions on hybrid architectures such as CPU-GPU systems methods in which the mesh is implicitly generated by em- where overlapping computation with host-device transfers bedding the domain in a Cartesian grid. The algorithm is of critical importance. Finally, we discuss other key as- naturally lends itself to a class of high-order discontinu- pects of our DAG approach including automated memory ous Galerkin methods (”tiny” cells are merged with neigh- reuse, thread-pooling, etc. bours) - we show some examples ranging from Poisson problems to multiphase incompressible fluid flow. James C. Sutherland Department of Chemical Engineering Robert Saye The University of Utah Dept. of Mathematics [email protected] University of California, Berkeley CS15 Abstracts 113

[email protected] Lois Curfman McInnes Mathematics and Computer Science Division Argonne National Laboratory MS130 [email protected] Terrain Following Versus Cut-Cells

A finite volume model is described with the same numerics MS131 for cut-cells and terrain-following layers. The model has The Future of CSE Education curl-free pressure gradients which eliminate the horizontal pressure gradient error. Some clean comparisons between This presentation will continue the discussion of the main cut-cells and terrain-following layers are made and, on tests ideas presented in the draft white paper on ”Future Direc- in which the flow interacts with the orography, the terrain- tions in CSE Education and Research”. It will focus on the following layers give better accuracy whereas the cut-cells future of CSE education, including expectations for gradu- can excite the computational mode of the Lorenz grid. ate degree outcomes, workforce development, and changes in educational infrastructure. Feedback will be solicited Hilary Weller from the broad CSE community. University of Reading, UK [email protected] Karen E. Willcox Massachusetts Institute of Technology James Shaw [email protected] University of Reading [email protected] Hans De Sterck University of Waterloo Applied Mathematics MS131 [email protected] Community feedback and discussion

This session will continue to solicit feedback and discussion MS132 from the CSE community on ”Future Directions in CSE Topological Sensitivity Analysis in Systems Biology Education and Research”. Mathematical models of natural systems are abstractions Hans De Sterck of much more complex processes. There are often many University of Waterloo potential models consistent with our existing knowledge Applied Mathematics and experimental data, so it is critical to understand the [email protected] impact of assumptions inherent to a selected model. Our method evaluates the dependence of inferences on the as- Ulrich J. Ruede sumed model structure. Failing to consider this structural University of Erlangen-Nuremberg uncertainty, as is often done in practice, can give rise to Department of Computer Science (Simulation) misleading conclusions. [email protected] Ann C. Babtie Lois Curfman McInnes Theoretical Systems Biology Mathematics and Computer Science Division Imperial College London Argonne National Laboratory [email protected] [email protected] Paul Kirk, Michael Stumpf Karen E. Willcox Imperial College London Massachusetts Institute of Technology Theoretical Systems Biology [email protected] [email protected], [email protected]

MS131 MS132 The Future of CSE Research Bayesian Updating for Dynamic Systems Using Subset Simulation (Beck) and Active Model Selec- This presentation will give an overview of the main points tion (Busetto) addressed in the draft white paper on ”Future Directions in CSE Education and Research”. It will comment on the First part by Prof. Beck: A new approximate Bayesian rapid expansion of CSE since the beginning of the 21st computation algorithm, ABC-SubSim, is presented and ap- century and the challenges the CSE field is encountering plied for Bayesian updating of model parameters. It uses in the context of recent disruptive developments that in- the Subset Simulation algorithm of Au and Beck (2001), a clude extreme-scale computing, data-driven discovery, and very efficient multi-level MCMC rare-event sampler. Sec- a comprehensive broadening of the application fields of ond part by Prof. Busetto: A method for active approx- CSE. The presentation will focus on the future of CSE imate inference of nonlinear dynamical systems is intro- research and will solicit feedback from the broad CSE com- duced, and its concrete results are discussed. The method munity. is computationally efficient and provides formal guarantees of near-optimal informativeness. Ulrich J. Ruede University of Erlangen-Nuremberg AlbertoGiovanni Busetto Department of Computer Science (Simulation) UCSB [email protected] [email protected] 114 CS15 Abstracts

James Beck Pdes with Random Inputs Division of Engineering and Applied Science California Institute of Technology By employing a hierarchy of both spatial approximations [email protected] and interpolations in stochastic parameter space, we de- velop a multilevel version of stochastic collocation meth- ods for random partial differential equations, leading to a MS132 significant reduction in computational cost. We provide a Bayesian Inference of Chemical Kinetic Models convergence and cost analysis of the new algorithm, and from Proposed Reactions demonstrate the gains possible on a typical random diffu- sion model problem. We present a new framework for tractable Bayesian infer- ence of chemical kinetic models in case of a large number Aretha Teckentrup of model hypotheses generated from a set of proposed reac- University of Bath tions. The approach involves imposing point-mass mixture [email protected] priors over rate constants and exploring the resulting pos- terior distribution using an adaptive Markov chain Monte Peter Jantsch Carlo method. We show that further gains in sampling ef- University of Tennessee ficiency can be realized by analyzing the chemical network [email protected] structure in order to reduce the space of MCMC explo- ration. Max Gunzburger Florida State University Nikhil Galagali,YoussefM.Marzouk School for Computational Sciences Massachusetts Institute of Technology [email protected] [email protected], [email protected] Clayton G. Webster MS132 Oak Ridge National Laboratory [email protected] Advanced Bayesian Computation for Challenging Problems in the Sciences and Engineering MS133 Bayesian approaches to Uncertainty Quantification rely on efficient Markov chain Monte Carlo methods especially for Hierarchical Acceleration of Stochastic Collocation models based on large systems of partial differential equa- Methods for PDEs with Random Input Data tions. This talk will present recent work on exploiting (1) Feynman-Kac identities defining the duality between nu- We will present an approach to adaptively accelerate a se- merical deterministic and stochastic (probabilistic) meth- quence of hierarchical interpolants required by a multilevel ods in obtaining solutions of certain classes of partial dif- sparse grid stochastic collocation (aMLSC) method. Tak- ferential equations, and (2) surrogate geometric structures ing advantage of the hierarchical structure, we build new in defining Markov transition kernels on symplectic mani- iterates and improved pre-conditioners, at each level, by us- folds. An illustration with shallow water models for global ing the interpolant from the previous level. We also provide climate models. rigorous complexity analysis of the fully discrete problem and demonstrate the increased computational efficiency, as Mark Girolami well as bounds on the total number of iterations used by University College London the underlying deterministic solver. [email protected] Guannan Zhang,ClaytonG.Webster Oak Ridge National Laboratory MS133 [email protected], [email protected] Multilevel Simulation of Mean Exit Times

Existing methods achieve ε RMS accuracy for the compu- MS134 tation of mean exit times for very general Brownian diffu- The Cost of Reliability: Iterative Linear Solvers sions, at a cost which is O(ε−3) for a large class of SDEs us- and Reactive Fault Tolerance ing the Euler-Maruyama discretisation. We present a new multilevel Monte Carlo method which achieves the same We analyze several soft fault models and reactive ap- result with a cost which is O(ε−2(log |ε|)3). This work re- proaches that may be used given a restarted solver or lies heavily on theoretical results derived by E. Gobet and nested solver. Assuming some portion of the solver re- others, and is supported by numerical experiments. quires reliability, we analyze the costs of reliable and unre- liable computations. We evaluate these costs given various MichaelB.Giles parameters to the solvers’ reactive fault tolerance. Mathematical Institute Oxford University James Elliott [email protected] North Carolina State University [email protected] Francisco Bernal Instituto Superior Tecnico, Portugal Mark Hoemmen fco [email protected] Sandia National Laboratories [email protected]

MS133 Frank Mueller A Multilevel Stochastic Collocation Method for North Carolina State University CS15 Abstracts 115

[email protected] Inria Bordeaux Sud-Ouest Joint Inria-CERFACS lab on HPC [email protected] MS134 Inherent Error Resilience of a Complex Moment- Emrullah Fatih Yetkin Based Eigensolver Inria [email protected] In this talk, we consider error resilience property of a com- plex moment-based parallel eigensolver for solving gener- alized eigenvalue problems. We show that the eigensolver MS135 with sufficient subspace size can achieve high accuracy for Model Calibration and Error Propagation for target eigenpairs, even if soft-errors like bit-flip occur in the Large-Eddy Simulation of Turbulent Flows most time-consuming part of the eigensolver. This prop- erty provides an inherent error resilience of the eigensolver We hypothesize that turbulence simulations of engineering that does not require checkpointing and replication tech- applications can be made affordable on the design time- niques. scale by improving model calibration and error estimation. This study considers a Bayesian calibration approach fol- Akira Imakura, Yasunori Futamura, Tetsuya Sakurai lowed by forward uncertainty quantification. Model pa- Department of Computer Science rameters are calibrated with DNS of isotropic turbulence University of Tsukuba and are then tested in an LES turbulent channel flow con- [email protected], futa- figuration. Polynomial Chaos expansions are used for ef- [email protected], [email protected] ficient propagation of uncertainties from input model pa- rameters to output quantities of interest.

MS134 Myra Blaylock, Cosmin Safta Analysis of Krylov Solver Resilience in the Pres- Sandia National Laboratories ence of Soft-Faults [email protected], [email protected] Convergence rates of Krylov iterative solvers are consid- Stefan P. Domino ered in the context of soft silent faults encountered in mod- Sandia. National Laboratories ern supercomputers. We propose an analytic hardware ag- [email protected] nostic fault model based on selective reliability, that can provide rigorous answers to important resilience questions. We prove convergence for a class of Krylov methods, where John C. Hewson, Jeremy Templeton the original iteration is coupled with periodic restarts (e.g., Sandia National Laboratories restarted GMRES). In addition, we derive optimal restart [email protected], [email protected] strategy that minimizes the resilience overhead.

Miroslav Stoyanov MS135 Oak Ridge National Lab Predictive Rans Simulations Via Bayesian Model- [email protected] Scenario Averaging

Clayton G. Webster The turbulence closure model is the dominant source of Oak Ridge National Laboratory error in Reynolds Averaged Navier-Stokes simulations, yet [email protected] no reliable estimators exist for this error component. Here we develop a stochastic, a posteriori error estimate, based on variability in model closure coefficients across multiple MS134 flow scenarios, for multiple closure models. The variabil- On the Reliability of Soft Error Detection in CG- ity is estimated using Bayesian Model-Scenario Averaging POP (BMSA), and used to obtain an stochastic solution esti- mate in an unmeasured (prediction) scenario. Soft errors that are not detected by hardware mechanisms may be extremely complex to detect at the software layer. Richard Dwight One option is to perform a full duplication of the compu- Delft University of Technology tation (and data) and check on a regular basis that inter- [email protected] mediate results are consistent. However, this mechanism may be prohibitive. In the context of CG solver, the most Wouter Edeling prohibitive operation to duplicate is SpMV. To avoid the TU Delft duplication of this operation, checksum mechanisms may [email protected] be employed. In this presentation, we investigate the relia- bility of such an approach in finite precision arithmetic. We Paola Cinnella illustrate our discussion with the CGPOP code, a miniapp ENSAM, ParisTech for performing the CG within the Parallel Ocean Program [email protected] (POP), which is a candidate for exascale climate simula- tions. MS135 Agullo Emmanuel Accounting for Model Error in the Calibration of Inria Physical Models [email protected] It is important to account for model error in the fitting of Luc Giraud physical models to data. In this talk, we discuss avail- 116 CS15 Abstracts

able Bayesian methods for accounting for model errors, as the 2D Cahn-Hilliard, and the Fitzhugh-Nagumo equa- highlighting the calibration of models of physical systems. tions. We introduce a Bayesian calibration framework, relying on probabilistic embedding of the error within the model, Andrew J. Christlieb allowing clear disambiguation of measurement errors and Michigan State Univerity model structural errors. The method is demonstrated in Department of Mathematics the calibration of chemical kinetic rate parameters. [email protected]

Habib N. Najm Matthew Causley Sandia National Laboratories Kettering University Livermore, CA, USA [email protected] [email protected] Hana Cho Khachik Sargsyan Michigan State University Sandia National Laboratories [email protected] [email protected]

Roger Ghanem MS136 University of Southern California Generalized Structure Additive Runge-Kutta Aerospace and Mechanical Engineering and Civil Methods Engineering [email protected] This presentation discusses a general structure of the ad- ditively partitioned Runge-Kutta methods by allowing for different stage values as arguments of different components MS135 of the right hand side. An order conditions theory is devel- Bayesian Model Calibration Techniques That In- oped for the new family of generalized additive methods, corporate Mixed Effects and Model Discrepancy and stability and monotonicity investigations are carried out. The new family, named GARK, introduces additional Measurement errors, model discrepancies, and variability flexibility when compared to traditional partitioned Runge- due to differing experimental conditions can produce un- Kutta methods, and therefore offers additional opportuni- certainty in model parameters estimated through Bayesian ties for the development of flexible solvers for systems with model calibration techniques. In many cases, model dis- multiple scales, or driven by multiple physical processes. crepancies and variability among data sets are neglected during model calibration. However, this can yield non- Adrian Sandu physical parameter values and produce prediction inter- Virginia Polytechnic Institute and vals that are inaccurate in the sense that they do not in- State University clude the correct percentage of future observations. In this [email protected] presentation, we discuss techniques to quantify model dis- crepancies and mixed effects due to multiple data sets in Michael Guenther a manner that yields physical parameters and correct pre- Bergische Universitaet Wuppertal diction intervals. We illustrate aspects of the framework [email protected] in the context of distributed models with highly nonlinear parameter dependencies. MS136 Brian Williams Efficient Exponential Integrators: Construction, Los Alamos National Laboratory Analysis and Implementation [email protected] We will provide an overview of the latest advances in ex- Kathleen Schmidt ponential integrators. In particular, we will discuss the ex- North Carolina State University ponential propagation iterative (EPI) methods framework [email protected] and describe different classes of these integrators such as the unsplit, split, hybrid and implicit-exponential methods. Construction of the exponential methods using both clas- Ralph C. Smith sical and stiff order conditions will be discussed. We will North Carolina State Univ also present the new software package that provides im- Dept of Mathematics, CRSC plementation of exponential schemes for serial and parallel [email protected] computing platforms.

Mayya Tokman MS136 University of California, Merced Resolvent Expansions for Higher-order Simulations School of Natural Sciences of PDEs [email protected]

By casting the solution to a PDE in terms of pseudo- differential operators, we leverage the use of resolvent ex- MS136 pansions, in combination with successive convolution, to K-Methods, An Extension of Exponential and arrive at high order time accurate solutions for both linear Rosenbrock Time Integrators and nonlinear PDEs. This class of solvers has the advan- tage that it naturally leads to a line-by-line approach that We present a new class of time integration schemes, so is well-suited to multi-core GPU computing. We consider called K-methods. We discuss the derivation of order several common examples to illustrate our method, such conditions for Rosenbrock-K and exponential-K methods. CS15 Abstracts 117

These schemes consider the time integration and the ap- figurations for nematic liquid crystals with applied electric proximation of linear system solutions, in the case of fields. The method targets minimization of system free Rosenbrock-K, or the approximation of matrix exponential energy based on the electrically augmented Frank-Oseen vector products, in the case of exponential-K, as a single free-energy model. We demonstrate the well-posedness of computational process. We also give some numerical re- the associated intermediate, discrete, linearization systems. sults showing favorable scalability properties for parallel Numerical simulations involving heterogenous constant co- implementations. efficients for both classical and complicated boundary con- ditions, relevant in ongoing research, are discussed and sup- Paul Tranquilli, Adrian Sandu port the established theory. Virginia Polytechnic Institute and State University David B. Emerson [email protected], [email protected] Tufts University Department of Mathematics Ross Glandon [email protected] Virginia Tech [email protected] James H. Adler Tufts University [email protected] MS137 Quantity-of-Interest Based Least-Squares Finite Scott Maclachlan Element Methods Department of Mathematics Tufts University We present an approach to augment least-squares finite el- [email protected] ement formulation with a user-specified quantity of inter- est (QoI). The method inherits the global approximation Timothy Atherton properties of the standard least squares formulation with Tufts University increased resolution of the QoI. We establish theoretical Department of Physics properties such as optimality and enhanced convergence [email protected] under a set of general assumptions. We also present an adaptive approach that results in approximations which possess high accuracy in global norms as well as in the QoI. MS137 Several numerical experiments are presented to support the Energy Laws and First-Order System Least theory and highlight the effectiveness of our methodology. Squares for MHD systems Jehanzeb H. Chaudhry Florida State University Energy principles play a crucial role in understanding the interactions and coupling between different scales or phases [email protected] in a physical system. This motivates one to investigate how well various discretization methods preserve the en- Thomas Manteuffel ergy laws associated with PDEs. We discuss this ques- University of Colorado tion in the context of First-Order System Least Squares [email protected] (FOSLS) finite element method applied to time-dependent heat equation and the equations of magnetohydrodynam- Luke Olson ics (MHD). Our study involves numerical experiments and Department of Computer Science some theoretical considerations. University of Illinois at Urbana-Champaign [email protected] Ilya Lashuk Georgia Institute of Technology Eric C. Cyr [email protected] Scalable Algorithms Department Sandia National Laboratotories James H. Adler [email protected] Tufts University [email protected] Kuo Liu Department of Applied Mathematics Scott Maclachlan University of Colorado at Boulder Department of Mathematics [email protected] Tufts University [email protected] Lei Tang Department of Applied Mathematics Ludmil Zikatanov University of Colorado-Boulder Pennsylvania State University [email protected] [email protected]

MS137 MS137 An Energy-Minimization Finite-Element Approach Nested Iteration and First-Order System Least for the Frank-Oseen Model of Nematic Liquid Squares for Preconditioning a Two-Fluid Electro- Crystals magnetic Plasma Model

We present an energy-minimization finite-element ap- A two-fluid plasma (TFP) model is presented both as a proach to the computational modeling of equilibrium con- stand-alone solver and as the preconditioner to a fully im- 118 CS15 Abstracts

plicit particle-in-cell (PIC) simulation. The model cou- [email protected] ples fluid conservation equations for ions and electrons to Maxwell’s equations. A Darwin approximation of Maxwell Francesco Rizzi, Khachik Sargsyan, Karla Morris is used to eliminate spurious light waves. After scaling Sandia National Laboratories and modification, the TFP-Darwin model yields a nonlin- [email protected], [email protected], ear, first-order system of equations whose Fr´echet deriva- [email protected] tive is shown to be uniformly H1-elliptic. This system is addressed numerically by nested iteration (NI) and a Bert J. Debusschere First-Order System Least Squares (FOSLS) discretization. Energy Transportation Center Numerical tests demonstrate the efficacy of this approach, Sandia National Laboratories, Livermore CA yielding an approximate solution within discretization er- [email protected] ror in a relatively small number of computational work units (WU). Omar M. Knio Chris Leibs Duke University University of Colorado Boulder [email protected] [email protected]

Thomas Manteuffel MS138 University of Colorado A Multilevel Solution Strategy for the Stochastic [email protected] Galerkin Method for PDEs with Random Coeffi- cients MS138 The stochastic Galerkin method for solving partial differ- Hierarchically Accelerated Stochastic Collocation ential equations (PDEs) with random coefficients yields for Random PDEs highly accurate numerical solutions yet can be compu- tationally demanding. In this talk, we present a multi- Stochastic collocation methods for partial differential equa- level approach to alleviate some of the prohibitive com- tions with high-dimensional random inputs generate large putational cost in the stochastic Galerkin method. Sim- collections of linear equations, and solving these linear sys- ilar multilevel methods have been successfully applied to tems is the dominant cost in the construction of an ap- Monte Carlo approaches and stochastic collocation meth- proximate solution. Interpolation on sequences of nested ods. We present numerical results for the proposed collocation nodes provides a natural multilevel hierarchy of multilevel method compared to the standard single-level sample points; thus, in this talk we present an accelerated method. method which utilizes this hierarchical structure to pro- vide linear solvers with improved initial guesses and strong, cheap preconditioners. For a standard elliptic model prob- Sarah Osborn lem we derive a priori estimates on the savings and compu- Texas-Tech University tational cost of constructing an approximate solution using [email protected] hierarchical acceleration. Victoria Howle Peter Jantsch Texas Tech University of Tennessee [email protected] [email protected] Jonathan J. Hu Diego Galindo, Clayton G. Webster, Guannan Zhang Sandia National Laboratories Oak Ridge National Laboratory Livermore, CA 94551 [email protected], [email protected], [email protected] [email protected]

Eric Phipps MS138 Sandia National Laboratories Parametric Uncertainty Propagation in Resilient Optimization and Uncertainty Quantification Department Domain Decomposition Methods [email protected] One challenging aspect of extreme scale computing con- cerns combining uncertainty quantification methods with MS138 resilient PDE solvers. We present and compare different approaches of propagating parametric uncertainty in re- Exploring Embedded Uncertainty Quantification silient domain decomposition methods. In such methods, Methods on Next-Generation Computer Architec- the PDE is solved on many subdomains whose boundary tures conditions become the unknowns of a global problem. We illustrate the implementation of the algorithms in light of We explore approaches for improving the performance of results obtained for a diffusion equation with an uncertain uncertainty quantification methods on emerging computa- diffusivity field. tional architectures. Our work is motivated by the trend of increasing disparity between floating-point throughput Paul Mycek and memory access speed. We describe rearrangements of Duke University classical uncertainty propagation methods leading to im- [email protected] proved memory access patterns and increased fine-grained parallelism. We then measure the resulting performance Olivier P. Le Maitre improvements on emerging multicore architectures in the LIMSI-CNRS context of computing solutions to PDEs with uncertain in- CS15 Abstracts 119

put data. davidsal@buffalo.edu

Eric Phipps Sandia National Laboratories MS139 Optimization and Uncertainty Quantification Department Towards Experimental Design Strategies for Inad- [email protected] equate Models

H. Carter Edwards Obtaining informative measurements is a fundamental Sandia National Laboratories problem when inadequate models are used to guide the de- [email protected] sign of experiments. The focus of this study is to develop a basic understanding of the impact that modeling errors have on experimental design strategies. Through a rigorous Jonathan J. Hu modeling of structural errors, new adaptive experimental Sandia National Laboratories design strategies can be obtained by exploiting structural Livermore, CA 94551 uncertainty. The feasibility of the proposed methodology [email protected] is demonstrated in the context of contaminant dispersion models.

MS139 Gabriel Terejanu Robust Optimization for Decision Making under University of South Carolina Uncertainty [email protected]

We present the derivative free trust-region algorithm Xiao Lin NOWPAC for solving nonlinear constrained optimization University of South Carolina problems. In this context we address optimization prob- University of South Carolina lems that are subject to two sources of uncertainties. First [email protected] are uncertainties inherent to the constraints and objective function, yielding problems of robust optimization. Second are uncertainties stemming from computational inaccura- MS140 cies in function evaluations; to detect these situations, we A Computational Model of Sperm Motility introduce a noise indication tool. We show results for a Through Viscoelastic Networks groundwater flow application. Elastic polymers and filamentous networks within a fluid Florian Augustin,YoussefM.Marzouk environment are ubiquitous. Mammalian sperm, for exam- Massachusetts Institute of Technology ple, must navigate through the highly heterogeneous envi- [email protected], [email protected] ronment of layers of viscoelastic networks. We present a discrete model of such a network coupled to a Stokes flow using the method of regularized Stokeslets. The network MS139 consists of links made of springs and dashpots (typical vis- Comparison of Laminar Flame Models in the Pres- coelastic elements). The results show the network effects ence of Uncertainty on the swimming patterns of the microorganism.

In this work, we study one-dimensional and two- Jacek Wrobel dimensional laminar flame models using Bayesian infer- Department of Mathematics, Tulane University ence. In particular, existing experimental data is used to Center for Computational Science calibrate, in the Bayesian sense, parameters in chemical ki- [email protected] netics mechanisms used in the laminar flame models. Both kinetics and diffusion models are varied. The evidence is Ricardo Cortez computed and the plausibility of the various models as- Tulane University sessed. Mathematics Department [email protected] Paul Bauman Mechanical and Aerospace Engineering Lisa J. Fauci University at Buffalo, State University of New York Tulane University pbauman@buffalo.edu Department of Mathematics [email protected] MS139 Liposome Vesicles in the Presence of Uncertainty MS140 Mathematical Modeling of Blood Clot Formation Liposome vesicles are artificially created vesicles and form Under Flow a model system for more complicated biological cells, such as red blood cells. To date, models of vesicles have been Vascular injury triggers two intertwined processes, platelet deterministic in nature. Recent work has demonstrated deposition and coagulation, and can lead to the forma- that thermal fluctuations and the variability of material tion of a blood clot that may grow to occlude a ves- parameters play an important role in vesicle behavior. This sel. Formation of the clot involves complex biochemical, talk will discuss the application of statistical approaches to biophysical, and biomechanical interactions that are also vesicle simulations. dynamic and spatially-distributed, and occur on multi- ple spatial and temporal scales. We previously developed David Salac a spatial-temporal mathematical model of these interac- University at Buffalo - SUNY tions and looked at the interplay between physical factors 120 CS15 Abstracts

(flow, transport to the clot, platelet distribution within the ing can be applied in communication-avoiding Lanczos- blood) and biochemical ones in determining the growth of based Krylov methods. We derive deflated communication- the clot. Recently, we extend this model to include re- avoiding CG, which is mathematically equivalent to de- duction of the advection and diffusion of the coagulation flated CG of Saad et al. [SIAM J. Sci. Comput., 21 (2000), proteins in regions of the clot with high platelet number pp.1909–1926], but performs asymptotically less commu- density. The effect of this reduction, in conjunction with nication. Numerical examples and performance modeling limitations on fluid and platelet transport through dense reveal complex, problem- and machine-dependent tradeoffs regions of the clot, can be profound. Our results suggest a between convergence rate and time per iteration. We dis- possible physical mechanism for limiting clot growth. cuss applications for which speedups can be obtained using this approach. Karin Leiderman Applied Mathematics Erin C. Carson, Nicholas Knight UC Merced UC Berkeley [email protected] [email protected], [email protected]

James W. Demmel MS140 University of California Experiment-Driven Surfactant Spreading Models Division of Computer Science [email protected] Surfactants are chemicals that lower surface tensions. They are used in many industrial applications as cleaners or sta- bilizers, but are also present in biological arenas such as the MS141 tear film of the eye and in the lungs. Surfactant spread- ing models often rely on an equation of state relating sur- Enlarged Krylov Subspace Methods for Reducing factant concentration to surface tension. To make math- Communication ematical analysis more tractable, models have often em- ployed simple functional relationships. However, to model In this talk we will describe enlarged Krylov subspace an experiment with a given fluid and surfactant, a phys- methods. From a partitioning of the input matrix into t ically meaningful equation of state can be derived from subdomains, these methods are based on adding t new vec- experimentally obtained isotherms. We compare model tors to the Krylov subspace at each iteration, instead of one and experiment for NBD-PC lipid (surfactant) spreading vector in classic methods. The new enlarged search space on glycerol for an empirically-determined equation of state, contains the classical Krylov search space based on the ini- and compare those results to simulations with traditionally tial residual, and hence the novel methods converge at least employed functional forms. In particular we compare the as fast as Classical CG in exact precision arithmetic. We timescales by tracking the leading edge of surfactant, the will discuss parallel versions that reduce communication, central fluid height and dynamics of the Marangoni ridge. and show that the methods converge at least as fast as We consider both outward spreading of a disk-shaped re- Classical CG in exact precision arithmetic. The conver- gion of surfactant and the hole-closure problem in which a gence results show that they also converge faster than CG disk-shaped surfactant-free region self-heals. in finite precision arithmetic. Rachel Levy Laura Grigori Harvey Mudd College INRIA [email protected] France [email protected]

MS140 Sophie Moufawad A Multi-Moment Approach to Modeling the Onset LRI - INRIA Saclay, France of Vortex Merger [email protected] We use a low order model to understand how two co- Frederic Nataf rotating vortices transition from a quasi-steady distance Laboratoire J.L. Lions from each other to convective merger. Experiments and [email protected] computations have shown that this rapid phenomena oc- curs after diffusion causes the vortex core size to exceed some critical fraction of the separation distance. This MS141 model was derived from the recently developed Multi- Moment Vortex Method and provides several physical in- Preconditioning Communication-Avoiding Krylov sights as well as pins down what causes the very initial Methods onset of convective merger. Krylov subspace projections methods are important for David T. Uminsky solving large-scale linear system of equations. Recent im- University of San Francisco provements in a communication avoiding s-step Krylov Department of Mathematics methods are important to the scalability of this approach [email protected] in future architectures. A key missing piece of these improvements are robust preconditioners for the s-step Krylov methods. We present a preconditioner framework, MS141 based on domain decomposition, to precondition s-step Efficient Deflated-Based Preconditioning for the Krylov methods without additional communication. We Communication-Avoiding Conjugate Gradient will present results on a hybrid CPU/GPU cluster. Method Siva Rajamanickam In this work, we demonstrate that deflation precondition- Sandia National Laboratories CS15 Abstracts 121

[email protected] North Carolina State University [email protected]

MS141 C.T. Kelley Hierarchical and Nested Krylov Methods for North Carolina State Univ Extreme-Scale Computing Department of Mathematics tim [email protected] We present hierarchical Krylov methods and nested Krylov methods to overcome the scaling difficulties for eigenvalue problems on extreme-scale computers. The work is inspired Andrew Salinger by our previous work for linear systems and the arising ap- CSRI plications. We demonstrate the impact at high core counts Sandia National Labs on the target applications. Because these algorithms can [email protected] be activated at runtime via the PETSc library, application codes that employ PETSc can easily experiment with such MS142 techniques. Accelerating the EM Algorithm for Mixture- Hong Zhang density Estimation MCS, Argonne National Laboratory The EM algorithm is widely used for numerically approx- [email protected] imating maximum-likelihood estimates in the context of missing information. This talk will focus on the EM al- Lois Curfman McInnes gorithm applied to estimating unknown parameters in a Mathematics and Computer Science Division (finite) mixture density, i.e., a probability density function Argonne National Laboratory (PDF) associated with a statistical population that is a [email protected] mixture of subpopulations, using “unlabeled” observations on the mixture. In the particular case when the subpopu- lation PDFs are from common parametric families, the EM MS142 algorithm becomes a fixed-point iteration that has a num- Anderson Acceleration: Convergence Theory and ber of appealing properties. However, the convergence of Numerical Experience the iterates is only linear and may be unacceptably slow if the subpopulations in the mixture are not “well-separated” In this talk I will begin with a description of Anderson in a certain sense. In this talk, we will review the EM al- acceleration and some motivating applications. This part gorithm for mixture densities, discuss applying Anderson of the talk should get anyone up-to-speed on the topic of acceleration to improve the convergence of the iterates, and the mini symposium I will state some new convergence and report on numerical experiments. close with a report on numerical experiments. Joshua H. Plasse, Homer F. Walker C.T. Kelley,AlexToth Worcester Polytechnic Institute North Carolina State Univ [email protected], [email protected] Department of Mathematics tim [email protected], [email protected] MS142 MS142 Anderson Acceleration for Parallel Applications On the Performance of Anderson Acceleration for Anderson acceleration has demonstrated significant ben- Multiphysics Problems efits in accelerating fixed point solutions in a number of applications. The method, however, adds new synchro- Anderson Acceleration (AA) has recently garnered atten- nization points that can slow down its use in parallel. In tion as an alternative to Picard and Newton-based nonlin- this presentation, we will examine the parallel communica- ear solution algorithms. This talk will discuss the efficiency tion requirements of Anderson acceleration and discuss its and robustness of the method compared to the traditional performance for parallel application. In addition, we will solution techniques. Examples will be drawn from produc- discuss use of communication-avoiding ideas within the An- tion simulation codes used for nuclear reactor core simula- derson acceleration algorithm and show results on model tion, magnetohydrodynamics and ice sheet modeling. We problems as well as a large-scale application. This work will additionally discuss augmentations to the general al- was performed under the auspices of the U.S. Department gorithm to improve performance. of Energy by Lawrence Livermore National Laboratory un- Roger Pawlowski der Contract DE-AC52-07NA27344. Lawrence Livermore Multiphysics Simulation Technologies Dept. National Security, LLC. Sandia National Laboratories John Loffeld [email protected] University of California Merced Steven Hamilton loff[email protected] ORNL [email protected] Carol S. Woodward Lawrence Livermore Nat’l Lab Mark Berrill [email protected] Oak Ridge National Laboratory [email protected] MS143 Alexander R. Toth Solution of the Full Waveform Inversion Problems 122 CS15 Abstracts

via Projection based Reduced Order Models Virginia Tech [email protected] Often discrete measurements of transfer functions in the time or frequency domains can be equivalently transformed Serkan Gugercin to projection based ROMs for the underlying PDEs. We Virginia Tech. use such ROMs for the numerical solution of the inverse hy- Department of Mathematics perbolic problems. Justification of our approach is based [email protected] on an intriguing connection of the ROMs with the discrete Krein-Marchenko-Gelfand-Levitan method. We show ap- plications to the time-domain full waveform inversion on Christopher A. Beattie an example of Marmousi model of seismic exploration in Virginia Polytechnic Institute and State University 2D. [email protected]

Vladimir L. Druskin Eric De Sturler Schlumberger-Doll Research Virginia Tech [email protected] [email protected]

Alexander V. Mamonov Misha E. Kilmer University of Texas at Austin Tufts University [email protected] [email protected]

Mikhail Zaslavsky Schlumberger-Doll Research MS143 [email protected] Efficiencies in Global Basis Approximation for Model Order Reduction in Diffuse Optical Tomog- raphy MS143 An Efficient Output Error Bound for Model Or- We consider the nonlinear inverse problem of reconstruct- der Reduction of Parametrized Nonlinear Evolu- ing parametric images of optical properties from diffuse tion Equations optical tomographic data. Recent work shows MOR tech- niques have promise in mitigating the computational bot- We present an efficient a posteriori output error bound for tleneck associated with solving for the parameters. In this model order reduction of parametrized (nonlinear) evolu- talk, we give an algorithm for efficiently computing the ap- tion equations. The error bound successfully avoids the proximate global basis needed in MOR by utilizing a new accumulation of the residual in time, which is a common interpretation of the transfer function and by capitalizing drawback in the existing error estimation for time-stepping on Krylov recycling in a novel way. schemes. The proposed error bound is applied to two kinds of parametrized instationary problems arising from Meghan O’Connell chromatographic separation processes. Numerical experi- Department of Mathematics ments demonstrate the performance and efficiency of the Tufts University proposed error bound. [email protected]

Peter Benner, Lihong Feng Misha E. Kilmer Max Planck Institute, Magdeburg, Germany Tufts University [email protected], [email protected] [email protected] Eric De Sturler Yongjin Zhang Virginia Tech Max Planck Institute for Dynamics of Complex [email protected] Systems,Germany [email protected] Serkan Gugercin Virginia Tech. MS143 Department of Mathematics [email protected] Overlapping Clustering and Ldeim in Model Re- duction for Nonlinear Inversion Christopher A. Beattie Projection-based parametric model reduction is success- Virginia Polytechnic Institute and State University fully employed in parameter inversion and optimization. [email protected] However, efficient reduced model evaluation requires an affine parametrization of the system matrices. When the system matrices do not have this property, Discrete Empir- MS144 ical Interpolation Method (DEIM) can produce an approx- Methods for Accurate and Efficient Computa- imate one. In this talk, we combine overlapping cluster- tion of the Proper-Orthogonal-Decomposition with ing algorithms and Local DEIM to generate a high-fidelity Large Data Sets affine approximation with minimal on-line cost. A numer- ical example arising in diffuse optical tomography is pre- Methods for calculating the proper orthogonal decomposi- sented. tion are investigated with regards to efficiency and accu- racy. The classical direct method, the snapshot method, Alexander Grimm and two new methods, one called ”the deflation method” Department of Mathematics and the other called the ”recursive snapshot method”, are CS15 Abstracts 123

compared. The sensitivity of the eigenvalue spectrum and [email protected] POD modes to round-off errors and errors caused by us- ing a reduced number of snapshots is investigated. Error bounds are given for these error sources. MS144 Proper Orthogonal Decomposition Based Reduced Brian Helenbrook, Fariddudin Behzad Order Modeling for Real Time Monte Carlo Simu- Clarkson University lation [email protected], [email protected] Monte Carlo simulations (MCS) are a powerful tool for modeling radiation transport (RT), but require signifi- cant computing resources to obtain accurate results. In MS144 this work, we develop a proper orthogonal decomposition (POD) based reduced order modeling (ROM) approach to Hierarchical Bayesian Sampling for Image Recon- reduce the number of MC particles that must simulated struction of X-Ray and Proton Radiographs to obtain statistically significant results. POD typically is done in space, but here we use it to generate orthogonal Reconstructing object densities by pulsing particles basis functions to describe the radiation energy spectrum. through a radially symmetric object and collecting them We apply the POD to generate ROMs for terrestrial radi- on a CCD results in an ill-posed Abel inversion problem. ation detection scenarios and present numerical results to We present a Markov Chain Monte Carlo approach for solv- show the improvement in accuracy that can obtained using ing Abel inversion, where we not only quantify uncertainty the ROM. on the image reconstruction, but also quantify uncertain- ties on the prior image covariance matrix and the precision Indika G. Udagedara, Brian Helenbrook parameter from the noise model. The data presented were Clarkson University obtained from high-energy X-ray and proton radiography udagedig@clarkson, [email protected] facilities. Aaron B. Luttman, Stephen Mitchell Marylesa Howard National Security Technologies, LLC National Security Technologies, LLC [email protected], [email protected] [email protected] MS145 Michael Fowler Mathworks An Adaptable, Application-Aware Task-Centric [email protected] Runtime System Abstract not available at time of publication. Aaron B. Luttman National Security Technologies, LLC George Bosilca [email protected] University of Tennessee - Knoxville [email protected] Margaret Hock Columbia University [email protected] MS145 Task-Based Parallelization of the Fast Multipole Method on NVIDIA GPUs and Multicore Proces- MS144 sors An MCMC Approach to Quantifying Uncertainties Fast Multipole Methods are a fundamental operation for in Neutron Tomography the simulation of many physical problems. In this talk, we present a new approach for implementing these methods that achieves high performance across many different com- Two of the most important properties characterizing puter architectures. Our method consists of expressing the pulsed fusion neutron sources are the time profile and FMM algorithm as a task flow and employing a state-of- the energy spectrum of the fusion neutrons. In this work the-art runtime system, StarPU, to process the tasks on we present a model for neutron creation as a function of the different computing units. time and energy, along with a Markov Chain Monte Carlo method for estimating the model parameters from neutron Eric F. Darve detector measurements. The formulation is demonstrated Stanford University on real data from a U.S. Department of Energy Dense Mechanical Engineering Department Plasma Focus fusion reactor. [email protected]

Aaron B. Luttman Emmanuel Agullo, Berenger Bramas, Olivier Coulaud National Security Technologies, LLC INRIA [email protected] [email protected], [email protected], [email protected] Eric Machorro National Security Technologies Matthias Messner [email protected] Stanford University [email protected] Daniel Lowe National Security Technologies, LLC Toru Takahashi 124 CS15 Abstracts

Nagoya University multimodal and having a lot of constrains. To solve the [email protected] problems we can use metaheuristic algorithm to get solu- tion that is near the optimal solution in reasonable time. In this research, the author solves several engineering prob- MS145 lems using Lvy-flights combination with the search strategy Sparse Direct Solvers on Top of a Runtime System via the FIrefly Algorithm that is first developed by XinShe Yang in 2010. Advisor: Kuntjoro Adji Sidarto To face the advent of multicore processors and the ever increasing complexity of hardware architectures, program- Fauziah Andini Putri ming models based on DAG parallelism regained popular- Bandung Institute of Technology ity in the high performance, scientific computing commu- [email protected] nity. Modern runtime systems offer programming models and interfaces that comply with this paradigm and power- ful engines for scheduling the tasks into which the applica- MS146 tion is decomposed. These tools have already proved their Higher Dimensional Smooth Data Interpolation: effectiveness on a number of dense linear algebra applica- Algorithmic Techniques from Computational Ge- tions. This talk evaluates the usability of runtime systems ometry for sparse matrix multifrontal factorizations which consti- tute irregular workloads, with tasks of different granular- In this paper, we derive a construction for computing ities and characteristics and with a variable memory con- smooth interpolants for a given dataset of 3+ dimensions, sumption. Experimental results on real-life matrices show and develop an algorithm for implementing our construc- that it is possible to achieve the same efficiency as with tion. The algorithm builds an n-dimensional cell complex an ad hoc scheduler which relies on the knowledge of the using Delaunay triangulation, where each cell has an as- algorithm. This talk also shows that thanks to the effec- sociated interpolation function that satisfies Lipschitz con- tiveness and expressiveness of these programming models, tinuity for each internal point. This algorithm is imple- it is possible to implement more complex algorithms that mented as a MATLAB package, and is the first of its kind achieve better performance. thatcanbeusedonactualdatasets.Advisor:Matthew Hirn, cole Normale Suprieure, Dpartement d’Informatique Emmanuel Agullo INRIA Ariel Herbert-Voss [email protected] University of Utah [email protected] Alfredo Buttari CNRS-IRIT, France MS146 [email protected] A Bioinformatic Approach to Colorectal Cancer Research Florent Lopez Enseeiht My project involved using the R programming language to fl[email protected] access metadata concerning colorectal cancer. We used epi- genetic data to look at colon cancer in a new way, and came Abdou Guermouche up with two novel pathways for its development, without LaBRI-INRIA futurs ever doing a wet lab ourselves. Our results shifted cur- [email protected] rent paradigms about colon cancer development. Advisor: Timothy Yeatman and Mingli Yang, Gibbs Cancer Center

MS145 A Task-Based Sparse Direct Solver Suited for Large Nicolas Limogiannis, Nick Napier Scale Hierarchical/heterogeneous Architectures Wofford College/Gibbs Cancer Center [email protected]fford.edu, We study the benefits and limits of replacing the highly [email protected]fford.edu specialized internal scheduler of our parallel sparse direct solver PaStiX with two generic runtime systems PARSEC and STARPU. The analysis highlights that these generic MS146 task-based runtimes achieve comparable results on homo- Interpreting Twitter Data from World Cup Tweets geneous platforms. Furthermore, they are able to signifi- cantly speed up the solver on heterogeneous environments Cluster analysis is a field of data analysis that extracts by taking advantage of the accelerators while hiding the underlying patterns in data. We clustered 30,000 tweets complexity of their efficient manipulation from the pro- extracted from Twitter just before the World Cup started grammer. and compared the results of k-means, a commonly used clustering algorithm, and Non-Negative Matrix Factoriza- Pierre Ramet tion (NMF). The two algorithms gave similar results, but LaBRI, Univ Bordeaux, France NMF proved to be faster and provided more easily inter- 701868 preted results. Advisor: Carl Meyer, NC State Carol Sadek, Caley Johns MS146 Wofford College Application of Lvy-Flight Firefly Algorithm in [email protected]fford.edu, [email protected]fford.edu Solving Several Engineering Problems

There are a lot of optimization problems in engineering MS146 field. The problems are generally in nonlinear equations, Valuation of American Options and E. Coli Muta- CS15 Abstracts 125

tions method as “kinetic theory molecular dynamics,’ or KTMD. The purpose of this paper is to derive KTMD from first Numerical methods for the valuation of American options principles and place it on a firm theoretical foundation. have long been an area of active research. Despite the The framework that KTMD provides for simulating plas- amount of research in this area, there is not enough at- mas in the hot, dense regime is particularly useful since tention given to potential applications of the optimized current computational methods are generally limited by numerical methods in use. Considering the valuation of their inability to treat the dynamical quantum evolution of American options intrinsic coupling with Brownian Mo- the electronic component. Using the N-body quantum von tion, a Levy Process, this should be surprising. An area of Neumann equation for the electron-proton plasma, we show promise seems to be in biological modeling, particularly E. how this can be mapped to a classical Liouville equation Coli Mutations. Advisor: Liming Feng, UIUC for the ions coupled to a set of quantum kinetic equations for the 1-particle and 2-particle distribution functions. James A. Stronz UIUC Frank Graziani [email protected] Lawrence Livermore National Laboratory graziani1@llnl MS146 The Effects of Chronic Wasting Disease on Penn- MS147 sylvania Deer and Coyote Populations Control Strategies for Multi-Agent Games Chronic Wasting Disease (CWD) is prevalent in cervids, We present an optimal control problem for a large system which can be transmitted directly and indirectly. Thus of interacting agents is considered using a kinetic perspec- far, CWD results in death, and no treatments exist. This tive. As a prototype model we analyze a microscopic model disease has captured the attention of officials and hunters. of opinion formation under constraints. For this problem In this presentation, we focus on the effects of CWD di- a Boltzmann–type equation based on a model predictive rectly on a Pennsylvania deer population and indirectly on control formulation is introduced and discussed. The rela- the predatory coyote population. We present a dynamical tion to meanfield is also explored and discussed. For nu- system describing the relationship between deer and coy- merical purposes a receding horizon strategy is introduced otes and some preliminary results. Advisor: Luis Melara, to embed the minimization of suitable cost functional into Shippensburg binary particle interactions. The corresponding Fokker- Planck asymptotic limit is also derived and explicit expres- Brandon D. Thrush sions of stationary solutions are given. Several numerical Shippensburg University results showing the robustness of the present approach are [email protected] finally reported. Michael Herty MS147 RWTH Aachen Universtiy Realizability in High-Order Numerical Solutions of Department of Mathematics Entropy-Based Moment Closures [email protected] Entropy-based moment closures for kinetic equations (col- loquially known as MN models) have attractive theoretical MS147 properties (hyperbolicity, entropy dissipation, and positiv- A High-Order / Low-Order Approach to Ocean ity) but are only defined in the set of realizable moment Modeling vectors, that is those which are consistent with a positive distribution. High-order numerical solutions do not always We examine a high-order/low-order approach for the free- stay in this set, so we investigate the use of a limiter to surface ocean equations based on an implicit/explicit handle nonrealizable moments in the implementation of a method. The two dimensional scalar continuity equation high-order discontinuous Galerkin method. is treated implicitly with a preconditioned Jacobian-free Newton-Krylov method (JFNK) and the remaining three Graham Alldredge dimensional equations are subcycled explicitly within the RWTH AACHEN University JFNK residual evaluation with a method. The method [email protected] is second-order accurate and scales algorithmically, with timesteps much larger than fully explicit methods. More- over, the hierarchical nature of the algorithm lends itself MS147 readily to emerging architectures. Kinetic Theory Molecular Dynamics Chris Newman, Geoff Womeldorff, Dana Knoll, Luis Electrons are weakly coupled in hot, dense matter that is Chacon created in high-energy-density (HED) experiments. They Los Alamos National Laboratory are also mildly quantum mechanical and the ions associated [email protected], [email protected], [email protected], cha- with them are classical and may be strongly coupled. In [email protected] addition, the dynamical evolution of plasmas under these hot, dense matter conditions involve a variety of transport and energy exchange processes. Quantum kinetic theory MS148 is an ideal tool for treating the electrons but it is not ade- Parameterized Reduced-Order Models for Shape quate for treating the ions. Molecular dynamics is perfectly Optimization of Flow Domains suited to describe the classical, strongly coupled ions but not the electrons. We develop a method that combines The proper orthogonal decomposition is combined with a Wigner kinetic treatment of the electrons with classical derivatives of flow solutions with respect to geometric pa- molecular dynamics for the ions. We refer to this hybrid rameters to build parametric reduced-order models. The 126 CS15 Abstracts

effectiveness of these models is shown by solving optimal analysis based on POD approximation theory and applica- control and shape optimization problems and comparing tions in realistic simulation and control problems will also the results to those obtained with full-order models. be discussed.

Jeff Borggaard S.S. Ravindran Virginia Tech University of Alabama in Huntsville Department of Mathematics [email protected] [email protected]

MS149 MS148 Strategies for Reducing Setup Costs in Algebraic Aeroelastic Design Optimization with Flutter Con- Multigrid straints and Local Rom Interpolation Algebraic multigrid (AMG) preconditioners are often em- Developing an efficient and fast algorithm in PDE- ployed in large- scale computer simulations to achieve scal- constrained optimization is an ongoing active research ability. AMG construction can be costly, sometimes as topic. One attempt is to replace PDE with a reduced order much as the solve itself. We discuss strategies for re- model (ROM). Unfortunately, ROMs are typically prone ducing expense through reuse of information from prior to parameter change, which is bad in optimization setting solves. The information type depends on the method. where a parameter space has to be explored. One remedy For smoothed aggregation AMG this includes aggregation is to construct a database of ROMs and interpolate them data, whereas for energy minimization it includes sparsity for a parameter point that is not in the database. This ap- patterns and prior interpolants. We demonstrate the effec- proach is applied to a real application of aeroelastic wing tiveness of such strategies in parallel applications. optimization problem with flutter constraints. Detailed ex- planation of how to construct a database and sensitivities Jonathan J. Hu and numerical results will be illustrated in this talk. Sandia National Laboratories Livermore, CA 94551 Youngsoo Choi [email protected] Farhat Research Group, Stanford University [email protected] Andrey Prokopenko Sandia National Laboratories David Amsallem, Charbel Farhat [email protected] Stanford University [email protected], [email protected] MS149 Next Generation Sparse Symmetric Factorization MS148 Projection-based ROMs for Parametrized PDE- Sparse direct solvers are important in the solution of scien- constrained Optimization and Control Problems tific problems but their parallel implementations typically exhibit poor scalability. Reducing synchronization and Projection-based ROMs provide efficient strategies to communication along the critical path is crucial to achieve tackle parametric optimization and parametrized control good performance on future architectures. In this context, problems, where parameters are related to control/design we are investigating a parallel implementation of sparse variables, or to relevant features of the state system, Cholesky factorization using the Fan-Both approach, and respectively. In this talk we show how to construct we will present our findings. projection-based ROMs in order to face the large com- putational costs arising in these cases, by discussing two Mathias Jacquelin general paradigms (optimize-then-reduce vs. reduce-then- Lawrence Berkeley National Lab optimize), and showing their performances by means of [email protected] numerical examples. Esmond G. Ng Andrea Manzoni Lawrence Berkeley National Laboratory EPFL, MATHICSE-CMCS [email protected] Switzerland andrea.manzoni@epfl.ch MS149 A Distributed CPU-GPU Sparse Direct Solver MS148 POD-G Reduced Order Models for Prediction and We present the hybrid MPI+OpenMP+CUDA implemen- Control of Turbulent Flows tation of a distributed memory right-looking sparse LU fac- torization algorithm. The difficulty is that small problem Model reduction has become an active area of scientific sizes dominate the workload, making efficient GPU utiliza- and engineering research in the past decade or so due to tion challenging. We find ways to aggregate collections of its ability to reduce the complexity of fluid dynamical sys- small BLAS operations into larger ones; to schedule opera- tems to enable simulation, optimization design and control. tions to achieve load balance and hide long-latency opera- Proper orthogonal decomposition Galerkin (POD-G) is one tions, such as PCIe transfer; and to exploit simultaneously of the most commonly used methods to generate reduced- all of a nodes available CPU cores and GPUs. order models for turbulent flow systems. In reduced-order modeling, balancing the accuracy and efficiency is crucial Xiaoye Sherry Li for their success. In this talk, we propose an improvement Computational Research Division to POD-G models to address this issue. A rigorous error Lawrence Berkeley National Laboratory CS15 Abstracts 127

[email protected] [email protected]

Piyush Sao, Richard Vuduc Georgia Institute of Technology MS150 [email protected], [email protected]. edu A Theoretical and Computational Framework for Measure-Valued Solutions to Conservation Laws

MS149 Recent results cast doubts on the appropriateness of the entropy weak solution for nonlinear systems of conserva- New Developments in hypres Interfaces and tion laws and it has been conjectured that the more gen- Solvers eral entropy measure-valued (emv) solutions might be the appropriate notion of solution. We proved that bounded The hypre software library provides high performance pre- solutions of an arbitrary high order space-time DG scheme conditioners and solvers for the solution of large sparse lin- combined with a nonlinear shock-capturing converge to ear systems on massively parallel computers via conceptual an emv solution. The novelty in our work is that no interfaces, which include a structured, a semi-structured, streamline-diffusion terms are used for stabilization. and a traditional linear-algebra based interface. We will discuss new algorithmic developments in hypre’s solvers, Zakerzadeh Mohammad as well as our efforts and plans to prepare hypre’s inter- RWTH Aachen University faces and solvers for heterogeneous architectures. [email protected] Ulrike Meier Yang Georg May Lawrence Livermore National Laboratory AICES [email protected] RWTH Aachen [email protected] MS150 An Implicit Les Strategy for High Order Discon- MS150 tinuous Galerkin Discretizations Understanding the Role of Spectral Vanishing Vis- cosity in High Reynolds Number Flows Due to their high scale-resolving capabilities per degree of freedom, high order Discontinuous Galerkin methods have To stabilize high Reynolds number simulations using Con- been shown to be very accurate and effective for implicit tinuous Galerkin spectral/hp element discretisations sta- LES simulations at moderate Reynolds number, if com- bilization is required, even after the application of de- bined with a polynomial de-aliasing strategy for stability. aliaising techniques, although apparently not in Discon- In this work, we present an implicit LES strategy suitable tinous Galerkin (DG) discretisations. For our complex ge- for high order spectral element methods based on a locally ometry high Reynolds number simulations we are applying and temporally adaptive de-aliasing, that ensures stability Spectral Vanishing Viscosity (SVV) for stabilization. In through physics-based indicators and models dissipation. this presentation we discuss the dispersion analysis of the SVV approach and demonstrate that appropriate choices Andrea D. Beck,DavidFlad of the SVV parameters recover characteristics observed in University of Stuttgart DG methods. [email protected], fl[email protected] Rodrigo Moura, Jean-Eloi Lombard, David Moxey, Yan Claus-Dieter Munz Bao, Spencer Sherwin Institut f¨ur Aerodynamik und Gasdynamik (IAG) Imperial College London [email protected] [email protected], jean- [email protected], [email protected], [email protected], [email protected] MS150 High-Order Finite-Volume Solution of Turbulent MS151 Aerodynamic Flows Resolving Uncomfortable Tradeoffs in Building Fast Boundary-Element Method Solvers: It’s Not Research in high-order unstructured solvers is encouraged the Hows, It’s the Whys by their accuracy advantages and flexibility for complex geometries. Traditionally, the finite-volume approach has Fast-multipole methods (FMMs) keep pace with parallel been employed in computational aerodynamics because of computing, so where are the scalable, open-source fast intrinsic conservative properties. A major step towards boundary-element method (BEM) libraries? We suggest the adoption of higher-order finite-volume methods in CFD that a general BEM requires suitable strategies to account solvers is turbulence modeling. We describe the integration for the additional abstraction layer (a fast summation algo- of the Spalart-Allmaras model into a higher-order finite- rithm) between elementwise computations and the Krylov volume solver and the treatments required to solve such a iteration. This perspective suggests an extensible archi- mathematically stiff problem on anisotropic meshes. tecture for general geometries, basis functions, colloca- tion/Galerkin discretizations, scalar and vector problems, Alireza Jalali and interfaces to ”downstream” applications, e.g. PDE- PhD Candidate, University of British Columbia constrained optimization and coupling to FEM. [email protected] Jaydeep Bardhan Carl Ollivier-Gooch Northeastern University University of British Columbia [email protected] 128 CS15 Abstracts

Matthew G. Knepley tations University of Chicago [email protected] We present a numerical routine that interpolates function values on rotated spherical grids via hybrid nonuniform FFTs. This routine can be used for evaluating singu- MS151 lar integral operators on smooth surfaces that are glob- BEM++ - Building Blocks for Galerkin Boundary ally parametrized by spherical coordinates. Problems of Element Methods this type arise, for example, in simulating Stokes flows with particulate suspensions and in multi-particle scatter- The BEM++ boundary element library (www.bempp.org) ing calculations. The algorithm has a small complexity constant, and the cost of applying the quadrature rule is is a versatile framework for the solution of boundary in- 4 tegral equations via Galerkin boundary element methods. nearly-optimal O(p log p) for a spherical harmonic expan- The focus on this talk is on the design decisions and chal- sion of degree p. This is joint work with Zydrunas Gimbu- lenges of developing BEM++. This includes basic mesh tas (NIST). representation, assembly of operators, FMM and H-matrix Shravan Veerapaneni methods, preconditioning, linear algebra, and user inter- Department of Mathematics facesinC++andPython. University of Michigan Timo Betcke, Simon Arridge, Elwin van’t Wout [email protected] University College London [email protected], [email protected], MS152 [email protected] Recovery Based a Posteriori Error Estimation for Finite Element Methods MS151 The recovery-based Zienkiewicz-Zhu (ZZ) a posteriori error Applications of Accelerated BEM in Aeronautics estimator has been widely used in the engineering practice due to the ease of implementation, generality, and accu- Airbus Group Innovations is, inside Airbus Group, an en- racy. However, it is well known that the ZZ estimator tity devoted to research and development for the usage of is inefficient for non-smooth problems on relatively coarse Airbus Group divisions (Airbus Civil Aircraft, Airbus De- meshes. In this talk, we will discuss three types of recovery- fence & Space, Airbus Helicopters). The numerical analysis based a posteriori error estimators based on the L2,the team has been working for now more than 20 years on in- equilibrium, and the H(div) recoveries, respectively. These tegral equations and boundary element methods for wave estimators are efficient, reliable, or/and robust. Moreover, propagation simulations, first in electromagnetism, later in they preserve the mathematical structure of the underlying acoustics and electrostatics. Since 2000, these BEM tools problem. have received a multipole algorithm (called Fast Multiple Method) extension that allows to solve very large prob- Zhiqiang Cai lems, with ten of millions of unknowns, in reasonable time Purdue University on parallel machines. Recently, H-matrix technics have Department of Mathematics given access to fast direct solvers, able to solve with a [email protected] very good accuracy problems with millions of unknowns without the problem induced by iterative resolution (no control on the number of iterations, difficulty to find a MS152 good preconditioned, etc.). The resulting software is used Robust a-Posteriori Error Estimation for Finite El- on daily basis in acoustics for installation effects compu- ement Approximation to H(curl) Problem tation, aeroacoustic simulation (in a coupled scheme with other tools), in electromagnetism for antenna siting, elec- In this talk, we will discuss the recovery-type a posteri- tromagnetic compatibility or stealth, and in electrostatics ori error estimation for the conforming finite element for- for fuel tank modelisation and lightning effects. The aim mulation of the positive definite H(curl)problem.Both 2 of this talk is to present a wide view of the realizations, to the L -recovery and H(curl)-recovery are discussed. The underline the recent developments (such as H-matrix) and global recovery problems are localized through weighted to present the main perspectives and futures directions of averaging, and a partition of unity of the magnetizing field research in a context of different physics and applicationsP respectively. Shuhao Cao Nolwenn Balin, Benoit Liz´e Pennsylvania State University Airbus Department of Mathematics [email protected], [email protected] [email protected]

Guillaume Sylvand MS152 EADS CCR, Centre de Toulouse [email protected] Localized H(div) Recovery-Based a Posteriori Er- ror Estimators

Isabelle Terrasse In this talk, we present recovery-based error estimators for Airbus conforming finite element approximation of second-order [email protected] elliptic problem. The flux is recovered in H(div) finite ele- ment subspaces by approximating equilibrium and consti- tutive equations simultaneously in a weighted H(div) norm. MS151 A posteriori error estimators are constructed locally on ap- A Numerical Routine for Fast Spherical Grid Ro- propriate patches of triangular elements. Reliability and CS15 Abstracts 129

efficiency of these local error estimators will be discussed. Department of Molecular Biophysics & Physiology Numerical results are provided to demonstrate features of dirk [email protected] these error estimators.

Xu Zhang MS153 Purdue University Dendritic Coincidence Detection Enabling [email protected] Wordspotting Computation

Zhiqiang Cai Dendritic computation is often ignored when building neu- Purdue University ron models. However, dendrites have been shown to per- Department of Mathematics form operations like non-linear filtering, spatial and tem- [email protected] poral summation of synaptic inputs, coincidence detection, synaptic scaling and sequence detection. We show that a network of dendrites and a Winner-Take-all network is sim- MS153 ilar to a Hidden Markov Model(HMM) classifier often used Continuum Spine Modeling with Application to for speech and pattern-recognition. We have developed a Outer Retina Neurocircuitry mathematical framework for Silicon dendrites, that models deep dendritic trees. The continuum theory for dendritic spines is an exten- sion of classical cable theory for which the distribution of Jennifer Hasler spines is treated as a continuum. With the continuum the- Electrical and Computer Engineering ory, different spine morphologies, multiple populations of Georgia Tech spines, and distributed physiological properties are repre- [email protected] sented compactly by relatively few differential equations. In this talk I will present a brief overview of continuum spine theory and discuss how to apply the theory to mod- MS154 eling neurocircuitry in the outer retina. Fast Spectral PDE Solvers for Complex Structures: the Fourier-Continuation Method Steven M. Baer Arizona State University We present fast spectral solvers for time-domain Par- School of Mathematical & Statistical Sciences tial Differential Equations. Based on a novel Fourier- [email protected] Continuation (FC) method for the resolution of the Gibbs phenomenon these methodologies give rise to time-domain solvers for PDEs for general engineering problems and MS153 structures which enjoy a number of desireable proper- Simulation of the Ephaptic Effect in the Cone- ties, including spectral time evolution essentially free of Horizontal Cell Synapse of the Retina pollution or dispersion errors for general PDEs in the time domain, with conditional/unconditional stability for The drift-diffusion (Poisson-Nernst-Planck) model— explicit/alternating-direction methods. A variety of appli- including a numerical model for cell membranes that cations to linear and nonlinear PDE problems, including resolves surface charge boundary layers—is applied to the the Maxwell equations, the Navier-Stokes equations, the cone-horizontal cell synapse in the outer plexiform layer elastic wave equation demonstrate the significant improve- of the retina in a two-dimensional cross-section geometry. ments the new algorithms can provide over the accuracy Numerical simulations reproduce the experimental calcium and speed resulting from other approaches. current-voltage curves for the goldfish retina in response to a bright spot, with and without an illuminated back- Oscar P. Bruno ground. The ephaptic (electrical) effect is demonstrated California Institute of Technology by computing the shift in the IV curve for background off [email protected] vs. background on.

Carl L. Gardner MS154 Arizona State University School of Mathematical and Statistical Sciences Frame Theoretic Convolutional Gridding [email protected] This talk is about reconstructing images from non-uniform Fourier data. This problem is relevant in applications MS153 such as magnetic resonance imaging (MRI) and synthetic aperture radar (SAR). The non-uniform FFT algorithm Modeling of Calcium-Induced Calcium Release provides a practical way to reconstruct images However, Calcium release through coordinated IP3 receptor and choosing the parameters can be difficult and in some cases ryanodine receptor (RyR) openings are important signaling the method may fail to converge. This talk provides events in neurons in which Ca2+ release from one channel a mathematical foundation, through the use of Fourier opens other nearby Ca2+ sensitive channels. This is mod- frames, for reconstructing functions from their non-uniform eled using extensive experimental data to compute how the Fourier data. As a result, the parameters for the NFFT can open/closed probability of RyR changes with Ca2+ con- be chosen to ensure numerical convergence under various centration and with RyR open/closed time. Simulations non-uniform sampling schemes common in MRI and SAR. show how neighboring channels are recruited and also give insights into how this positive feedback mechanism termi- Anne Gelb nates. Arizona State University [email protected] Dirk Gillespie Rush University Medical Center Guohui Song 130 CS15 Abstracts

Clarkson University [email protected] [email protected]

MS155 MS154 Large-Scale Forward and Inverse Numerical Simu- Optimized Fourier Continuation Methods lations of Crustal and Lithospheric-Scale Deforma- tion

Fourier continuation/extension (FC) methods, have been Geological processes occur over long timescales and involve shown to achieve arbitrary orders of accuracy in generating nonlinear constitutive relationships. We discuss a parallel Fourier approximations of smooth but non-periodic func- 3D code to simulate such processes, based on a marker-and- tions from evenly spaced data. The stability of PDE solvers cell technique with a staggered finite difference discretiza- based on FC methods is heavily dependent on the param- tion and visco-elasto-plastic rheologies. We show a few eters of the continuation. Optimized FC methods will be examples of geological modelling applications. In addition, presented that balance accuracy with sufficient conditions we demonstrate how the forward models can be combined for stability within a FC based PDE solver. The inherent with geophysical data and a MC Monte Carlo-based inver- trade-off between accuracy and stability will be discussed sion approach to constrain the rheology and structure of in detail. mountains belts.

Mark Lyon Boris Kaus University of New Hampshire Johannes Gutenberg University Mainz [email protected] Institute of Geosciences [email protected]

MS154 Anton Popov, Tobias Baumann A New Radial Basis Functions (RBF)-based Frame Johannes Gutenberg University Mainz Institute of Method to Bypass the Runge Phenomenon Geosciences [email protected], [email protected] Approximating nonperiodic analytic functions with spec- tral accuracy is not an easy task. RBFs, just like poly- nomials and other pseudospectral methods, are susceptible MS155 to suffer from the Runge phenomenon, spurious oscillations HPC Finite Elements for Nonlinear Stokes Flow near the edges of the domain, and from the ill-conditioning of the method’s associated system. Recently, Adcock et Rock deformation over geological time scales can be ex- al have introduced a method which combines frames the- pressed as a nonlinear, incompressible Stokes problem in ory and Fourier extensions in [Adcock, Huybrechs, Martin- which the viscosity is highly heterogeneous. Algorithmic Vacquero, On the numerical stability of Fourier extensions, and computationally scalable preconditioners are necessary Found Comp Math 14, 635-687]. The method is not only to achieve high resolution 3D simulations. Here I present spectrally convergent, it is also free from the Runge phe- a mixed FE method employing a multilevel preconditioner nomenon even when the data is equispaced. We will use the which exploits matrix-free kernels. Trading flops for mem- fact that pseudospectral methods can be seen as particular ory bandwidth, significant speedups compared to precon- cases of RBFs to construct an RBF-based frame method ditioners requiring assembled operators are obtained. Per- that generalized Adcocks Fourier extensions method. formance is demonstrated using a simplified model of slab detachment. Cecile M. Piret Universit´e catholique de Louvain Dave A. May [email protected] ETH Zurich [email protected]

MS155 Jed Brown Mathematics and Computer Science Division Parallel and Adaptive Mantle Convection Simula- Argonne National Laboratory and CU Boulder tion in Aspect [email protected] In this talk, we are presenting the open source mantle con- vection code ASPECT to solve large scale convection prob- MS155 lems. The main numerical ingredients are higher order fi- Three-Field Block-Preconditioners for Models of nite elements with adaptive mesh refinement, stabilization Coupled Magma/mantle Dynamics schemes, and linear/nonlinear solvers. The talk will also cover our software design approach to engineer a flexible, We discuss the iterative solution of a finite element discreti- extensible, code with a healthy community that can sup- sation of the magma dynamics equations. These equations port the project in the long run. Finally, we will talk about share features of the Stokes equations, however, Elman- examples and show benchmark results. Silvester-Wathen (ESW) preconditioners for the magma dynamics equations are not optimal. By introducing a new Timo Heister field, the compaction pressure, into the magma dynamics Clemson University equations, we have developed a new three-field precondi- Mathematical Sciences tioner which is optimal in terms of problem size and less [email protected] sensitive to physical parameters compared to the ESW pre- conditioners. Wolfgang Bangerth Texas A&M University Sander Rhebergen CS15 Abstracts 131

University of Oxford [email protected] Mathematics Institute and Department of Earth Sciences [email protected] MS156 Garth Wells Multiphysics Lagrangian/Eulerian Modeling and Department of Engineering deRham Complex Based Algorithms University of Cambridge [email protected] Multiphysics modeling in an arbitrary La- grangian/Eulerian (ALE) framework leads naturally to numerical algorithms matching the geometric meaning Andrew J. Wathen of the operators in the deRham complex. We discuss Oxford University our experience with this approach relative to solid Numerical Analysis Group kinematics, magnetohydrodynamics and full Maxwell [email protected] hydrodynamic modeling. Sandia National Laboratories is a multi-program laboratory managed and operated Richard F. Katz by Sandia Corporation, a wholly owned subsidiary of University of Oxford Lockheed Martin Corporation, for the U.S. Department of [email protected] Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. Laura Alisic, John Rudge Bullard Laboratories Allen C. Robinson University of Cambridge Sandia National Laboratories [email protected], [email protected] [email protected]

MS156 MS156 Mimetic Finite-Difference Methods A Sub Cell Dynamics Based Closure Model The mimetic finite difference method (J. of Comput. Phys. for Multimaterial Arbitrary Lagrangian Eulerian 257(2014)1163) mimics fundamental properties of mathe- Codes matical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self- Arbitrary Lagrangian Eulerian (ALE) codes introduce mul- adjointness of differential operators, and exact mathemati- timaterial cells to represent material interfaces that may cal identities of the vector and tensor calculus. We describe undergo high deformation. A closure model is then re- the major mimetic ideas and their relevance to academic quired to close the governing equations, which are oth- and real-life problems. The supporting applications include erwise underdetermined, this defines how volume frac- diffusion, electromagnetics, fluid flow, and Lagrangian hy- tions and state variables of individual material components drodynamics problems on different type of meshes. within these multimaterial cells evolve. The requirements for these models will be presented and a interface aware Mikhail Shashkov sub-scale-dynamics closure model will be described that Los Alamos National Laboratory has been developed to meet these requirements. [email protected]

Andrew J. Barlow MS157 Atomic Weapons Esatblishment, United Kingdom [email protected] Representing Topography in Earth System Models with Porous Barriers

The ocean boundary (coasts and sea-floor) is fractal and MS156 exhibits features (e.g. ridges and passages) that are critical to shaping ocean circulation. These features are typically A High-Order/Low-Order Exponentially- not resolvable in contemporary global earth system mod- Convergent IMC Method els. We explore an extension of cut-cells that represents the topography via porous barriers between cells. We provide It is well known that standard Monte Carlo converges as an algorithm to calculate the porous barrier data and il- the inverse of the square root of the number of particle lustrate improved fidelity in coarse-resolution models using histories executed. We demonstrate that exponential con- the porous barrier representation of topography. vergence is possible using a defect approach in which each succeeding Monte Carlo batch estimates only the additive Alistair Adcroft error in the solution from previous batches. This solution is Princeton obtained by projection of the Monte Carlo solution onto a [email protected] FEM space. A refinement strategy is required to maintain exponential convergence. MS157 A Higher-Order Cut Cell Finite Volume Method Simon Bolding, Jim E. Morel For Advection-Diffusion Texas A&M [email protected], [email protected] We present a higher-order cut cell algorithm for the advection-diffusion equation in irregular domains. The Robert B. Lowrie finite volume operators are constructed using a unique Los Alamos National Laboratory weighted least-squares approach, which reduces the sensi- Los Alamos, NM 87545 USA tivity to small cells despite the flux-difference conservation 132 CS15 Abstracts

form. A higher-order RK time discretization treats dif- the usual definition of constraints to include adherence to fusion terms implicitly, so the overall algorithm is limited a theoretical model governed by differential equations. only by the advection term explicit CFL constraint, regard- less of small cells. Accuracy and stability are demonstrated Dave A. Campbell with several simple tests. Simon Fraser University [email protected] Dharshi Devendran University of Chicago Shirin Golchi [email protected] Columbia University [email protected] Hans Johansen Lawrence Berkeley National Laboratory Computational Research Division MS158 [email protected] On the Use of Particle Based Methods for the Real Time Identification and Control of Nonlinear Dy- namical Systems MS157 A Mixed Explicit Implicit Time Stepping Scheme The field of structural dynamics is inherently related to for Cartesian Embedded Boundary Meshes the simulation, identification and control of structural sys- tems. This task is not a straightforward one; firstly, due to We present a mixed explicit implicit time stepping scheme potential nonlinear behavior; and secondly, due to uncer- for solving the advection equation on Cartesian embedded tainties relating to erroneous modeling assumptions, impre- boundary meshes. The implicit scheme is used to overcome cise sensory information, ageing effects, varying loads, and the small cell problem and ensure stability at the cut cells. lack of a priori knowledge of the system itself. This talk It is coupled to a standard explicit scheme which is used discusses the implementation of methodologies capable of over most of the mesh. We present a theoretical result successfully simulating such systems by encompassing the about the coupling, and show numerical results in one and aforementioned complexities. more dimensions. Eleni Chatzi Sandra May Institute of Structural ENgineering ETH Zurich ETH Zurich [email protected] [email protected]

Marsha Berger MS158 Courant Institute of Mathematical Sciences New York University Bayesian Uncertainty Quantification and Prop- [email protected] agation for Molecular Dynamic Simulations in Nanoscale Fluid Mechanics

MS157 For five decades, molecular dynamics (MD) simulations, in synergy with experiments, have elucidated critical mecha- Inverse Lax-Wendroff Procedure for Numerical nisms in a broad range of physiological systems and tech- Boundary Conditions of Hyperbolic Equations nological innovations. However, in nanofluidics, the re- We develop a high order finite difference numerical bound- sults of experiments and MD simulations may differ by ary condition for solving hyperbolic Hamilton-Jacobi equa- several orders of magnitude. We show that experimen- tions and conservation laws on a Cartesian mesh. The chal- tal and large scale MD investigations can be consolidated lenge results from the wide stencil of the interior high order through a Bayesian framework. Our findings indicate that scheme and the fact that the boundary may not be aligned it is essential to revisit MD simulations in the context of with the mesh. Our method is based on an inverse Lax- uncertainty quantification. Wendroff procedure for the inflow boundary conditions. Petros Koumoutsakos Extensive numerical examples are provided to illustrate its Chair of Computational Science, ETH Z¨urich good performance of our method. This is a joint work with [email protected] Ling Huang and Mengping Zhang, and with Sirui Tan and Francois Vilar. Panagiotis Angelikopoulos Chi-Wang Shu Computational Science, ETH Zurich, Switzerland Brown University [email protected] Div of Applied Mathematics [email protected] Costas Papadimitriou University of Thessaly Dept. of Mechanical Engineering MS158 [email protected] Sequentially Constrained Monte Carlo

Constraints in the parameter or model space typically make MS158 sampling from distributions more complex (although more Computationally Efficient Tools for Bayesian Un- interpretable) than their unconstrained counterparts. We certainty Quantification and Propagation in Struc- define a Sequentially Constrained Monte Carlo algorithm tural Dynamics connecting a simple distribution, to the target distribu- tion by a path defined by the strictness of constraint en- Bayesian uncertainty quantification, including Bayesian hi- forcement. We show general applicability by expanding erarchical modelling, are becoming standard tools in struc- CS15 Abstracts 133

tural dynamics for model selection, model parameter cali- [email protected] bration, uncertainty propagation and SHM using vibration measurements. For complex linear/nonlinear models, the computations involved in Bayesian asymptotic approxima- MS159 tions and MCMC sampling tools may be excessive. Dras- tic reduction in computational effort in model intrusive Adaptive Monte Carlo and Quasi-Monte Carlo In- and/or non-intrusive schemes is achieved by integrating tegration model reduction techniques, adjoint methods, surrogate models, parallel computing and highly-parallelizable sam- Monte Carlo methods are used for computing means of pling schemes. Acknowledgement: This research has been random variables with complex distributions. Both Monte implemented under the ARISTEIA Action of the Opera- Carlo methods and quasi-Monte Carlo methods are also tional Programme Education and Lifelong Learning and used for computing high dimensional integrals. A key was co-funded by the European Social Fund (ESF) and question in these computations is when to stop, while en- Greek National Resources. suring that the desired accuracy is obtained. Adaptive (quasi-)Monte Carlo algorithms rely on data-based error Costas Papadimitriou bounds to answer this question. This talk describes re- University of Thessaly cent work to construct such error bounds and ensure that Dept. of Mechanical Engineering they are trustworthy. We also derive upper bounds on [email protected] the computational costs of our adaptive algorithms. A key idea is to consider cones of random variables or in- tegrands. Our new algorithms have been implemented Panagiotis Angelikopoulos in the Guaranteed Automatic Integration Library (GAIL) Computational Science, ETH Zurich, Switzerland https://code.google.com/p/gail/. [email protected]

Panagiotis Hadjidoukas Fred J. Hickernell Computational Science Illinois Institute of Technology ETH Zurich, Switzerland Department of Applied Mathematics [email protected] [email protected]

Petros Koumoutsakos Lan Jiang Chair of Computational Science, ETH Z¨urich Dpet. of Applied Mathematics [email protected] Illinois Institute of Technology [email protected]

Antoni Lu´ıs Jim´enez Rugama MS159 Department of Applied Mathematics Illinois Institute of Technology H-Matrix Accelerated Second Moment Analysis for [email protected] Potentials with Rough Correlation

We consider the efficient solution of strongly elliptic poten- MS159 tial problems with stochastic Dirichlet data by the bound- Application of Quasi-Monte Carlo Methods to ary integral equation method. The computation of the so- PDEs with Random Coefficients lutions two-point correlation is well understood if the two- point correlation of the Dirichlet data is known and suffi- ciently smooth. Unfortunately, the problem becomes much PDEs with random coefficients are an important source more involved in case of rough data. We will show that the of high dimensional problems. One example is the flow concept of the H-matrix arithmetic provides a powerful tool through porous medium: because of the near impossibility to cope with this problem. By employing a parametric sur- of modeling the microscopic channels through which wa- face representation, we end up with an H-matrix arithmetic ter can flow in a porous layer, it is common engineering based on balanced cluster trees. This considerably simpli- practice to model the porous medium as a random per- fies the implementation and improves the performance of meability field. The quantity of interest is therefore an the H-matrix arithmetic. Numerical experiments are pro- expected value with respect to the random field, leading to vided to validate and quantify the presented methods and a high dimensional integral where the number of variables algorithms. is as high as the number of parameters needed to model this random field (it can be infinite). In this talk I will explain how quasi-Monte Carlo (QMC) methods can be Helmut Harbrecht, Juergen Doelz tailored to a prototype of such integrals. I will discuss the Universitaet Basel fast construction of higher order QMC methods to improve Departement of Mathematics and Computer Science the convergence rate and the use of multi-level techniques [email protected], [email protected] to improve the computational cost. The talk will touch on a number of joint works with Ivan Graham and Rob Sche- Michael Peters ichl (Bath), Dirk Nuyens (KU Leuven), Christoph Schwab University of Basel (ETH Zurich), and Ian Sloan, James Nichols, Josef Dick [email protected] and Quoc Le Gia (UNSW).

Christoph Schwab Frances Y. Kuo ETH Zuerich School of Mathematics and Statistics SAM University of New South Wales 134 CS15 Abstracts

[email protected] broader class of applications with hierarchy.

Anshu Dubey MS159 Lawrence Berkeley National Laboratory Option Pricing and the Anova Decomposition of a [email protected] Function of An Infinite Number of Variables Hajime Fujita In this work we consider the ANOVA decomposition of the Department of Computer Science integrand in a continuous version of a path-dependent op- University of Chicago tion pricing problem. We show that in the Brownian bridge [email protected] (or Levy-Ciesielski) formulation, every term in the (in- finite) ANOVA decomposition is smooth.Withthis Zachary Rubenstein result we are preparing for an error analysis of the cuba- Department of Computer Science, The University of ture problem for the option pricing problem, in which the Chicago discrete-time problem is approximated by the continuous [email protected] problem, and the error analysis then applied to the trun- cated ANOVA expansion, in which every term is smooth. Brian Van Straalen Lawrence Berkeley National Laboratory Ian H. Sloan Compuational Research Division University of New South Wales [email protected] School of Mathematics [email protected] Andrew A. Chien The University of Chicago Frances Y. Kuo Argonne National Laborator School of Mathematics and Statistics [email protected] University of New South Wales [email protected] MS160 Michael Griebel Resilience Properties of Gossip-Style Algorithms Universitat Bonn Inst fur Angewandte Mathematik Gossip algorithms have interesting resilience properties [email protected] which can potentially complement and extend state-of-the- art approaches towards algorithmic fault tolerance. We will review the latest developments in gossip-based all-reduce MS160 operations and some distributed linear algebra kernels built Adaptive Determination of Optimal Multilevel on top of them. Moreover, we will discuss how gossip- Monte Carlo parameters in the Presence of Fail- based approaches compare to state-of-the-art fault toler- ures ant algorithms, such as ABFT methods. By combining gossip-based approaches with existing fault tolerant high In the multilevel Monte Carlo (MLMC) method numerous performance algorithms, resilience at the algorithmic level parameters have to be determined. Their choice is crucial can potentially be strengthened further. for the work and error of the method. We propose to de- termine the number of samples per level, the finest and Wilfried N. Gansterer coarsest level by solving an integer optimization problem. University of Vienna Faults influence the MLMC levels to a different extent. We Department of Computer Science and Business present a fault tolerant MLMC method that adapts to ex- Informatics perienced failures without a priori knowledge of the failure [email protected] distribution. Gerhard Niederbrucker, Michael Moldaschl, Karl Prikopa Peter Arbenz University of Vienna ETH Zurich [email protected], Computer Science Department [email protected], [email protected] [email protected]

Stefan Pauli ETH Zurich Computer Science Department MS160 [email protected] Spatial Decomposition for Resilient Extreme-Scale Scientific Simulations

MS160 We present a probabilistic approach to PDEs, where com- Hierarchical Resilience for Structured AMR putational results are viewed as data that is used in a re- silient iterative fashion to update information about the Structured AMR (SAMR) has hierarchy in spatial and solution until convergence. We rely on a domain decompo- temporal resolution that can be exploited for devising flex- sition method such that the original problem is reduced to ible and customizable resiliency strategies. We prototyped solving the PDE on subdomains with uncertain boundary a hierarchical approach to resilience in Chombo, an SAMR conditions. Resilience to both hard and soft errors is in- library, using the Global View Resiliency (GVR) library tegrated within the algorithm. We show promising results that takes differentiated state snapshots for localized re- for elliptic PDEs. covery. SAMR is used in various domains, so our strat- egy may benefit those applications, and perhaps an even Francesco Rizzi, Khachik Sargsyan, Karla Morris, Cosmin CS15 Abstracts 135

Safta Sandia National Laboratories Sandia National Laboratories [email protected] [email protected], [email protected], [email protected], [email protected] Jaideep Ray Sandia National Laboratories, Livermore, CA Paul Mycek, Omar M. Knio [email protected] Duke University [email protected], [email protected] Srinivasan Arunajatesan, Lawrence Dechant Sandia National Laboratories Olivier LeMaitre [email protected], [email protected] LIMSI-CNRS [email protected] MS161 Habib N. Najm Formulation and Calibration of a Stochastic Model Sandia National Laboratories Form Error Representation for Rans Livermore, CA, USA [email protected] We develop a stochastic model inadequacy representation for the RANS equations for wall-bounded flows. The model takes the form of a stochastic PDE governing the error Bert J. Debusschere in the Reynolds stress computed according to an eddy- Energy Transportation Center viscosity-based turbulence model. Further, the model is Sandia National Laboratories, Livermore CA constructed to conform to available knowledge about the [email protected] performance of typical turbulence models—e.g., that the models are constructed to capture the log layer. We test MS161 the model inadequacy representation using DNS data. Uncertainty in Reynolds Stress Closures for Tur- Robert D. Moser bulent Flow Calculations University of Texas at Austin [email protected] Reynolds-averaged Navier-Stokes (RANS) simulations are a practical approach for solving complex multi-physics tur- bulent flows, but the underlying assumptions of the turbu- Todd Oliver lence models introduce errors and uncertainties in the sim- PECOS/ICES, The University of Texas at Austin ulation outcome. We present a framework to characterize [email protected] these uncertainty based on perturbations of the eigenval- ues of the anisotropic Reynolds stress tensors which bias Bryan Reuter the model towards specific turbulent states. Results are University of Texas, Austin presented for a broad class of turbulent flows and illustrate [email protected] the potential for this approach to capture the salient un- certainties introduced by simplified modeling assumptions. MS161 Gianluca Iaccarino Estimating a Model Discrepancy Term for the Stanford University Community Land Model Using Latent Heat and Mechanical Engineering Runoff Observations [email protected] We estimate three hydrological parameters of the CLM Michael A. Emory (Community Land Model) using runoff and latent heat flux Stanford University measurements gathered from sites with a similar hydrolog- [email protected] ical environment. The estimates are developed as probabil- ity density functions, using a CLM surrogate. Two struc- tural error models were to used represent the discrepancy Catherine Gorle between model and data and selected by their ability to re- EMAT, UA produce data. The sensitivity of the structural error model [email protected] form to the two types of observations is also investigated.

Jaideep Ray MS161 Sandia National Laboratories, Livermore, CA Eddy Viscosity Model Selection for Transonic Tur- [email protected] bulent Flows Using Shrinkage Regression

Linear eddy viscosity models (LEVM), when used in k- Laura Swiler epsilon models, often fail to capture complex turbulent Sandia National Laboratories phenomena. Our previous work has revealed the structural Albuquerque, New Mexico 87185 shortcomings of LEVMs in simulations of jet-in-crossflow [email protected] interactions. We address this issue by calibrating a cubic eddy viscosity model using limited measurements from a Maoyi Huang, Zhangshuan Hou jet-in-crossflow experiment. We use shrinkage regression Pacific Northwest National Lab to identify the terms that need to be retained. Improve- [email protected], [email protected] ment over LEVM predictions is quantified and presented. MS162 Sophia Lefantzi Optimal Convergence Rates of Co-Simulation Us- 136 CS15 Abstracts

ing Fine Structure Analysis Alan Hindmarsh Lawrence Livermore National Laboratory For coupled systems, where the monolithic simulation is Center for Applied Scientific Computing difficult, co-simulation is an important methodology in [email protected] time domain. In contrast to coupled ODEs, for coupled DAEs convergence can only be guranteed if certain contrac- tion properties are given. Here, the fine structure analysis MS162 is used to verify that the corresponding recursion estimates Fast Time-Domain Simulation for Reliable Fault are attained upper bounds on the convergence rate. Fur- Detection thermore we verify that numerical convergence might not be detacted. The relation of iterations and order of the Imperfections in manufacturing processes may cause un- time integrations is discussed. wanted connections (faults) that are added to the nom- inal, ”golden”, design of an electronic circuit. By fault Andreas Bartel, Kai Gausling simulation we simulate all situations: a huge number of University of Wuppertal new connections and each with many different values, up [email protected], to the regime of large deviations, for the newly added ele- [email protected] ment. We also consider ”opens” (broken connections). A strategy is developed to efficiently simulate the faulty so- Sebastian Sch¨ops lutions until their moment of detection. We fully exploit Theorie Elektromagnetischer Felder (TEMF) and GSCE the hierarchical structure of the circuit. Fast fault simula- Technische Universit tion is achieved in which the golden solution and all faulty [email protected] solutions are calculated over a same time step.

E. Jan W. ter Maten MS162 NXP Semiconductors, Corp IT, DMS-PDM-Mathematics Trigonometric Integration Methods in Circuit Sim- [email protected] ulation Bratislav Tasic The numerical calculation of the limit cycle of oscillators NXP Semiconductors with resonators exhibiting a high quality factor Q such [email protected] as quartz crystals is a difficult task in the time domain. Time domain integration formulas may introduce numeri- Jos J. Dohmen cal damping which leads to erroneous limit cycles. A novel NXP Semiconductors, the Netherlands class of adaptive multistep integration formulas is derived [email protected] which circumvent the aforementioned problems. The re- sults are compared with the well-known Harmonic Balance Theo G.J. Beelen (HB) technique. Moreover the range of absolute stability NXP Semiconductors and error estimates are derived for these methods. [email protected] Hans-Georg Brachtendorf, Kai Bittner University of Applied Sciences Upper Austria Rick Janssen [email protected], kai.bittner@fh- NXP Semiconductors, the Netherlands hagenberg.at [email protected]

Wil Schilders MS162 Eindhoven University of Technology Modelling Transmission Power Systems with the [email protected] Implicit DAE Solver, IDA Michael Guenther The main flow of power on a transmission power system Bergische Universitaet Wuppertal can be modeled as a coupled set of differential-algebraic [email protected] equations. Transmission models of interest, however, in- clude limits on output and internal states as well as limits on state rates of change, deadbands, and positivity con- MS163 straints. In this talk, we will outline how we are using a Sparse QR Factorization on Heterogenous Plat- general DAE solver package, IDA, for solution of transmis- forms with Multiple GPUs sion grid models incorporating many of these conditions within our simulation. This work was performed under the We present a sparse multifrontal QR Factorization method auspices of the U.S. Department of Energy by Lawrence on a heterogeneous CPU-GPU platform. Our method is Livermore National Laboratory under contract DE-AC52- extremely efficient for different sparse matrices sizes and 07NA27344. Lawrence Livermore National Security, LLC. structures even for matrices that don’t fit in GPU mem- ory. Our method benefits from both the highly parallel general-purpose computing cores available on a single GPU Philip Top and from multiple GPUs on a single platform. This pre- Lawrence Livermore National Laboratory sentation focuses on parallelism over multiple GPU cores. [email protected]

Carol S. Woodward Mohamed Gadou Lawrence Livermore Nat’l Lab University of Florida [email protected] [email protected]fl.edu CS15 Abstracts 137

Timothy A. Davis GPU and greatly reducing the required PCIe communica- Texas A&M tion. Computer Science and Engineering [email protected] Steven C. Rennich NVIDIA Sanjay Ranka [email protected] CISE, University of Florida, USA [email protected]fl.edu Timothy A. Davis Texas A&M Computer Science and Engineering MS163 [email protected] Sparse Communication Avoiding Pivoting and GPUs Darko Stosic NVIDIA Modern GPUs provide a window on future hardware plat- [email protected] forms that we need to design for. In this talk we de- scribe our experience in implementing direct methods for sparse symmetric indefinite matrices in CUDA, a topic MS164 that presents both mathematical and technical challenges. A Fast N-body Algorithm for Kernel Sums in High Whilst a number of communication-avoiding methods have Dimensions been developed for dense linear algebra, their applicability to sparse linear algebra is limited as they ignore sparsity in In computational statistics kernelized methods require the selecting pivots, generating significant fill. We will describe rapid evaluation of kernel sums. We present a fast al- heuristics that attempt to manage this complexity through gorithm for such sums and introduce novel methods for a series of fall-back strategies that in the best case have sim- pruning and for approximating the far field. The scheme ilar communication properties to the unpivoted Cholesky is kernel-independent (does not use analytic expansions) factorization, but for numerically challenging problems de- and the pruning is combinatorial (not geometric). Its com- liver stability on a par with the best existing sparse sym- plexity depends linearly on the dimension. We present the metric indefinite direct solvers. structure of the algorithm and experimental results that demonstrate is performance. As a highlight, we report re- Jonathan Hogg sults for Gaussian kernel sums for one million points in STFC Rutherford Appleton Lab, UK 1000 dimensions and for problems in which the kernel has [email protected] variable bandwidth.

Jennifer Scott George Biros, Bill March Rutherford Appleton Laboratory University of Texas at Austin Computational Science and Engineering Department [email protected], [email protected] [email protected] Bo Xiao School of Computational Science and Engineering MS163 Georgia Institute of Technology GLU: LU Re-Factorization on the GPU [email protected]

In realistic applications we often solve a sequence of similar linear systems that arise as part of a non-linear iteration MS164 process. In this talk we focus on the design and implemen- Information-Theoretic Tools for Uncertainty Quan- tation of the parallel LU re-factorization on the GPU. It tification of High Dimensional Stochastic Models. can be performed on the linear systems that have the same sparsity pattern, pivoting and reordering to minimize fill-in We present mathematical tools for deriving optimal, com- as the original system. We also discuss batched version of putable bounds on sensitivity indices of observables for the algorithm and present relevant numerical experiments. complex stochastic models arising in biology, reaction ki- netics and materials science. The presented technique al- Maxim Naumov, Sharan Chetlur, Lung Sheng Chien lows for deriving bounds also for path-dependent function- NVIDIA als and risk sensitive functionals. The use of variational [email protected], [email protected], representation of relative entropy also allows for error es- [email protected] timation and uncertainty quantification of coarse-grained models.

MS163 Paul Dupuis Division of Applied Mathematics Accelerating the Supernodal Sparse Cholesky Fac- Brown University torization on GPUs [email protected] Achieving high performance sparse Cholesky factorization on a GPU is difficult due to irregular computation, limited Markos Katsoulakis GPU memory, and PCIe communication. Previous work University of Massachusetts at Amherst showed how some PCIe communication could be hidden [email protected] behind CPU and GPU computation. This work shows how a larger portion of the factorization can be accelerated on Yannis Pantazis the GPU, and overall performance substantially improved, University of Massachusetts, Amherst by moving entire branches of the elimination tree to the Department of Mathematics and Statistics 138 CS15 Abstracts

[email protected] Numerical and Modeling Error Uncertainty

Petr Plechac In this talk we will explore the use of adjoint based esti- University of Delaware mates of numerical error (upper bounds where available) Department of Mathematical Sciences in quantities of interest to aid in the construction of more [email protected] effective surrogates. This will complement the vast body of work on constructing such surrogates for model parameter uncertainty characterization. MS164 Hossein Aghakhani Use of Parallel MCMC Methods with the Commu- University at Buffalo, SUNY nity Land Model haghakha@buffalo.edu

We present the development of a parallel Delayed Rejection AbaniK.Patra Adaptive Metropolis (DRAM) algorithm and its use with SUNY at Buffalo the Community Land Model for Bayesian calibration of Dept of Mechanical Engineering model parameters. Bayesian calibration of expensive sim- [email protected] ulations is often done with emulators because of the com- putational cost of Monte Carlo Markov Chain (MCMC) Elaine Spiller sampling. In this case, we chose not to use emulators and Marquette University instead use a parallel chain scheme directly on CLM to [email protected] obtain reasonable run times.

Jaideep Ray MS165 Sandia National Laboratories, Livermore, CA Calibration of the Spalart-Allmaras Turbulence [email protected] Model for Blunt Body Re-Entry Vehicle Flows Us- ing DNS Data Laura Swiler Sandia National Laboratories The Spalart-Allmaras turbulence model is calibrated for Albuquerque, New Mexico 87185 use in predictions of transonic, chemically reacting bound- [email protected] ary layers with favorable pressure gradients similar to those observed on blunt body re-entry vehicles. The calibration Maoyi Huang takes the form of a Bayesian update for the model pa- Pacific Northwest National Lab rameters. We detail DNS cases specially designed for this [email protected] calibration, uncertainty estimates for the resulting DNS data, a simple model inadequacy representation used for Jason Hou the calibration, and the posterior results for the model pa- Pacific Northwest National Laboratory rameters. [email protected] Robert D. Moser University of Texas at Austin MS164 [email protected]

Highly Scalable Hierarchical Sampling Algorithms Todd Oliver for Gaussian Random Fields PECOS/ICES, The University of Texas at Austin [email protected] The ability to generate samples of random fields with pre- scribed statistical properties is a key ingredient for many Victor Topalian uncertainty quantification methods. In this talk, we will PECOS/ICES present a highly scalable multilevel hierarchical sampling The University of Texas at Austin technique that has linear complexity. Samples are gener- [email protected] ated on a coarse grid using the truncated Karhunen-Lo´eve expansion, and then extended to the finer levels by solving a stochastic partial differential equation. An application Rhys Ulerich to Multilevel Monte Carlo simulations of subsurface flows The Univeristy of Texas at Austin will be presented to demonstrate the good scalability of our [email protected] method. MS165 Panayot Vassilevski Lawrence Livermore National Laboratory Quantifying the Impact of Numerical Errors Along [email protected] with Other Uncertainties on Probabilistic Hazard Mapping Umberto E. Villa A probabilistic hazard map requires: 1) a stochastic sce- Center for Advanced Scientific Computing nario model – incorporating data and expert opinion – that Lawrence Livermore National Laboratory describes the system’s aleatory variability, and 2) a physi- [email protected] cal model which lets one explore catastrophic hazards (in- undation by flooding, landslides, tsunamis, etc). Geophys- ical modelers often assume that uncertainty >> numerical MS165 error and ignore impacts of the later. We have devised a Construction of Gaussian Surrogate Process Using surrogate-based strategy using adjoint error estimates to CS15 Abstracts 139

quantify the effects numerical errors and other uncertain- [email protected] ties on hazard probabilities.

Elaine Spiller MS166 Marquette University [email protected] Optimization of Computational Simulation Set for Quantification of Hurricane Surge Extreme-Value Statistics Hossein Aghakhani University at Buffalo, SUNY haghakha@buffalo.edu Extreme-value hurricane flooding statistics are essential for effective coastal risk assessment. The joint probabil- ity method is a robust and reliable approach for quantify- MS165 ing these statistics and their uncertainty. Yet, the array of hurricane possibilities and complexity of physical pro- Predictive Uncertainty Quantification of An Ablat- cesses that must be simulated result in an unmanageable ing Entry Vehicle Heatshield computational burden. Here, optimal sampling to reduce this burden is achieved with physics-based, algebraic surge Simulations of hypersonic reacting flow require the integra- response functions to define continuous probability density tion of a number of complex physical models with uncer- functions for hurricane flood elevation. tain parameters, evaluated at conditions for which exper- imental data may be sparse. We discuss calibration and Jennifer L. Irish forward propagation of uncertainty in the context of the Virginia Polytechnic Institute and State University atmospheric re-entry of a symmetric capsule body with an [email protected] ablating heatshield, focusing on cycles of calibration and prediction for aerothermochemistry, surface ablation, tur- bulence, and other submodels. Multiple years’ results will MS166 be presented. Hurricane Storm Surge Risk Analysis for the US Roy Stogner North Atlantic Coast University of Texas at Austin [email protected] In this work, we use a physically based assessment to es- timate the risk of hurricane storm surge in Narragansett Bay, RI, Jamaica Bay, NY, Atlantic City, NJ, and Norfolk, MS166 VA. Using a novel approach to risk analysis, we estimate Mathematical Modeling of Gliomas: Implications storm surge recurrence intervals for the current and future for Interpreting Therapeutic Efficacy Through climate by forcing a hydrodynamic model with thousands Imaging of synthetic hurricanes generated using data from obser- vations and global climate models. Our results have been Glioblastoma is the most aggressive form of primary brain used to inform a multi-institutional, interdisciplinary re- tumor. Traditional clinical images, such as magnetic res- search effort to develop “Structures of Coastal Resilience.” onance images, are limited in their ability to capture the full extent of the diffuse disease both prior to therapy and, even more, post therapy. In this talk, we will discuss how Talea Mayo, Ning Lin mathematical modeling can lend insights for interpreting Princeton University these images on a patient-specific basis by estimating the [email protected], [email protected] extent of the disease not visible on imaging.

Andrea Hawkins-Daarud MS166 Department of Neurological Surgery Northwestern University Representing model inadequacy: A stochastic op- [email protected] erator approach We investigate model form uncertainty for a reaction mech- Russell Rockne anism model in hydrocarbon combustion. In a typi- Northwestern University cal reaction, the complete mechanism is either not well- [email protected] understood, or too complex to effectively use as part of a larger combustion problem, necessitating a reduced model. David Corwin To account for the discrepancy between the full model and LaunchPad Lab its reduced version, we propose an additive, linear, prob- [email protected] abilistic formulation. This representation is encoded in a random matrix, whose entries are calibrated using a hier- Alexander R.A. Anderson archical Bayesian scheme. In particular, this formulation Moffitt Cancer Center is designed to respect certain physical constraints, but also alexander.anderson@moffitt.org be flexible enough to apply to multiple reactions.

Paul Kinahan Rebecca Morrison University of Washington UT Austin [email protected] [email protected]

Kristin R. Swanson Robert D. Moser Northwestern University University of Texas at Austin 140 CS15 Abstracts

[email protected] [email protected], [email protected]

MS167 MS167 Reconnection ALE in a Massively-Parallel, Adaptive Reconnection-Based Arbitrary La- Staggered-Grid, Multi-Physics Code grangian Eulerian Method The development of Reconnection-based Arbitrary We describe a new h-adaptive ReALE (A-ReALE) method. Lagrangian-Eulerian (ReALE) methods has focused on The adaptive rezone of A-ReALE is proposed based on cell-centered discretizations for Lagrangian hydrodynam- the equidistribution principle of centroidal Voronoi tes- ics to greatly simplify the conservative remapping of sellations (CVTs). In the rezone phase, we introduce a fluid variables. Our approach is different, using both quadtree based initialization to determine the initial guess spatially-staggered and subzonal discretizations. This of the cell generators. A new CVT is generated by mini- talk will focus on the benefits of this discretization in the mizing the mesh energy of the Voronoi tessellation. For 2D context of multi-physics, the unique challenges it presents examples of time-dependent simulations, A-ReALE shows in the context of ReALE, and the novel techniques we better mesh convergence than ReALE. have developed to address these challenges.

Wurigen Bo David Starinshak CCS-2, LANL Lawrence Livermore National Laboratory [email protected] [email protected]

Misha Shashkov J. Michael Owen, Douglas S. Miller Los Alamos National Laboratory Lawrence Livermore Nat. Lab [email protected] [email protected], [email protected]

MS168 MS167 Interpolatory Model Reduction for Nonlinear In- Multimaterial Simulation in Reale Framework version

In the ReALE method presented here, connectivity of the Model reduction by rational interpolation has been effec- mesh is allowed to change during the reconnection phase. tively used for producing accurate, in some cases, optimal The main idea is to define a new grid using specific move- reduced models in a numerically feasible way. In this talk, ment of generators and formalism of Voronoi diagrams. we will show that interpolatory methods can be also eas- This method leads to general polygonal mesh and allows to ily employed in nonlinear inversion problems to reduce the follow Lagrangian features of the mesh much better than cost of the overall inversion process with little loss of ac- for standard ALE methods. Furthermore, in the context curacy. We will present the framework in the application of multimaterial computations using ReALE method (as setting of diffuse optical tomography. for standard ALE method), grid and fluid move separately, Serkan Gugercin and mixed cells containing two or more materials could ap- Virginia Tech. pear. These mixed cells contain material interfaces, which Department of Mathematics need special treatment to be taken into account. This is [email protected] done using the Moment of Fluid (MOF) method.

Jerome Breil MS168 CELIA, UMR 5107 CNRS, University of Bordeaux and Nonlinear Model Order Reduction Using CEA, 351 Co Pod/DEIM 4-D Var with Trust Region Ap- [email protected] plied to a Spherical Shallow Water Equations Model

MS167 We address a very large-scale optimization problem with PDE constraints governed by a spherical shallow water Triangular Metric-Based Mesh Adaptation for equations as proxy for an atmospheric model.( 4-D VAR) Compressible Multi-Material Flows in Semi- MOR with POD/DEIM and trust region model using both Lagrangian Coordinates forward and adjoint snapshots opens opportunity of reduc- ing computational cost of 4-D VAR data assimilation. Im- Lagrangian methods for multi-material flows are very at- pact of number of POD basis functions, DEIM points along tractive (precision, contact discontinuity preservation), but with choice of snapshots and optimization algorithm and fail to calculate vertexes or shears. Classical remedy is ALE finally CPU-speed-up will be investigated. method which consists defining a ”smoother” mesh with- out changing its connectivity and the remap the solution Ionel M. Navon on it. The next step is mesh adaptation to improve robust- Florida State University ness and precision. In this context, we present a metric- Department of Scientific Computing based triangular mesh adaptation method in 2D, using an [email protected] interface reconstruction approach to address the numerical dissipation of material interfaces. Fangxin Fang Department of Earth Science and Engineering Stephane Del Pino, Isabelle Marmajou Imperial College London, U.K. CEA [email protected] CS15 Abstracts 141

Juan Du [email protected] IAP, Academia Sinica, Beijing, China [email protected] Christopher A. Beattie Virginia Polytechnic Institute and State University [email protected] MS168 Reduced Order Modelling for Fluid-Structure In- Serkan Gugercin teraction Problems Virginia Tech. Department of Mathematics We present some advances in Reduced Order Modelling ap- [email protected] plied to fluid structure interaction problems, modelled as inverse problems within a parametric setting. Special at- tention is devoted to the coupling between fluid and struc- MS169 ture through the interface in order to apply reduced com- Certified Reduced Basis Model Reduction for putational models to fluid and structure and manage the Maxwell’s Equations interface deformation with efficient algorithms. A special emphasis is devoted to the coupling between optimization The Reduced Basis Method generates low-order models for and fluid-structure interaction problems. the efficient evaluation of parametrized PDEs in many- query and real-time contexts. The approximation quality Francesco Ballarin is certified by using rigorous error estimators. We apply the Politecnico di Milano, Italy Reduced Basis Method to systems of Maxwell’s equations [email protected] arising from electrical circuits. Using microstrip models, the input-output behaviour of interconnect structures is Gianluigi Rozza approximated for a certain frequency range, parametrized SISSA, International School for Advanced Studies geometry like distance between microstrips and material Trieste, Italy coefficients. [email protected] Martin W. Hess Max-Planck-Institute for Dynamics of Complex Technical MS168 Systems Magdeburg Aposteriori Error Estimates and Adaptive Re- [email protected] duced Order Modeling Data Assimilation Peter Benner We will develop goal-oriented aposteriori estimators of the Max Planck Institute, Magdeburg, Germany error in the strong constraint reduced order 4DVar solu- [email protected] tion. Specifically we will formulate goals as functions that depend on the analysis obtained by minimizing a standard data assimilation cost function. The novel framework will MS169 be used to guide an adaptive efficient choice of snapshots, Parameter Estimation for Inverse Problems location of discrete empirical interpolation points (DEIM) and matrix DEIM indexes leading to suboptimal reduced As mathematical models continue to grow in size and com- solutions that approximate well the full data assimilation plexity, the efficiency of the numerical methods used to analyses. solve their corresponding inverse problems becomes in- creasingly important. With differential equation models, Razvan Stefanescu for example, avoiding the computation of the forward solu- Virginia Tech tion is desirable. Constructing a “nearby” inverse problem [email protected] avoids this computation to create a numerically robust ap- proach while also providing parameter estimates suitable Adrian Sandu for the solution of the original inverse problem. Virginia Polytechnic Institute and State University Justin Krueger [email protected] Department of Mathematics Virginia Tech [email protected] MS169 Numerical Stability Issues in H2 approximation Methods MS169 Stochastic Approach to Nonlinear Inversion Com- We discuss the fine details of numerical implementation of bining Simultaneous Random and Deterministic the IRKA and the VF algorithms for H2 rational approx- Sources imations of linear systems, i.e. turning the methods into reliable mathematical software. Our thesis is that such fi- We discuss parametric inversion for diffuse optical tomog- nal step is by no means simple or routine task, even with raphy using simultaneous random sources and detectors to the state of the art numerical software packages. We tackle drastically reduce the costs of the expensive solution of the problems of the underlying Cauchy and Vandermonde many large linear systems to be solved. Each linear sys- structures, moment matching, as well as convergence issues tem corresponds to a solving a 3D PDE. We compare this in the appropriate function spaces. with inversion approaches using reduced order models. In addition, we consider methods to improve solution quality Zlatko Drmac at low cost. University of Zagreb Department of Mathematics Selin Sariaydin 142 CS15 Abstracts

Department of Mathematics [email protected] Virginia Tech [email protected] MS170 Eric De Sturler Statistical Tests for Total Variation Regularization Virginia Tech Parameter Selection [email protected] We explore three new algorithms for choice of scaling or regularization parameter in Total Variation denoising. TV Serkan Gugercin regularization is viewed as an M-estimator and it is as- Virginia Tech. sumed to converge to a well defined limit even if the Department of Mathematics probability model is not correctly specified. The Dis- [email protected] 2 crepancy Principle, a modified version of the χ method for Tikhonov regularization and an empirically Bayesian Misha E. Kilmer approach are implemented and compared on benchmark Tufts University problems in digital image processing. [email protected] Jodi Mead Boise State University MS170 Department of Mathematics Using Numerical Optimization Methods for Sam- [email protected] pling in Inverse Problems MS170 Many solution methods for inverse problems compute the maximum a posteriori (MAP) estimator, or equivalently, Constrained Iterative Solver for Sparse Unmixing the regularized solution, by solving an optimization prob- and Deblurring of Hyperspectral Images lem. Uncertainty quantification (UQ), on the other hand, Spectral unmixing involves the computation of fractional typically requires sampling from the Bayesian posterior contributions of elementary spectra, called endmembers. density function. In this talk, we bring these two ideas to- The forward model involves a linear mixture of endmem- gether and present posterior sampling methods that make bers, with nonnegative sparse coefficients, and a wave- use of existing algorithms for computing regularized so- length dependent blurring operation. The inverse (recon- lutions/MAP estimators. Theoretically correct samplers struction) problem requires solving a large scale, struc- for both linear and nonlinear inverse problems will be pre- tured, constrained least squares problem. We show that sented. by exploiting structure of the coefficient matrix, and using known properties of the endmembers, iterative methods Johnathan M. Bardsley can be used to efficiently reconstruct the fractional abun- University of Montana dance coefficients. [email protected] Sebastian Berisha University of Pennsylvania MS170 [email protected] Point Spread Reconstruction from the Image of a Sharp Edge: Computation and Uncertainty Quan- James G. Nagy tification Emory University Department of Math and Computer Science The blurring of an image is often modeled as convolution [email protected] with a point spread function (PSF) specific to the imaging instrument. We present a method for estimating the PSF Robert Plemmons that is suitable for applications where it is possible to image Wake Forest University a sharp edge. In our model, the PSF is a solution to a [email protected] Fredholm integral equation of the first kind, known to be ill-posed. We employ optimization and sampling methods to compute several stable estimates of the solution. MS171 Task Based Programming with Pycompss: Lever- Kevin Joyce aging Python in Parallel Platforms University of Montana Department of Mathematical Sciences StarSs is a family of task-based programming models which [email protected] is based on the idea of writing sequential code which is ex- ecuted in parallel at runtime taking into account the data dependences between tasks. COMPSs is an instance of Johnathan M. Bardsley StarSs, which intends to simplify the execution of Java ap- University of Montana plications in distributed infrastructures, including clusters [email protected] and Clouds. The talk will focus in PyCOMPSs, a binding for the Python language which will enable a larger number Aaron B. Luttman of scientific applications in fields such as lifesciences and National Security Technologies, LLC in the integration of COMPSs with new Big Data resource [email protected] management methodologies developed at BSC.

Peter Golubstov Rosa M. Badia Moscow State University Barcelona Supercomputing Center / CSIC CS15 Abstracts 143

[email protected] Airbus Group Innovations [email protected]

MS171 Coarse Grained Task-Based Parareal Parallel-In- MS172 Time Applications in Fusion Energy Estimation of Unmodeled Gravitational Wave Parallelization in the temporal domain has recently Transients: an Application of Spline Based Regres- emerged as a promising approach to utilize the massive sion and Particle Swarm Optimization concurreny at the heart of existing and emerging comput- ing platforms. We present an event-driven task-based for- Detecting and estimating unmodeled transient gravita- mulation of the parareal algorithm, implemented using a tional wave (GW) signals in noisy data is a major challenge flexible, lightweight Python framework for coupled simula- in GW data analysis. This paper explores a solution that tions. We describe recent applications of this framework combines spline regression with particle swarm optimiza- to various problems in fusion modelling and simulation, tion for knot placement and directional parameter estima- including turbulance, advanced tokamak scenario analysis, tion. Analyses of data from a network of detectors show and plasma edge dynamics. fairly good directional estimates, with reasonable fidelity in the reconstruction of both GW polarization waveforms, Wael R. Elwasif at a signal to noise ratio capped at 15. Advisor: Soumya Oak Ridge National Laboratory Mohanty, U Texas, Brownsville [email protected] Calvin Leung Debasmita Samaddar Harvey Mudd College CCFE [email protected] UK Atomic Energy Authority [email protected] MS172 MS171 Persistent Random Walk of Microorganisms in a A Task-Based Computational Astronomy Applica- Porous Medium tion We develop a persistent random walk model for the mo- The European Extremely Large Telescope project is one tion of swimming cells in an idealized lattice-like porous of Europe’s highest priorities in ground-based astronomy. medium. The walk is described by a Markov chain in phase The core implementation of the simulation lies in the in- space, tracking both position and velocity. Physical param- tensive computation of a tomographic reconstructor, which eters, including the overall geometry, bulk flow, and scat- is used to drive the deformable mirror in real-time from tering laws, are incorporated into the memory-dependent the measurements. A new task-based numerical algorithm transition amplitudes. We numerically compute first pas- is proposed to capture the actual experimental noise and sage times in MATLAB to predict the effects of lattice to substantially speed up previous implementations by ex- structure on microbial transport. Advisor: Joern Dunkel posing more concurrency, while reducing the number of (Massachusetts Institute of Technology) floating-point operations.

Hatem Ltaief Grace Lim Extreme Computing Research Center California State Polytechnic University, Pomona KAUST [email protected] [email protected] Aden Forrow MIT MS171 [email protected] Applications at Airbus Group of a Task-Based H- Matrix Solver MS172 The Boundary Element Method (BEM) requires the solv- ing of large, ill-conditionned, dense linear systems with a Mean Squared Displacement and Mean First Pas- large number of righ-hand sides. A H-Matrix is a hierachi- sage Time in Fluids with Memory cal, approximate, data-sparse storage format for matrices that can be manipulated to produce a fast direct linear Modeling the motion of passive particles in a viscous fluid is solver. We consider the H-Matrices for the BEM, with well studied and understood. Extensions to passive motion applications to Airbus Group industrial test cases ; and in a complex fluid which exhibits both viscous and elastic we present the parallelization of this algorithm in shared properties have been developed in recent years. However, and distributed memory, using the StarPU runtime sys- questions remain on the characterization of mean-square tem. An almost optimal parallel efficiency is achieved in displacement and mean first passage for different theoret- shared memory, along with promising results in distributed ical models. We present a statistically exact covariance memory. based algorithm implemented in parallel C++ to generate particle paths to answer these questions. Advisor: Chris- Guillaume Sylvand tel Hohenegger, Department of Mathematics, University of EADS CCR, Centre de Toulouse Utah [email protected] Michael Senter Benoit Lize University of Utah 144 CS15 Abstracts

[email protected] the case of high order reconstructions. The first order ac- curate semi-Lagrangian scheme is supplemented with poly- nomial reconstructions of the distribution function and of MS172 the collisional operator leading to an effective high order Pymethyl: A Bioinformatic Approach to Methyla- accurate numerical scheme for all regimes, from extremly tion Patterns and their Epigenetic Effects on Risk rarefied to highly collisional. The limitation of the recon- of Breast Cancer structions to avoid spurious oscillations is made a poste- riori using polynomial order decrementation. This later is The study looked at the genomes of two different groups based on so-called detection criteria which filter problem- of parous and nulliparous women and their risk for breast atic cells which need limitation from acceptable cells which cancer. These genomes were sequenced for their genomic are updated with an optimal accurate scheme. methylation patterns. The information was then processed by a high throughput, brute force algorithm to look for Giacomo Dimarco places of hypermethylation within the promoter regions or Universit`a degli Studi di Ferrara transcribable regions of specific genes. This information [email protected] helps us gain information on the epigenetic effects to the risk of breast cancer. Advisor: Jose Russo, Fox Chase Cancer Center Mentor MS173 Practical Numerical Methods for Solving the Boltz- Cody Watson mann Transport Equation in Nuclear Reactor Wofford College Analysis [email protected]fford.edu The numerical solution of the linearized form of the Boltz- mann Transport Equation (BTE), as applied to the trans- MS172 port of neutrons within a ”multiplicative” medium, results Modeling Bull Sperm Motility Using Image Pro- in the characterization of various macroscopic quantities cessing of interest such as criticality, power distribution, and com- positional changes in a nuclear reactor. For the purpose We use image processing to determine whether the chemi- of practical reactor analysis and design, various physical cal heparin may change bending in a bull sperm flagellum. approximations are introduced in order to reduce the size Experimental movies for several sperm are analyzed to de- of the neutral-particle phase-space. The goal of this talk termine sperm location. From this data, curvature of bend- is twofold: first, to review current standard numerical ing and swimming speeds are analyzed. We also compute methods used for the solution of BTE, and secondly, to bending forces and resulting fluid flow using the method present recent progress in the spatial discretization of the of regularized Stokeslets. We conclude that heparin does BTE in the context of lattice physics calculations. The change bending in the neck region as well as changing hy- Method of Characteristics (MoC), used to solve BTE in drodynamic efficiency and energy. Advisor: Sarah D. Ol- lattice physics, has become ubiquitous in design calcula- son, Worcester Polytechnic Institute tions. However, the order of accuracy of this scheme, as a Linan Zhang function of mesh size, remains first-order. In order to relax Worcester Polytechnic Institute this limitation, a spatially-linear scheme is introduced in [email protected] the MoC scheme in order to obtain second-order accuracy. Although general high-order discretizations have been de- rived, the spatially-linear scheme remains an optimal com- MS172 promise between run time and storage, for an equal level of Bounds on Electrical Fields in Two-Component In- accuracy. Numerical results will be presented to support homogeneous Bodies the conclusions sketched above and realistic numerical sim- ulations will presented and discussed. We investigate bounds on the maximum value of electrical field in two-component inhomogeneous bodies. We assume Rodolfo Ferrer the conductivities of the inclusions and the surrounding Studsvik body are known, with no assumptions on the precise ge- [email protected] ometry of the inclusions. Results are in terms of values of the voltage and current that can be attained from mea- surements on the boundary of the body. This research has MS173 potential applications in preventing electrical breakdown in A Deterministic-Particle Transport Solver for composite materials. Advisor: Graeme Milton, University Scale-Bridging Simulation of Thermal Radiative of Utah Transfer

Zoe Koch, Michael Primrose, Michael Zhao A high-order, low-order (HOLO) algorithm is a moment- University of Utah based, scale-bridging algorithm for transport equations. [email protected], tba, [email protected] HOLO algorithms have recently made significant efficiency and accuracy impacts in thermal radiative transfer (TRT) problems. The goal of this work is to develop an efficient, MS173 robust, Lagrangian, characteristic-based transport solver On a New Class of Semi-Lagrangian Schemes for for TRT problems within the context of a HOLO algo- Kinetic Equations rithm. A preliminary example has shown that a new HO solver can achieve a factor of 100 reduction in computa- In this talk we introduce a new class of semi-Lagrangian tional effort compared to both Monte Carlo and Sn for schemes for simulating kinetic type equations. In this ap- and equivalent accuracy. proach we genealize the fast semi-Lagrangian scheme devel- oped in [J. Comput. Phys., Vol. 255, 2013, pp 680-698] to Hyeongkae Park CS15 Abstracts 145

Los Alamos National Laboratory [email protected] [email protected]

MS174 MS173 Reduced Order Models for Nonlinear PDE- A Hierarchy of Hybrid Numerical Methods for Constrained Optimization Problems in Fluid Dy- Multi-Scale Kinetic Equations namics

In this work, we construct a hierarchy of hybrid numerical We propose a model order reduction framework for methods for multi-scale kinetic equations based on moment parametrized optimization problems constrained by non- realizability matrices, a concept introduced by Levermore, linear PDEs. First, we build – by means of either RB- Morokoff and Nadiga. Following such a criterion, one can greedy or POD methods – the reduced order model follow- consider hybrid scheme where the hydrodynamic part is ing a suitable all-at-once optimize-then-reduce paradigm. given either by the compressible Euler or Navier-Stokes Then, combining rigorous error bounds with some heuris- equations, or even with more general models, such as the tic computational strategies, we provide cheap yet reliable Burnett or super-Burnett systems. The efficiency of the a posteriori error estimates. The methodology is applied method obtained can sometimes match the one of a fluid to the boundary optimal control of parametrized Navier- method, with the accuracy of a kinetic one. Stokes equations.

Thomas Rey Federico Negri University of Maryland Mathematics Institute of Computational Science and [email protected] Eng, EPFL federico.negri@epfl.ch Francis Filbet University of Lyon Andrea Manzoni fi[email protected] EPFL, MATHICSE-CMCS Switzerland andrea.manzoni@epfl.ch MS174 HJB-POD Feedback Control for Advection- Alfio Quarteroni Diffusion Equations Ecole Pol. Fed. de Lausanne Alfio.Quarteroni@epfl.ch We present an algorithm for the approximation of an infinite horizon optimal control problem for advection- diffusion equations. The method is based on the coupling MS174 between a POD representation of the solution and a Dy- Reduced Basis Method for Hamilton-Jacobi- namic Programming approximation scheme for the corre- Bellman Equations sponding stationary Hamilton-Jacobi equation. We discuss several features regarding the selection of the snapshots for We consider the Hamilton-Jacobi-Bellman (HJB) equa- advection dominated terms. Some test problems are pre- tion of the form −∂tv +supα − a(α; μ)Δv − b(α; μ) · sented to illustrate the method.  ∇v − f(α; μ) = 0 for numerous different parameters Alessandro Alla μ ∈D⊂IR p by applying the Reduced Basis Method. In Department of Mathematics our approach, the HJB equation is separated into an equa- University of Hamburg, Germany tion which determines v and another which yields α.To [email protected] obtain an error estimator, we use a space-time formulation of these equations and apply the Brezzi-Rappaz-Raviart Michael Hinze theory for quadratic non-linearities. The implementation Universit¨at Hamburg shows that this error estimator is efficient for the chosen Department Mathematik examples. [email protected] Sebastian Steck Institute for Numerical Analysis MS174 University of Ulm, Germany Application of Discrete Empirical Interpolation [email protected] Method to Reduced Order Modeling of Nonlinear Parametric Systems Karsten Urban Institute of Numerical Mathematics, University of Ulm We study two approaches of applying discrete empirical in- [email protected] terpolation method (DEIM) in the finite element context, one applied to the assembled and the other to the unassem- bled form of the nonlinearity. We carefully examine how MS175 DEIM is applied in each case, and the substantial efficiency Application of Algebraic Multigrid (PETSc) for gains obtained by the DEIM. In addition, we demonstrate Block Structured Adaptive Mesh Refinement Ap- how to apply DEIM to obtain ROMs for a class of param- plications (Chombo) eterized system that arises, e.g. in shape optimization. We report on progress in using algebraic multigrid (AMG) Harbir Antil methods in the numerical library PETSc for challeng- George Mason University ing problems in block structured adaptive mesh refine- Fairfax, VA ment (BSAMR) applications that use the Chombo library. 146 CS15 Abstracts

Chombo’s built-in geometric multigrid (GMG) solvers are der and stable ImEx simulations, while HYPRE excels at fast for simple operators but for problems with complex massively-parallel linear systems and is used to precondi- geometry GMG is not effective and AMG is an effective tion the implicit solves within ARKode. solution. We discuss new capabilities in Chombo for con- structing matrices, required for AMG, from BSAMR prob- Daniel R. Reynolds lems. Southern Methodist University Mathematics Mark Adams [email protected] Lawrence Berkeley Laboratory [email protected] MS176 Aerodynamic Simulations Using a High-Order Dis- MS175 continuous Galerkin Solver Solvers and Error Control for Atmospheric Column Physics A parallel high-order Discontinuous Galerkin solver is de- veloped to simulate aerodynamic problems. The solver Atmospheric column physics involves coupling of nons- capabilities include: mixed hybrid elements, hp-adaption, mooth processes such as phase change and nonlocal/stiff and an exact linearization used in an implicit precon- processes like radiation and precipitation, along with strict ditioned Newton-Krylov solver. Preconditioners include positivity constraints. The splitting schemes currently Gauss-Seidel relaxation, line implicit Jacobi, and ILU(0). used by CAM are not convergent in time and have been Flowswithstrongshocksaresimulatedonsimplegeome- calibrated to compensate for systematic numerical errors. tries using a PDE based artificial viscosity. Also, turbulent In this talk, we investigate the use of more rigorous flows are simulated on 2D airfoils and a full 3D aircraft us- ODE/DAE approaches using PETSc and Sundials on the ing the new negative Spalart-Almaras RANS model. basis of accuracy and efficiency. Michael Brazell Jed Brown University of Wyoming Mathematics and Computer Science Division [email protected] Argonne National Laboratory and CU Boulder [email protected] Dimitri Mavriplis Department of Mechanical Engineering MS175 University of Wyoming [email protected] FASTMath Unstructured Mesh (MOAB) Solver (PETSc) Interactions

High fidelity applications typically rely on unstructured MS176 meshes representing complex geometry, and interoperable Superconvergent HDG Methods with Symmetric solver interfaces are critical for optimal mesh based traver- Stress Approximations for Stokes Flow (and Linear sal and operator assembly procedures. We present devel- Elasticity) opments on a discretization manager DM implementation that utilizes array-based mesh database MOAB that ex- We present an abstract framework to obtain superconver- poses scalable mesh handling capabilities to simulators, re- gence of HDG methods with symmetric stress approxi- sulting in reduced memory and communication overhead. mations (HDG-S methods) for the Stokes flow. Several Several scalar and multi-component solver demonstrations 2D methods are constructed based on local enrichment of employing combinations of geometric multigrid and alge- the stress spaces of existing (suboptimal) HDG-S methods. braic preconditioners is discussed. Numerical results are provided to show their superior per- formance. Extension of the results to linear elasticity with Vijay Mahadevan, Iulian Grindeanu symmetric stress approximations is discussed. And chal- Argonne National Laboratory lenges for constructing 3D superconvergent HDG-S meth- [email protected], [email protected] ods are addressed.

Barry F. Smith Bernardo Cockburn, Guosheng Fu Argonne National Lab School of Mathematics MCS Division University of Minnesota [email protected] [email protected], [email protected]

MS175 MS176 Scalable Adaptive ImEx Integration with ARKode Active Fluxes; A New High-Order Paradigm and HYPRE We consider finite-volume schemes in which the interface Computational science increasingly focuses on simulations fluxes are independent degrees of freedom, as proposed by of complex systems, typically involving interacting physical van Leer in 1977. In the semi-discrete limit these are processes and large data/computational requirements. In similar to, and in some cases identical to, Discontinuous this talk, we consider the solution of a system of interacting Galerkin methods, but are naturally fully discrete and in advection-diffusion-reaction equations, decomposing these that case have several advantages, being more accurate, into stiff (reaction-diffusion) and non-stiff (advection) por- faster and requiring less storage. tions. For this problem, we apply two open-source solver li- braries within the FASTMath project. The ARKode solver Philip L. Roe (part of the SUNDIALS library suite) enables high or- Ann Arbor CS15 Abstracts 147

[email protected] optimizations including distributed and shared memory parallelism, integration with co-processors, vectorization and cache optimization. We also integrate our method MS176 with GMRES in PETSc to compute solutions to variable Riemann-Solver-Free Space Time Discontinuous coefficient Stokes problems and demonstrate scalability to Galerkin Method for General Conservation Laws thousands of compute nodes on TACC’s Stampede super- computer. We will talk about a Riemann-solver-free space-time dis- continuous Galerkin method for general conservation laws. Dhairya Malhotra The method uses staggered space-time mesh to enforce Institute of Computational Engineering and Sciences space-time flux conservation in the DG framework. The The University of Texas at Austin resulting method is of high order and Riemann-solver free. [email protected] The method is able to solve general conservation laws such as compressible Euler equations, shallow water equations George Biros and magnetohydrodynamics equations without the need of University of Texas at Austin any type of Riemann solvers. [email protected] Shuang Z. Tu Jackson State University MS177 [email protected] Robust Implementation of Quadrature by Expan- sion (QBX)

MS177 QBX is a quadrature scheme for computing singular in- ScalFMM: A Generic Parallel Fast Multipole Li- tegrals that arise from the discretization of integral equa- brary tions. In its standard (global) form, it fails to be robust for close to touching geometries. In this talk, we introduce a ScalFMM (Parallel Fast Multipole Library for Large Scale local variant of QBX. The local variant is computationally Simulations) offers all the functionalities needed to perform more expensive, and therefore should only be used judi- large parallel simulations while enabling an easy customiza- ciously when needed. We provide details of a robust hybrid tion of the simulation components: kernels, particles and implementation of global and local QBX which uses local cells. We will present how we use our library on two kinds QBX only in areas of complicated geometry. of application involving boundary integral representations of physical fields. The first one implements isotropic dislo- Manas Rachh cation kernels for Dislocation Dynamics and the second a Courant Institute time dependent kernel for acoustic problems. NYU [email protected] Pierre Blanchard Inria Leslie Greengard [email protected] Courant Institute New York University Berenger Bramas, Olivier Coulaud [email protected] INRIA [email protected], [email protected] Michael O’Neil New York University Eric F. Darve [email protected] Stanford University Mechanical Engineering Department Andreas Kloeckner [email protected] Department of Computer Science University of Illinois at Urbana-Champaign Laurent Dupuy [email protected] CEA-Saclay [email protected] MS177 Arnaud Etcheverry ExaFMM – a Testbed for Comparing Various Im- Inria plementations of the FMM [email protected] The software design space for the fast multipole method Guillaume Sylvand (FMM) is large, where various schemes exist for partition- EADS CCR, Centre de Toulouse ing, communication, tree traversal, and translation opera- [email protected] tors. The optimal choice is problem and architecture de- pendent, and most FMM codes focus on a specific combina- tion of the two. ExaFMM is a open source FMM code that MS177 provides the capability to explore this vast design space PVFMM: A Parallel Fast Multipole Method for without sacrificing speed, scalability, or readability. Volume Potentials Rio Yokota PVFMM is a scalable FMM library for computing solu- King Abdullah University of Science and Technology tions to constant coefficient elliptic PDEs (Poisson, Stokes, [email protected] Helmholtz) on cubic domain with free-space and periodic boundary conditions. In this talk, we discuss performance David E. Keyes 148 CS15 Abstracts

KAUST periments reveal a competitive performance. [email protected] Abner J. Salgado Lorena A. Barba Department of Mathematics Department of Mechanical and Aerospace Engineering University of Tennessee George Washington University [email protected] [email protected] MS178 MS178 Robust a Priori and a Posteriori Error Estimates for Diffusion Problems with Discontinuous Coeffi- A Posteriori Error Estimation in the Maximum cients Norm for Finite Element Methods For diffusion problems of discontinuous coefficients, the Adaptive finite element methods are designed to control quasi-monotonicity assumption (QMA) is a very impor- the error in measuring a specific norm or functional of the tant condition to guarantee the robustness of problems in- solution. In some situations it is of interest to control the dependent of the coefficients. In this talk, new results of maximum error. In this talk we will discuss recent progress robust and optimal a priori and a posteriori error estimates in developing a posteriori error estimates in the maximum for various finite element approximations of the diffusion norm for elliptic problems, with special focus on singularly problem with discontinuous coefficients with and without perturbed reaction-diffusion equations. Time allowing, we QMA are discussed. With new tools, we show that Con- will also discuss the sharpness of logarithmic factors which forming FEM is only optimal and robust in 2D with low appear in our estimates. regularity, while Mixed FEM, Nonconforming FEM, and DGFEM are both robust with respect to coefficients and Alan Demlow optimal with respect to local regularities. For a posteri- Texas A&M University ori error estimates, using nodal interpolations in stead of [email protected] Clement interpolations, we show the robustness of CFEM, MFEM, NFEM, and DGFEM without GMA.

MS178 Shun Zhang Robust Residual-Based a Posteriori Error Estima- City University of Hong Kong tion for Interface Problems: Nonconforming Ele- [email protected] ments MS179 A robust residual-based a posteriori error estimation for the non-conforming linear finite element approximation to Primal-Dual Newton Conjugate Gradients for the interface problem is studied. We introduce a new and Compressed Sensing Problems with Coherent and direct approach, without using the Helmholtz decomposi- Redundant Dictionaries tion, to analyze the reliability of the estimator. It is proved Abstract not available at time of publication. that our estimator is reliable with the constant indepen- dent of the jump of the interfaces, without the assumption Kimon Fountoulakis that the diffusion coefficient is quasi-monotone. Numerical University of Edinburgh results are also presented. [email protected] Cuiyu He Purdue University MS179 [email protected] Augmented Lagrangian Methods for Large-Scale Nonlinear Optimization Zhiqiang Cai Purdue University Abstract not available at time of publication. Department of Mathematics [email protected] Sven Leyffer Argonne National Laboratory Shun Zhang leyff[email protected] City University of Hong Kong [email protected] MS179 Column Generation Techniques for Large Mixed- MS178 Integer Programs A PDE Approach to Fractional Diffusion: a Poste- We study two-stage mixed-integer programs (MIP) that riori Error Analysis arise from co-generation in smart buildings. These MIP problems are beyond the capability of available MIP solvers We derive a computable a posteriori error estimator due to a large number of binary variables in the second- for the α-harmonic extension problem, which localizes stage problem. We develop a column generation approach the fractional powers of elliptic operators supplemented that reduces problem size by building a coarser MIP model. with Dirichlet boundary conditions. The derived estima- The first-stage solutions are validated using a rolling hori- tor relies on the solution of small discrete problems on zon method. We test our approach using data sets from anisotropic cylindrical stars. It exhibits built-in flux equili- different types of buildings. bration and is equivalent to the error up to data oscillation. A simple adaptive algorithm is designed and numerical ex- Fu Lin CS15 Abstracts 149

Mathematics and Computer Science Division One of the advantages of this approach is that computa- Argonne National Laboratory tions can be carried out using fast Fourier transforms on [email protected] a nearly uniform grid. Approximations are obtained on overlapping domains and a global solution is obtained by weighted average. MS179 Convexification Methods for Sequential Quadratic Rodrigo B. Platte Programming Arizona State University [email protected] Abstract not available at time of publication.

Elizabeth Wong MS180 University of California, San Diego A Fast and Well-Conditioned Spectral Method Department of Mathematics [email protected] We describe a spectral method for the solution of linear or- dinary differential equations that leads to well-conditioned matrices that are banded except for a few rows. We ex- MS180 tend this to a spectral method for the solution of linear Gaussian-Localized Polynomial Interpolation (Her- partial differential equations using low rank approximation mite Function Interpolation) on a Finite Interval: and generalized Sylvester matrix equations. Techniques Are Spectrally-Accurate Rbfs Obsolete? from automatic differentiation and preconditioning are em- ployed to develop an automatic, adaptive, and spectrally Spectrally-accurate radial basis functions (RBFs) such as accurate solver. Gaussians often succeed where polynomial interpolation fails because of the Runge Phenomenon. Why? Compar- Alex Townsend ative analysis of RBF and polynomial cardinal functions Oxford University (nodal bases) shows that RBF cardinals are much more [email protected] localized. This motivated us to abandon RBFs in favor of Gaussian-mollified polynomial cardinal functions: much more accurate, cheaper to construct and much better con- MS181 ditioned than RBFs. Using potential theory, we prove an Recent Advances in Numerical Modelling of exponential, geometric rate of convergence. On a uniform Thermo-Chemically Coupled Two-Phase Flow grid, the Runge Phenomenon is not completely annulled, but the Runge Zone is an order of magnitude smaller than Many processes in geodynamics involve a significant for polynomial interpolation. Applications to solving dif- amount of active magmatism. Recent advances in compu- ferential equations, especially in complicated geometry, are tational magma dynamics have allowed formulating a novel in progress. A note was published as “Hermite Function multi-component two-phase flow model including a realis- Interpolation ..., Appl. Math. Letters, 26, 10, 995-997 tic visco-plastic rheology for host rock deformation and a (2013). basic thermodynamic disequilibrium model describing the simplified petrology of a multi-phase silicate material. The John P. Boyd model has been implemented numerically using a parallel University of Michigan finite-difference method in 2-D for the use in studies of Ann Arbor, MI 48109-2143 USA volatiles (H2O, CO2) in magmatic systems. [email protected] Tobias Keller University of Oxford MS180 Department of Earth Sciences Automatic Multivariate Approximation [email protected]

Fully automatic one-dimensional approximation can be im- plemented successfully using Chebyshev polynomial expan- MS181 sions, as demonstrated in the Chebfun software project. In Scalable Nonlinear Solvers for Magma Dynamics higher dimensions, dimensionality and geometry are major new challenges. One proposal for automatic approximation We present new nonlinear solvers for magma dynamics in two and three dimensions using partition of unity, spec- problems based upon the nonlinear preconditioning frame- tral methods, and radial basis functions will be presented. work in PETSc. We demonstrate their effectiveness on model problems, and examine a possible direction for con- vergence analysis. Tobin Driscoll University of Delaware Matthew G. Knepley Mathematical Sciences University of Chicago [email protected] [email protected]

Richard F. Katz MS180 University of Oxford A Windowed Fourier Method for Computations on [email protected] the Sphere

A spectral method based on windowed Fourier approxima- MS181 tions for computations on the sphere is presented. It relies Multi-Scale Modelling of Granular Avalanches on domain decomposition, such as in the cubed sphere, and is suitable for adaptive and parallel implementation. It is important to be able to predict the distance to which a 150 CS15 Abstracts

hazardous natural flows travel. In dense flows the large par- [email protected] ticles segregate to the surface, where they are transported to the margins forming bouldery flow fronts. In natural flows these bouldery margins experience a much greater MS182 frictional force, leading to frontal fingering instabilities. A Project Jupyter: a Language-Independent Archi- multiscale model for this fingering instability is compared tecture for Cse, from Interactive Computing to Re- in terms of cost and accuracy to full-scale discrete particle producible Publications simulations.

Anthony R. Thornton Project Jupyter is the evolution of the IPython interac- University of Twente tive computing system into language-agnostic components Multi-scale mechanics group to support all aspects of computational research. Jupyter [email protected] abstracts the basic elements of interactive computing into openly documented file formats and protocols. Using these, ”Jupyter kernels” can execute code in any language and MS182 communicate with clients that range from simple termi- nals to the rich web-based Jupyter Notebook that supports Domain Specific Languages and Automated Code code, results, rich media, text and mathematics. Generation:HighExpressivenessandHighPerfor- mance Fernando Perez Helen Wills Neuroscience Institute Software should be carefully designed to closely follow the University of California, Berkeley mathematical abstractions of the problem domain. We [email protected] demonstrate this principle with FEniCS, which employs a domain-specific language, UFL, that mimics the math- ematics of variational forms for finite element discretisa- MS183 tions. By following this principle, we demonstrate how UFL and the FEniCS code generation techniques can be Bayesian Global Optimization of Expensive Func- used to automatically derive extremely high-performance tions with Low-Dimensional Noise code for adjoints of PDEs, for use in sensitivity analysis, optimisation, and inverse problems. Motivated by the design of cardiovascular bypass grafts using computationally-expensive physics-based stochastic Patrick E. Farrell simulators, we consider optimizing an objective function Department of Mathematics that is an integral of some expensive-to-compute function University of Oxford over a low-dimensional space. While such problems can [email protected] be solved using an optimization solver for expensive deter- ministic functions, or for expensive noisy functions, neither uses the low-dimensional structure of the noise. We provide MS182 a new Bayesian global optimization method that exploits Moose: An Open Source Platform For Rapid De- this problem structure to improve performance. velopment of Multiphysics Simulation Tools Jing Xie Many physical phenomena can be modeled with systems of Cornell University partial differential equations. Some examples include nu- [email protected] clear reactors, geothermal flow, microstructural evolution, and fluid-structure interaction. Solving systems of non- Sethuraman Sankaran linear equations has typically been achieved with custom Heartflow, Inc. software or by combining existing simulation tools. The ssankaran@heartflow.com open-source Multiphysics Object-Oriented Simulation En- vironment (MOOSE; mooseframework.org) employs a dif- Abhay Ramachandra ferent approach: it provides a generic, common platform Department of Mechanical and Aerospace Engineering for solving multiphysics problems. This technique allows University of California, San Diego scientists and engineers to focus on the physics while the [email protected] framework manages the task of parallel, nonlinear solver development. A discussion of the platforms capabilities Saleh Elmohamed and software development model will be followed by sev- Cornell University eral example applications in nuclear physics, geophysics, [email protected] chemistry, and material science.

Derek R. Gaston Alison Marsden Idaho National Laboratory Department of Mechanical and Aerospace Engineering [email protected] University of California, San Diego [email protected] Cody Permann Center for Advanced Modeling and Simulation Peter I. Frazier Idaho National Laboratory Cornell University [email protected] [email protected]

David Andrs, John Peterson, Andrew Slaughter MS183 Idaho National Laboratory [email protected], [email protected], an- Modeling An Augmented Lagrangian for Improved CS15 Abstracts 151

Blackbox Constrained Optimization Piotr Putek Bergische Universit¨at Wuppertal We propose a combination of response surface modeling, [email protected] expected improvement, and the augmented Lagrangian nu- merical optimization framework, allowing the statistical model to think globally and the augmented Lagrangian to MS183 act locally. We focus on problems where the constraints A Model and Variance Reduction Method for Com- are the primary bottleneck, requiring expensive simulation puting Statistical Outputs of Stochastic Partial Dif- to evaluate and substantial modeling effort to map out. In ferential Equations that context, our hybridization presents a simple yet ef- fective solution that allows existing objective-oriented sta- We present a model and variance reduction method for tistical approaches, like those based on Gaussian process computing statistical outputs of stochastic PDEs. We com- surrogates and expected improvement heuristics, to be ap- bine the hybridizable discontinuous Galerkin (HDG) and plied to the constrained setting with minor modification. the reduced basis discretization of elliptic PDEs with a multilevel variance reduction method, exploiting the sta- Robert Gramacy tistical correlation among the HDG and reduced basis ap- University of Chicago proximations to accelerate the convergence of Monte Carlo [email protected] simulations. We develop a posteriori error estimates for the statistical outputs, and propose an optimal selection of Genetha Gray multilevel structure. Sandia National Laboratories [email protected] Ferran Vidal-Codina, Cuong Nguyen, Jaime Peraire Massachusetts Institute of Technology Sebastien Le Digabel [email protected], [email protected], [email protected] GERAD - Polytechnique Montreal [email protected] Michael B. Giles Mathematical Institute Herbert Lee Oxford University UC Santa Cruz [email protected] [email protected] MS184 Pritam Ranjan Acadia University Accurate All-Electron Electronic Structure Theory [email protected] for Large Systems This contribution focuses on algorithmic developments to- Garth Wells wards efficient, accurate all-electron methods for com- Department of Engineering putational simulations of materials and nanostructures University of Cambridge from first principles. We demonstrate (i) accurate nu- [email protected] meric atom-centered basis sets for ground-state density functional theory as well as perturbative methods such Stefan Wild as GW or RPA, (ii) the open-source, massively paral- Argonne National Laboratory lel eigenvalue solver library ELPA and developments con- [email protected] nected to it, essential for parallel scalability towards sys- tem sizes of ∼1000s of atoms, (iii) first steps towards a mixed, load-balanced CPU-GPU implementation real MS183 space integrals required in electronic structure theory. Topology Optimization of a Permanent-Magnet The methods described are implemented in the general- Synchronous Machine under Uncertainties purpose all-electron electronic structure code FHI-aims [http://aims.fhi-berlin.mpg.de] The modeling and simulation of a permanent-magnet syn- chronous machine requires the application of Maxwell’s Volker Blum equations. Within a two-dimensional finite element model, Duke University the shapes of rotor poles, which are represented by zero- [email protected] level sets, are optimized by a redistribution of an iron and a magnetic material using an iterative process. More specif- ically, we consider a stochastic problem, where random MS184 fields due to unknown variations of material properties are Enabling Large-Scale Hybrid Density Functional taken into account to model the propagation of uncertain- Theory Calculations ties. Furthermore, in a robust optimization formulation, a multi-objective functional, which includes the mean and Hybrid density functional theory (DFT), in conjunction the standard deviation, is minimized subject to constraints. with a treatment of van der Waals/dispersion interactions, For this purpose, we apply methods dedicated to stochas- provides a substantial improvement over popular DFT tic problems such as e.g. polynomial chaos expansions. functionals based on the generalized gradient approxima- Finally, the results of numerical simulations show that the tion, in the modeling of condensed-phase molecular sys- proposed methods are robust and efficient. tems such as liquid water, albeit with a prohibitively large computational cost. In this work, we will demonstrate how Roland Pulch novel theoretical and algorithmic developments, coupled University of Greifswald with efficient utilization of supercomputer architectures, [email protected] enable large-scale hybrid DFT calculations on condensed- 152 CS15 Abstracts

phase molecular systems of interest. Mario Berljafa School of Mathematics Robert A. DiStasio, Jr. The University of Manchester Princeton University [email protected] [email protected]

MS185 MS184 Solving Optimal Feedback Control Problems for Finite Elements for Large, Accurate Quantum Me- Partial Differential Equations Using Adaptive chanical Materials Calculations: from Classical to Sparse Grids Enriched to Discontinuous An approach to solve finite time horizon optimal feedback We discuss recent developments in finite-element (FE) control problems for partial differential equations using based methods for the solution of the Kohn-Sham equa- adaptive sparse grids is proposed. A semi-discrete optimal tions that have made possible smaller basis sets and control problem is introduced and the feedback control is larger calculations than possible by current state-of-the-art derived from the corresponding value function. The value planewave (PW) based methods, in some cases by an order function can be characterized as the solution of an evo- of magnitude or more. We begin with classical FE based lutionary Hamilton-Jacobi Bellman (HJB) equation which approaches, then discuss recent enriched partition-of-unity is defined over a state space whose dimension is equal to FE (PUFE) methods, which build known atomic physics the dimension of the underlying semi-discrete system. Be- into the basis while retaining strict locality and system- sides a low dimensional semi-discretization it is important atic improvability. By incorporating known physics, these to solve the HJB equation efficiently to address the curse bases can achieve the required accuracies with an order of dimensionality. We propose to apply a semi-Lagrangian scheme using spatially adaptive sparse grids. Sparse grids of magnitude fewer degrees of freedom (DOF) than tradi- allow the discretization of the high(er) dimensional value tional PW based methods. However, with such enrichment functions arising in the numerical scheme since the curse of comes more expensive quadrature and some degree of ill- dimensionality of full grid methods arises to a much smaller conditioning. By incorporating not only local-atomic but extent. For additional efficiency an adaptive grid refine- also environmental physics into the basis, recent Discontin- ment procedure is explored. We present several numerical uous Galerkin (DG) based approaches can achieve larger examples studying the effect of the parameters character- reductions in DOFs still, while retaining strict locality and izing the sparse grid on the accuracy of the value function systematic improvability. Most notably, the DG formu- and optimal trajectories. Furthermore we analyze the be- lation allows for orthonormality as well, alleviating con- haviour of the trajectories in case of noise. ditioning issues and allowing for the solution of standard rather than generalized discrete eigenproblems in the crit- 3 Jochen Garcke ical N scaling step of the Kohn-Sham solution. Accurate University of Bonn quantum mechanical forces and molecular dynamics have [email protected] been demonstrated. Incorporation of Pole Expansion and Selected Inversion (PEXSI) has been undertaken to elim- inate the need for diagonalization entirely. We conclude Axel Kroner with an outlook and applications interests going forward. RICAM, Austria [email protected] John Pask Lawrence Livemore National Lab MS185 [email protected] Dimension-Independent, Likelihood-Informed Mcmc Sampling Algorithms for Bayesian Inverse MS184 Problems Enabling Large Scale LAPW DFT Calculations by Many Bayesian inference problems require exploring the a Scalable Iterative Eigensolver posterior distribution of high-dimensional parameters, which in principle can be described as functions. By ex- In LAPW-based methods a sequence of dense generalized ploiting the intrinsic low dimensionality of the likelihood eigenvalue problems appears. Traditionally these prob- function, we introduce a suite of MCMC samplers that lems were solved using direct eigensolvers from standard can adapt to the complex structure of the posterior dis- libraries like ScaLAPACK. We developed a subspace it- tribution, yet are well-defined on function space. Posterior eration method pre-conditioned with Chebyshev polyno- sampling in nonlinear inverse problems arising from various mials of optimal degree (ChFSI). This algorithm is con- partial differential equations and also a stochastic differen- sistently competitive with direct eigensolvers and greatly tial equation are used to demonstrate the efficiency of these enhance performance and scalability. ChFSI is included in dimension-independent likelihood-informed samplers. the FLEUR software and improves its scaling behaviour for calculations of large physical systems on modern super- Kody Law computers. SRI UQ Center, CEMSE, KAUST [email protected] Daniel Wortmann Institute for Asvanced Simulation Tiangang Cui, Youssef M. Marzouk Forschungszentrum Juelich Massachusetts Institute of Technology [email protected] [email protected], [email protected]

Edoardo A. Di Napoli Juelich Supercomputing Centre MS185 [email protected] Numerical Solution of Elliptic Diffusion Problems CS15 Abstracts 153

on Random Domains Lawrence Berkeley National Laboratory [email protected] In this talk, we provide regularity results for the solution to elliptic diffusion problems on random domains. Especially, Alex Druinsky, Xiaoye Sherry Li based on the decay of the Karhunen-Loeve expansion of Computational Research Division the domain perturbation field, we establish rates of de- Lawrence Berkeley National Laboratory cay which imply the tractability of the Quasi-Monte Carlo [email protected], [email protected] method. By taking into account only univariate deriva- tives, the regularity results can considerably be sharpened Osni A. Marques in order to show also the applicability of the stochastic Lawrence Berkeley National Laboratory collocation method and related rates of convergence. We Berkeley, CA moreover employ parametric finite elements to compute [email protected] the solution of the diffusion problem on each particular realization of the domain generated by the perturbation field. This simplifies the implementation and yields a non- Eric Roman intrusive approach. The theoretical findings are comple- Lawrence Berkeley National Laboratory mented by numerical examples. [email protected]

Michael Peters University of Basel MS186 [email protected] Parallel Spectral Element-Based Agglomeration Algebraic Multigrid for Porous Media Flow Helmut Harbrecht Universitaet Basel We present an element based algebraic multigrid strat- Departement of Mathematics and Computer Science egy for scalable parallel simulation of porous media flow. [email protected] Coarse basis functions in the multigrid algorithm are adapted to the high contrast coefficients by solving sparse MS185 or dense local eigenvalue problems. An advantage of the approach is that setup and application are based on sparse Data and Uncertainties: Representation of High- matrix-vector and matrix-matrix products, so that any re- Dimensional Dependencies Using Adaptive Sparse silient implementations of these components will be inher- Grids ited by the entire algorithm. Wherever simulations depend on parameters, high- dimensional problems arise, and the representation of high- Andrew T. Barker dimensional dependencies based on data and/or uncertain- Center for Applied Scientific Computing ties is required. Where the dependencies are non-smooth, Lawrence Livermore National Laboratory adaptive refinement and basis functions with local sup- [email protected] port are able to avoid Gibbs phenomenon. Sparse grids, together with suitable refinement strategies, provide such Delyan Kalchev a hierarchical and incremental approach. We will discuss University of Colorado some of their properties and give best practice examples. [email protected] Examples stem from uncertainty quantification, data min- ing, and density estimation. Panayot Vassilevski Lawrence Livermore National Laboratory Dirk Pfluger [email protected] University of Stuttgart Dirk.Pfl[email protected] Umberto E. Villa Center for Advanced Scientific Computing Fabian Franzelin Lawrence Livermore National Laboratory Universit¨at Stuttgart [email protected] [email protected]

MS186 MS186 Incorporating Error Detection and Recovery into Attaining High Arithmetic Intensity in Finite- Hierarchically Semi-Separable Matrix Operations volume Methods through High-order Quadratures

Hierarchically semi-separable (HSS) matrix factorizations Finite-volume discretizations in production codes are typ- are promising components for high-performance linear ically only second-order accurate, resulting in methods solvers. To construct a fault-tolerant HSS solver, we have with low arithmetic intensity. The widening performance identified several checksum relationships that are preserved gap between processor and memory motivates developing during HSS matrix-vector multiplication. Whenever these schemes that do more work for less data motion. We checksum assertions fail, the Containment Domains library present an arithmetic intensity analysis for finite-volume restores the faulty arrays and re-executes the necessary re- methods with high-order flux approximations. The model gion of the code. The timing profile of our algorithm is suggests the flops-to-byte ratio of the methods increases used to parametrize a Markov model and determine the rapidly with order of accuracy. We also discuss perfor- optimal granularity of the checksum tests. mance measurements of the methods on current multicore hardware. This work was performed under the auspices of Brian Austin the U.S. Department of Energy by Lawrence Livermore Na- NERSC tional Laboratory under Contract DE-AC52-07NA27344. 154 CS15 Abstracts

Lawrence Livermore National Security, LLC. Bayesian inverse problem, time-dependent optimal control problems, convergence of reduced basis method for high- John Loffeld dimensional or possibly infinite-dimensional problems, etc. University of California Merced Peng Chen loff[email protected] ETH Zurich [email protected] Jeffrey A. Hittinger Center for Applied Scientific Computing Gianluigi Rozza Lawrence Livermore National Laboratory SISSA, International School for Advanced Studies [email protected] Trieste, Italy [email protected] MS186 Controlling Numerical Error in Particle-In-Cell MS187 Simulations of Collisionless Dark Matter Recent Advances in Reduced Order Modelling in Computational Fluid Dynamics within EU- Particle-in-cell (PIC) methods are commonly used to sim- MORNET COST Activities ulate the gravitational evolution of collisionless dark mat- ter in cosmological settings. However, such methods are We provide some recent updates about reduced order mod- known to be prone to numerical error on scales below the elling techniques in computational fluid dynamics with a mean inter-particle separation. An understanding of these special focus on flow instabilities and bifurcations for time errors is crucial, both for correctly interpreting simulation dependent non-linear flows. A special attention is devoted results, and for designing higher-order PIC methods. We to parameter sampling techniques and approximation sta- discuss the use of two techniques: regularization and adap- bility. A posteriori error bounds are recalled. A cardio- tive phase-space remapping, to improve the accuracy of vascular application is presented as benchmark example. cosmological PIC simulations. This work wants to provide a general overview on some recent tasks of the EU-MORNET COST activities (Euro- Andrew Myers pean Union MOdel Reduction NETwork, Cooperation in Computational Research Division Science and Technology). Lawrence Berkeley National Laboratory [email protected] Gianluigi Rozza SISSA, International School for Advanced Studies Brian Van Straalen Trieste, Italy Lawrence Berkeley National Laboratory [email protected] Compuational Research Division [email protected] Giuseppe Pitton SISSA, International School for Advanced Studies Trieste Colella Phillip Italy LBNL [email protected] [email protected] Annalisa Quaini Department of Mathematics, University of Houston MS187 [email protected] Accelerating the Solution of Inverse Problems Us- ing Reduced-Order Models MS187 Inverse problems are a special class of PDE-constrained optimization problems for which model parameters are es- A Minimum-residual Mixed Reduced Basis timated. This inverse problem often needs to be solved Method: Exact Residual Certification and Simul- in real-time based on measurements obtained on the field. taneous Finite-element Reduced-basis Adaptive The computational complexity associated with the opti- Refinement mization problem of interest generally prevents its fast so- lution. To accelerate its solution, a strategy based on a We present a reduced basis method for parametrized PDEs database of pre-computed reduced-order model is here cho- certified by a dual-norm bound of the residual computed sen. Special attention will be given to the training of such a not in the typical finite-element “truth’ space but rather in database in the case of high-dimensional parameter spaces. an infinite-dimensional function space. The bound, which admits an efficient offline-online decomposition, builds on a David Amsallem minimum-residual mixed finite-element method and an as- Stanford University sociated reduced-basis approximation. The method, com- [email protected] bined with a spatio-parameter adaptation strategy, yields an online system that meets any user-specified residual tol- erance for any parameter value. MS187 Reduced Basis Method for Uncertainty Quantifica- Masayuki Yano tion Problems: A Recent Update Massachusetts Institute of Technology [email protected] In this talk, we present a recent update of the development and application of reduced basis method for forward and inverse uncertainty quantification (UQ) problems. Specific MS188 topics include reduced basis method for time-dependent A New Look at Global Error Estimation in Differ- CS15 Abstracts 155

ential Equations [email protected]

Global error represents the actual discretization error re- sulting after solving a system of differential equations. I MS189 will introduce new time-stepping methods with built-in Adaptive Compressive Sensing Method for Uncer- global error estimates for ordinary and differential alge- tainty Quantification braic equations. Calculating and controlling a posteriori errors is an expensive process, and therefore in practice The standard generalized polynomial chaos (gPC) method only the (local) error from one step to the next is used to in uncertainty quantification (UQ) selects basis functions estimate the global errors. However, local error estimation based on the randomness of the input. However, this may is not always suitable and may lead to error underestima- not be an efficient way. We propose a new method to tion. I will review several strategies for a posteriori error construct the basis functions based on the output of the estimation and discuss new approaches that generalizes the system. With the new gPC expansion, the system has a classical strategies. sparser representation, hence sparse recovery approaches, e.g., compressive sensing technique, can be more effective.

Emil M. Constantinescu Xiu Yang Argonne National Laboratory Pacific Northwest National Laboratory Mathematics and Computer Science Division [email protected] [email protected] Xiaoliang Wan Louisiana State University MS188 Department of Mathematics On the Construction of Robust Additive Runge- [email protected] Kutta Methods Huan Lei, Guang Lin Space discretization of some PDEs gives rise to systems of Pacific Northwest National Laboratory ODEs in additive form whose terms have different stiffness [email protected], [email protected] properties. Sometimes, the solution to these PDEs have qualitative properties which are relevant in the context of George E. Karniadakis the problem. In these cases, it is convenient to preserve nu- Brown University merically these properties. In this talk we show how robust Division of Applied Mathematics schemes can be constructed for this class of problems. We george [email protected] will also show their performance on nontrivial problems. MS189 Inmaculada Higueras Departamento de Ingenieria Matematica e Informatica Stochastic Collocation Methods Via L1 Minimiza- Universidad Publica de Navarra tion [email protected] In this talk, we discuss the stochastic collocation meth- ods via L1 minimization. The motivation it to construct polynomial approximations for parametric functions. Two MS189 sampling strategies, that is, the random sampling and the A Sparse Multiresolution Regression Framework deterministic sampling methods will be introduced. We for Uncertainty Quantification shall also discuss how to handle derivative information in this framework.

A novel nonintrusive, i.e., sampling-based, framework is Tao Zhou presented for approximating stochastic solutions of inter- Institute of Computational Mathematics, AMSS est admitting sparse multiresolution expansions. The co- Chinese Academy of Sciences efficients of such expansions are computed via greedy ap- [email protected] proximation techniques that require a number of solution realizations smaller than the cardinality of the multireso- Ling Guo lution basis. The effect of various random sampling strate- Department of Mathematics, Shanghai Normal gies is investigated. The proposed methodology is verified University, China on a number of benchmark problems involving nonsmooth [email protected] stochastic responses. Dongbin Xiu Daniele E. Schiavazzi Purdue University University of California, San Diego [email protected] [email protected]

Alireza Doostan MS190 Department of Aerospace Engineering Sciences Development of a Time-Dependent Ice Flow Model University of Colorado, Boulder Adjoint and Its Applications [email protected] The adjoint approach is quite popular in fitting glacial ice Gianluca Iaccarino flow models to observations. For the most part, however, Stanford University the approaches are time-independent. As remote sensing Mechanical Engineering data becomes more frequent and more complete, it is fair to 156 CS15 Abstracts

expect that time-dependent models of ice dynamics might [email protected] be constrained with transient data, providing better cap- ture of transient state, and a better representation of un- known properties, such as bed topography or sub-ice shelf MS190 melt. Improving the Efficiency of the Adjoint of Fixed- Point Iterations Daniel Goldberg University of Edinburgh Reverse mode automatic differentiation (AD) computes the [email protected] adjoints of codes precisely and efficiently. The reverse mode employs checkpointing to store data between its for- Patrick Heimbach ward and the reverse computational sweeps. When the Massachusetts Institute of Technology code contains fixed point iterations, unecessary checkpoint- [email protected] ing can result in excessive memory or disk usage. Refor- mulating the adjoint of the fixed point iteration, drastically reduces the usage. An implementation of the reformulation MS190 and its use in an ice sheet model will be presented. Parallel 4D Variational Data Assimilation Sri Hari Krishn Narayanan Argonne National Laboratory A parallel algorithm to solve the inverse problem associated [email protected] with the 4D Var Data assimilation problem is described. The inverse problem is solved in the variational framework. Daniel Goldberg The optimization required to evaluate the analysis is per- University of Edinburgh formed using augmented Lagrangian technique. The eval- [email protected] uation of the cost function and the derivative information required to perform the optimization is computed in par- Paul D. Hovland allel using forward and adjoint sensitivity analysis. Argonne National Laboratory MCS Division, 221/C236 Vishwas Hebbur Venkata Subba Rao [email protected] Virginia Polytechnic Institute and State University [email protected] MS191 Adrian Sandu Multivariate Weighted Least-squares using Monte Virginia Polytechnic Institute and Carlo Samples State University [email protected] We propose and analyze an algorithm for computing polynomial discrete least-squares approximations to high- dimensional parameterized systems. Our sample grid for MS190 discrete least-squares is generated using Monte Carlo sam- An Adjoint Based Analysis of the Physical Drivers ples, and we show that our method exhibits several asymp- of Uncertainty in Air-Sea Exchange and Ocean totically optimal properties. Stability and accuracy can be Draw Down of Co2 established when the number of samples scales log-linearly with the dimension of the approximation space. This anal- We describe the use of an innovative adjoint approach to ysis relies on results from the fields of orthogonal polyno- quantify and attribute uncertainty in model estimate of air- mial and pluripotential theory. Our method is straight- sea CO2 exchange. The adjoint approach provides a com- forward and efficient to apply, addresses approximations putationally efficient way to capture spatio-temporal vari- for general random variables with bounded and unbounded ability in the sensitivity of net air-sea exchange to physical range, and easily extends to cases of epistemic uncertainty processes represented in a model. In this study we focus on when the distribution of the parametric random variable diapycnal mixing in the upper ocean, which can vary widely is not known. We validate the algorithm on several low- in space and time. The processes by which the ocean re- and high-dimensional examples that are common in the sponds to disequilibrium with atmospheric CO2 are key uncertainty quantification community. attributes of the Earth system decadal-centenial-millenial response to changes in CO2 emissions. The study provides Akil Narayan quantitative insight into where and how diapycnal mixing University of Massachusetts Dartmouth processes contribute to that response. The study makes [email protected] extensive use of the open-source automatic differentiation tool, OpenAD. MS191 Chris Hill Title Not Available at Time of Publication Earth, Atmospheric and Physical Sciences Abstract not available at time of publication. M.I.T. [email protected] Raul F. Tempone Mathematics, Computational Sciences & Engineering Oliver Jahn King Abdullah University of Science and Technology MIT [email protected] [email protected]

Jean Utke MS191 Argonne National Laboratory Local Polynomial Chaos Methods for High Dimen- CS15 Abstracts 157

sional SPDE sulted in increasing Sybil attacks where an adversary forges many fake identities (called Sybils) to disrupt or control the We present a localized polynomial chaos expansion for normal functioning of the system. Proposed attack miti- PDE with random inputs. We focus on problems with gation schemes primarily work by computing the landing input random fields of short correlation length, resulting probability or statistical distribution of the visiting fre- in high dimensional random inputs. The local polynomial quency of short random walks and are dependent on ac- chaos method employs a domain decomposition technique curate trusted nodes identification. In this talk, we will to approximate the stochastic solution locally and indepen- present SybilExposer, an algorithmic framework which ad- dently with very low dimensions and then obtains the cor- dresses these limitations. Our experiments on several large rect global solution via sampling. The drastic dimensional graphs validate the effectiveness of SybilExposer. reduction makes the method highly efficient for practical problems. Satyajayant Misra Department of Computer Science Yi Chen New Mexico State University Purdue University [email protected] [email protected]

John D. Jakeman MS192 Sandia National Labs The Dynamics of Co-Evolution of Health Behaviors [email protected] in College Population

Xueyu Zhu, Dongbin Xiu Abstract not available at time of publication. University of Utah Anuj Mubayi [email protected], [email protected] Arizona State University [email protected] MS191 Uncertainty Propagation Using Infinite Mixture of MS192 Gaussian Processes and Variational Bayesian Infer- Analysis of Information Diffusion on Social Net- ence works

Uncertainty propagation (UP) is a very challenging mathe- Abstract not available at time of publication. matical and computational problem. Among other things, UPs difficulty is due to the limited number of model eval- Daniel Romero uations, the curse of dimensionality, discontinuities, and School of Information multivariate responses with non-trivial correlations. In or- University of Michigan der to deal with all these problems simultaneously, we de- [email protected] velop an infinite mixture of multi-output Gaussian process model. We train the model using variational Bayesian in- ference and we obtain highly competing results in porous MS193 flow problems. Fluctuating Hydrodynamics of Suspensions of Rigid Particles Peng Chen, Nicholas Zabaras Cornell University We develop a computational method for fluid-structure [email protected], [email protected] coupling at small Reynolds numbers that consistently in- cludes the effects of thermal fluctuations. This is impor- Ilias Bilionis tant in problems involving Brownian rigid and semi-rigid Purdue University structures immersed in a fluid. We couple an immersed- [email protected] boundary Lagrangian representation of rigid bodies to a fluctuating finite-volume fluid solver. We handle com- plex rigid (e.g., synthetic nanorods) and semi-rigid (e.g., MS192 short DNA segments) bodies by composing each structure The Collective Impact of Social Factors and Inter- from a collection of spherical particles constrained to move ventions on the Dynamics of Reported Narcotic- (semi)rigidly. The underlying fluctuating hydrodynamics Related Criminal Cases in the Community Areas formulation automatically ensures the correct translational of Chicago and rotational Brownian motion.

Abstract not available at time of publication. Aleksandar Donev Courant Institute of Mathematical Sciences Maryam Khan New York University SAL Mathematical Computational Modeling Science [email protected] Center Arizona State University [email protected] MS193 Boltzmann’s State of Motion: Phenomenological Modeling of Chemical and Ecological Systems MS192 An Effective Community-based Approach to Miti- We carry out a mathematical analysis, `alaHelmholtz’s gate Sybil Attacks in Online Social Networks and Boltzmann’s 1884 studies of monocyclic Newtonian mechanics, for chemical reaction and ecological systems The popularity of online social networks (OSNs) has re- containing oscillatory dynamics. One of the important 158 CS15 Abstracts

features of the systems considered, absent in the classical Wenxiao Pan mechanical model, is a natural stochastic dynamic formu- Pacific Northwest National Laboratory lation of which the deterministic differential equation is [email protected] the infinite population limit. We separate the conserved dynamics from the dissipative models and show how the conservation law along a single trajectory can be extended MS194 to incorporate both variations in model parameters and in Computing Exactly and Eficiently Arbitrarily- the initial conditions: Helmholtz’s theorem establishes a High-Order Response Sensitivities to Model Pa- broadly valid conservation law in a class of chemical and rameters ecological dynamics. Further analysis identifies an entire orbit as a stationary behavior, and establishes the notion This work presents a new methodology for computing ex- of an “equation of behavioral state’. Studies of the stochas- actly and (most) efficiently response sensitivities, of arbi- tic dynamics shows the conserved dynamics as the robust, trarily high-order, to model parameters. This new method fast cyclic underlying behavior. The mathematical narra- generalizes the adjoint method for sensitivity analysis of tive provides a novel way of capturing long-term dynamical nonlinear systems originated by Cacuci (1981), requiring behavior with an emergent conservative motion. at most O(NK-1) large-scale adjoint computations per re- sponse to obtain exact Kth-order sensitivities for a sys- Yian Ma tem with N parameters. In contradistinction, conventional University of Washington methods require O(NK) large-scale computations to obtain [email protected] approximate values for the Kth-order sensitivities. Dan G. Cacuci Hong Qian University of South Carolina Department of Applied Mathematics [email protected] University of Washington [email protected] MS194 MS193 Toward New Applications of the Adjoint Tools in 4D-Var Data Assimilation A Nano Pore-Scale Model for the Nanostructured Cathode of Lithium-Oxygen Batteries The development of efficient methodologies to assess and improve the information content (’value’) of high-resolution We propose a nano pore-scale model that bridges the gap atmospheric measurements is an imperative task. This between continuum models and atomistic models to study talk presents recent advances in the adjoint-based evalua- the impact of cathode microstructure and rate-dependent tion of the model forecast sensitivity to observations, error morphology of Li2O2 on the discharge performance of Li- covariance parameter specification, and impact estimation O2 batteries. The model captures the micro-scale resolved in a four-dimensional variational data assimilation system. nanostructure of cathode with varying porosities, pore size The practical significance and further research directions distributions and surface-to-volume ratios, the diffusion- are discussed together with preliminary experiments and limited transport of oxygen across the porous structure of the current status of implementation at numerical weather the cathode, and the morphology of Li2O2 growth at dif- prediction centers. ferent current densities. Dacian N. Daescu Wenxiao Pan Portland State University Pacific Northwest National Laboratory Department of Mathematics and Statistics [email protected] [email protected]

Ricardo Todling MS193 NASA/GSFC Global Modeling and Assimilation Office SPH Model for Landau-Lifshitz Navier-Stokes and [email protected] Advection-Diffusion Equations Rolf Langland We propose a novel Smoothed Particle Hydrodynamics Naval Research Laboratory (SPH) discretization of the fully-coupled Landau-Lifshitz- Monterey, CA Navier-Stokes (LLNS) and advection-diffusion equations. [email protected] The accuracy of the SPH solution is demonstrated by test- ing the scaling of velocity variance and self-diffusion co- Austin Hudson efficient with kinetic temperature and particle mass, the Portland State University spatial covariance of pressure and velocity fluctuations, the Portland, OR, USA so-called giant fluctuations of the front between light and [email protected] heavy fluids with and without gravity, and the effect of thermal fluctuation on the Rayleigh-Taylor instability. MS194 Alexander Tartakovsky Dealing with Nonsmoothness in Data Assimilation Pacific Northwest National Laboratory [email protected] The theory of adjoints and their use in inverse problems usually assumes that the state equations and error norms Jannes Kordilla are smooth. In practice this assumption may be violated Geoscientific Centre through the use of nonsmooth norms or due to nonsmooth University of Goettingen modification of the state equations, e.g. the use of flux [email protected] limiters in spatial discretizations. We analyze the theoret- CS15 Abstracts 159

ical and practical effects and discuss suitable algorithmic work for unit commitment under uncertainty. We present modifications. a new type of uncertainty set induced by correlated sce- nario samples to capture spatial-temporal correlations of Andreas Griewank the uncertainties. Furthermore, for large-scale problems, HU Berlin, Germany we propose an efficient approximation of the Scenarios In- [email protected] duced Uncertainty (SIU) set using Principal Component Analysis. Computational results demonstrate the economic benefits of using SIU sets and the efficacy of the proposed MS194 solution approach. Second Order Analysis in Variational Data Assim- ilation Richard L. Chen Sandia National Laboratories The problem of Variational Data Assimilation, considered Livermore, CA in the framework of Optimal Control Theory, leads to an [email protected] Optimality System containing all the available information : model, data and statistics, its solution gives a neces- Cosmin Safta sary condition for optimality. Introducing a second order Sandia National Laboratories adjoint a second order analysis can be carried out with [email protected] important applications such as: -Improvement of the opti- mization algorithms - Sensitivity Analysis - Estimation of Jean-Paul Watson a posteriori statistics on the solution. Theory and applica- Sandia National Laboratories tions will be presented. Discrete Math and Complex Systems Francois-Xavier L. Le-Dimet [email protected] University Joseph Fourier [email protected] Habib N. Najm Sandia National Laboratories M Yousuff Hussaini Livermore, CA, USA Florida State University [email protected] [email protected] Ali Pinar Ha Tran Thu Sandia National Labs Vietnamese Academy of Sciences [email protected] [email protected] MS195 MS195 Economic Impacts of Wind Covariance Estimation Data-Driven Model for Solar Irradiation Based on on Power Grid Operations Satellite Observations We study the impact of capturing spatiotemporal corre- We construct a data-driven model for solar irradiation lations between multiple wind supply points on economic based on satellite observations. The model yields prob- dispatch procedures. Using a simple dispatch model, we abilistic estimates of the irradiation field every thirty first show analytically that over/underestimation of corre- minutes starting from two consecutive satellite measure- lation leads to positive and negative biases of dispatch cost, ments.The probabilistic nature of the model captures pre- respectively. A rigorous, large-scale computational study diction uncertainties and can therefore be used by solar for the State of Illinois transmission grid with real topol- energy producers to quantify the operation risks. The dy- ogy and physical constraints reveals similar conclusions. namics are represented in a nonlinear, nonparameteric way For this study, we use the Rao-Blackwell-Ledoit-Wolf es- by a recursive Gaussian process. The predictions of the timator to approximate the wind covariance matrix from model are compared with observed satellite data as well as a small number of wind samples generated with the nu- with a similar model that uses only ground observations at merical weather prediction model WRF and we use the the prediction site. We conclude that using satellite data in covariance information to generate a large number of wind an area including the prediction site significantly improves scenarios. The resulting stochastic dispatch problems are the prediction compared with models using only ground solved by using the interior-point solver PIPS-IPM on the observation site data. BlueGene/Q (Mira) supercomputer at Argonne National Laboratory. We find that strong and persistent biases re- Ilias Bilionis sult from neglecting correlation information and indicate Purdue University to the need to design a market that coordinates weather [email protected] forecasts and uncertainty characterizations. Cosmin G. Petra Emil M. Constantinescu, Mihai Anitescu Argonne National Laboratory Argonne National Laboratory Mathematics and Computer Science Division Mathematics and Computer Science Division [email protected] [email protected], [email protected] Victor Zavala MS195 Argonne National Laboratory Two-Stage Adaptive Robust Unit Commitment [email protected] Using Scenarios Induced Uncertainty Set Elias Nino-Ruiz In this talk, we propose a new robust optimization frame- Virginia Polytechnic Institute and State University 160 CS15 Abstracts

[email protected] Saint Anthony Falls Lab, Civil Engineering department University of Minnesota Mihai Anitescu [email protected] Argonne National Laboratory Mathematics and Computer Science Division Lian Shen [email protected] University of Minnesota [email protected]

MS195 An Efficient Approach for Stochastic Optimization MS196 of Electricity Grid Operations Topological Change with a Cut Cell based Sharp Interface Method for Multi-phase Flows Stochastic unit commitment optimization problems typi- cally handle uncertainties in forecast demand by consider- In the conservative, consistent, all-speed, sharp-interface ing a finite number of random realizations from a stochas- method presented by Chang, Deng & Theofanous 2013, a tic process model for uncertain loads. In this paper we free interface is represented by cut faces and evolved with propose a more efficient approach using Polynomial Chaos the help of a level set function. It shows good performance representations valid over the range of the forecast uncer- on simulating multi-phase flow problems with clear inter- tainty. We demonstrate the approach for several power faces, but cannot deal with topological change. By switch- grid models with and without transmission constraints. ing between this cut cell/level set mixed method and a pure level set method, topological change can be realized Cosmin Safta smoothly. Sandia National Laboratories [email protected] Xiao-Long Deng Beijing Computational Science Research Center Habib N. Najm [email protected] Sandia National Laboratories Livermore, CA, USA MS196 [email protected] High Resolution PDE Solvers on Octree Grids and Parallel Architectures Richard L. Chen Sandia National Laboratories Abstract not available at time of publication. Livermore, CA [email protected] Frederic G. Gibou UC Santa Barbara Ali Pinar [email protected] Sandia National Labs [email protected] MS196 Jean-Paul Watson A Second Order Virtual Node Algorithm for Sandia National Laboratories NavierStokes Flow Problems with Interfacial Discrete Math and Complex Systems Forces and Discontinuous Material Properties [email protected] We present a numerical method for the solution of the Navier-Stokes equations in three dimensions that handles MS196 interfacial discontinuities due to singular forces and discon- tinuous fluid properties such as viscosity and density. We On the Coupling of Far-Field Wind-Wave Simula- discretize the equations using an embedded approach on a tion and Near-Field Free-Surface Flow Simulation uniform MAC grid to yield discretely divergence-free ve- We develop a computational framework for simulating in a locities that are second order accurate. The method leads coupled manner the interaction of large-scale ocean waves to a discrete, symmetric KKT system for velocities, pres- and winds with the presence of complex floating structures. sures, and Lagrange multipliers. We also present a novel We employ an efficient large-scale model to develop offshore simplification to the standard combination of the second wind and wave environmental conditions, which are then order semi-Lagrangian and BDF schemes for discretizing incorporated to a high resolution two-phase flow solver the inertial terms. Numerical results indicate second order spatial accuracy for the velocities (L∞ and L2) and first with fluid-structure interaction (FSI). The far-field/near- ∞ 2 field coupling algorithm is validated under several test cases order for the pressure (in L ,secondorderinL ). involving simple wave trains as well as three-dimensional Joseph Teran directional waves. UCLA Antoni E. Calderer [email protected] Saint Anthony Falls Lab, Civil Engineering department University of Minnesota MS197 [email protected] Asynchronous Preconditioning on Accelerators Xin Guo This talk focuses on how preconditioners can be con- UC Berkeley structed using asynchronous algorithms. Such algorithms [email protected] are fine-grained and can tolerate memory latency, making them suitable for modern architectures, particularly ac- Fotis Sotiropoulos celerators. Preconditioners including incomplete factoriza- CS15 Abstracts 161

tions and sparse approximate inverses may be constructed many applications than the LINPACK benchmark. After this way. We discuss convergence of various types of asyn- introducing this new benchmark that reported rankings for chronous algorithms applied to constructing precondition- the first time in June 2014 we show its implementation and ers, necessary implementation differences on GPUs and In- performance on CPUs only and on hybrid nodes with Intel tel Xeon Phi, and inner-outer asynchronous iterations de- Phi accelerators, connected by a QDR InfiniBand intercon- signed to reduce communication volume from low levels of nect. the memory hierarchy. Adam Cunningham, Gerald Payton, Jack Slettebak Edmond Chow University of Maryland, Baltimore County School of Computational Science and Engineering [email protected], [email protected], Georgia Institute of Technology [email protected] [email protected] Jordi Wolfson-Pou Department of Physics MS197 University of California, Santa Cruz Overview and Contrast of Modern Computer Ar- [email protected] chitectures Including the Intel Phi

State-of-the-art distributed-memory clusters today contain MS198 multi-core CPUs with 8 to 12 cores, massively parallel GPUs with thousands of computational cores, and many- Creating the Largest Decoys Database to Improve core accelerators such as the 60-core Intel Phi, connected Scoring Functions Using Machine Learning by high-performance networks such as InfiniBand intercon- nect. This talk will give an overview of their features, show In the protein structure prediction field it is absolutely vi- sample code how to use GPUs and the Intel Phi processor tal to develop reliable scoring functions that will allow re- in hybrid mode, and contrast performance results for basic searchers to efficiently identify the very best models out test problems. of hundreds of thousands and sometimes even millions of predictions. Such scoring functions have proven to be dif- Jonathan Graf, Samuel Khuvis, Xuan Huang ficult to produce. The protein folding community believes Department of Mathematics and Statistics that machine learning techniques will advance the capa- University of Maryland, Baltimore County bilities of scoring functions. Datasets of computationally [email protected], [email protected], [email protected] generated models known as decoys are used to train and test the scoring functions that are created. While there Matthias K. Gobbert are decoys datasets available to perform these tests, these University of Maryland, Baltimore County datasets are very small in comparison to the amount of Department of Mathematics and Statistics protein models that are created during the Critical As- [email protected] sessment of protein Structure Prediction (CASP) competi- tions. Larger datasets are essential to create more accurate scoring functions. The WeFold collaboration mediated by MS197 the homonymous gateway gathers an enormous amount of Offloading Computational Kernels in Long-Time models, which are shared by its users. We are creating Simulations to the Intel Phi the largest database of decoys to make available to the machine learning community. The database does not only Simulating calcium waves in a heart cell requires both fine store models, but also numerical features that describe im- meshes and large final times to match laboratory exper- portant characteristics of protein models. MongoDB is be- iments. This is a perfect example of a problem that can ing used to store all of this information and an interface is profit from offloading numerical kernels to accelerators such being created to integrate MongoDB with the WeFold gate- as the 60-core Intel Phi processor on each hybrid compute way. Users will be able to submit queries to the database node, combined with pooling memory from several nodes and download all models created by all groups, all mod- to allow for the desired spatial resolutions. We report re- els created by specific groups, specific features for specific sults for special-purpose code for this problem. models, and even more. Speakers: Ricardo Ferreira and Christopher Cook Samuel Khuvis, Xuan Huang, Jonathan Graf Department of Mathematics and Statistics Ricardo Ferreira, Christopher Cook University of Maryland, Baltimore County Mountain View Community College [email protected], [email protected], [email protected] [email protected], [email protected]

Matthias K. Gobbert University of Maryland, Baltimore County MS198 Department of Mathematics and Statistics WeFold: a Collaborative and Educational Experi- [email protected] ment

Determining protein structure is key to advances in sci- MS197 ence and medicine. To advance this field a social-media The HPCG Benchmark Using Intel Phi Accelera- based consortium of labs worldwide was created to bring tors together researchers from all walks and disciplines. Re- cently, the project added an educational component by The High Performance Preconditioned CG (HPCG) bringing a group of students and faculty under one roof Benchmark, developed by Sandia National Laboratories, to discuss protein folding. We will discuss the results of uses a preconditioned conjugate gradient method to solve WeFold both as a new way to conduct research and engage the Poisson equation, since this may be more relevant to students to learn computational science. Speakers: Silvia 162 CS15 Abstracts

Crivelli, John Hatherill, and Jesse Fox. a time-centered, implicit scheme, which is converged non- linearly. The nonlinear solver is accelerated by a moment- Silvia N. Crivelli based preconditioner. We demonstrate the properties of Lawrence Berkeley National Laboratory the algorithm with several verification examples, includ- [email protected] ing a Weibel instability and a Kinetic Alfven wave ion-ion streaming instability. John Hatherill Del Mar Community College Guangye Chen, Luis Chacon [email protected] Los Alamos National Laboratory [email protected], [email protected] Jesse Fox Mountain View Community College [email protected] MS199 A Moment Model for the Vlasov Fokker Planck Equation MS198 Reducing the Data Complexity with Filtering and We present a moment method based on spherical harmon- Clustering ics for the Vlasov equation coupled with some common col- lision operators. A transformation in phase space is used Wefold maintains hundreds of thousands of models ob- to enable the moments to give a perturbation around the tained from participants like Foldit. Model computation is equilibrium solution in phase space. Furthermore, we give time intensive due to NP complete nature, thus this team numerical results which show the difference between us- sought smaller accurate protein conformation datasets. ing/not using a transformation in phase space. Preliminary results from our filter concluded the filtration achieved a decrease in set size with an accuracy increase. Charles K. Garrett, Cory Hauck However, this set retains unworkable complexity. Different Oak Ridge National Laboratory parallel clustering algorithms and metrics were analyzed to [email protected], [email protected] find accurate clusters and representatives to finally reduce the set. Speakers: Davis, Ogden, and Raiyyani MS199 Rachel A. Davis Modeling Non-Ideal Plasmas: a Hyrbid Quan- Drake University tum Hydrodynamics and Molecular Dynamics Ap- [email protected] proach

Jennifer Ogden Abstract not available at time of publication. Saint Mary’s College of California [email protected] Michael Murillo Los Alamos National Laboratory [email protected] Rehan Raiyyani University of California, San Diego [email protected] MS199 iFP: An Optimal, Fully Conservative, Fully Im- MS198 plicit, Vlasov-Fokker-Planck Solver The Maintenance of the WeFold Gateway for We introduce a new, exactly conservative (mass, momen- CASP11 tum, and energy), and fully nonlinearly implicit solver for The protein structure prediction and refinement methods a multi-species 1D-2V Vlasov-Rosenbluth-Fokker-Planck generated by the WeFold community in the context of the system. The new solver optimizes mesh resolution require- CASP11 competition were executed as pipelines of com- ments by 1) adapting the velocity-space mesh based on the ponents contributed by different labs. Twenty labs world- species’ local thermal-velocity, and 2) treating the cross- wide including more than 100 researchers participated in species collisions exhibiting disparate thermal velocities by this collaboration. Because of deadlines to submit predic- an asymptotic formulation. We demonstrate the efficiency tions to the competition, it was important to facilitate the and accuracy properties of the approach with challenging execution of the pipelines. I will discuss the maintenance numerical examples. of the WeFold gateway as well as the results achieved. William T. Taitano, Luis Chacon, Andrei Simakov Anthony Lopez Los Alamos National Laboratory Del Mar Community College [email protected], [email protected], [email protected] [email protected] MS200 MS199 Current Challenges in Mesh Partitioning for An Implcit, Conservative Vlasov-Darwin Pic Physics Simulations Solver in Multiple Dimensions For modern and complex physics simulations on very large We propose a new, implicit 2D-3V particle-in-cell algo- data, achieving a good load balancing of the computations rithm for non-radiative, electromagnetic kinetic plasma at every time step is still a hard problem. For mesh based simulations. Local charge, global energy, and canonical simulations, load balancing is achieved by performing mesh momentum are exactly conserved. The Darwin-Vlasov partitioning. In this talk, we shall define what can be the equations are discretized with particles on a grid, using goals of mesh partitioning. We shall also present main CS15 Abstracts 163

problems we are currently working on at CEA: - Multi cri- SCOREC teria (re-)partitioning, in order to deal with multi physics [email protected] simulations; - Memory constrained (re-)partitioning, to model layers of ghost cells which can fill up the available Mark S. Shephard memory. Rensselaer Polytechnic Institute Scientific Computation Research Center C´edric Chevalier [email protected] French Alternative Energies & Atomic Energy Commission (CEA) [email protected] MS200 Zoltan2 for Extreme-Scale Data Partitioning

MS200 As the number of cores in modern high performance com- The Zoltan2 Toolkit: Partitioning, Task Place- puting architectures has increased, data partitioning algo- ment, Coloring, and Ordering rithms have struggled to scale. As part of the DOE Sci- DAC FastMATH Institute, we have been attempting to ad- Zoltan2 is a toolkit of partitioning, coloring, and order- dress this problem in our load-balancing software Zoltan2. ing algorithms for use in parallel scientific applications. A Specifically, we have be focusing on developing partitioners successor to the Zoltan toolkit, Zoltan2 is designed to ad- to create high quality partitions for 100k-1M cores. In this dress current issues in scientific computing: extreme data- talk, we discuss many of the techniques that we have found set sizes, parallel computers built of multicore processors, useful in achieving this goal. and sustainable software design. Zoltan2 is built on the templated software stack in the Trilinos solvers framework, Michael Wolf and, thus, provides more seamless integration with Trilinos’ Sandia National Laboratories data structures. This presentation provides an introduc- [email protected] tion to the design and capabilities of Zoltan2.

Karen D. Devine MS201 Sandia National Laboratories Block-Structured AMR: Applications Using [email protected] BoxLib

Erik G. Boman BoxLib is a publicly available software framework for build- Sandia National Labs, NM ing parallel block-structured AMR applications using both Scalable Algorithms Dept. MPI and OpenMP. It supports grid-based and particle- [email protected] mesh operations on adaptive hierarchical meshes with op- tional subcycling in time. This talk focuses on the common Siva Rajamanickam, Lee Ann Riesen components that form the basis of existing codes in astro- Sandia National Laboratories physics, cosmology, combustion and porous media, and al- [email protected], [email protected] low construction of new application codes and extension to AMR of existing single-level codes, in a variety of applica- tion areas. Mehmet Deveci The Ohio State University Ann S. Almgren [email protected] Lawrence Berkeley National Laboratory [email protected] Umit V. Catalyurek The Ohio State University Department of Biomedical Informatics MS201 [email protected] Preconditioners for Implicit Atmospheric Climate Simulations in the Community Atmosphere Model

MS200 High resolution, long-term climate simulations are essential Unstructured Mesh Partitioning to over 500k Parts to understanding regional climate variation on the decade scale. To maintain accuracy with time steps commensu- Parallel unstructured mesh-based applications running on rate with the physical processes of interest, the spectral the latest petascale systems require partitions with over element dynamical core of the Community Atmosphere 500k parts. Methods combining the most powerful graph Model (CAM-SE) implements fully implicit schemes uti- based and geometric methods with diffusive methods di- lizing FASTMath Trilinos solvers. We discuss the develop- rectly operating on the unstructured mesh will be dis- ment of preconditioners to reduce the computational cost cussed. Initial partitioning results on meshes with over 12 of ancillary linear system solves within each time step to billion elements and over 512k parts indicate that these improve solver efficiency and scalability. methods maintain quality while keeping run times to a small fraction of application run time. David J. Gardner Lawrence Livermore National Laboratory Cameron Smith [email protected] Scientific Computation Research Center Rensselaer Polytechnic Institute Katherine J. Evans [email protected] Oak Ridge National Laboratory [email protected] Dan A. Ibanez Rensselaer Polytechnic Institute Aaron Lott 164 CS15 Abstracts

D-Wave Systems, Inc. from Multiple Data Modalities [email protected] Fluorescence tomographic reconstruction can be used to re- Andrew Salinger veal the internal elemental composition of a sample while CSRI transmission tomography can be used to obtain the spatial Sandia National Labs distribution of the absorption coefficient inside the sample. [email protected] In this work, we integrate both modalities and formulate an optimization approach to simultaneously reconstruct the composition and absorption effect in the sample. By using Carol S. Woodward multigrid-based optimization framework (MG/OPT), sig- Lawrence Livermore Nat’l Lab nificant speedup and improvement of accuracy has shown [email protected] for several examples.

Zichao Di MS201 Argonne National Lab Gyrokinetic Poisson Equation Solvers with Explicit [email protected] Flux Surface Averaging in XGC1 with PETSc Sven Leyffer An accurate representation of the flux surface averaging Argonne National Laboratory term in the gyrokinetic Poisson equation is explored for the leyff[email protected] first time, to our knowledge, in a global extreme-scale Toka- mak code XGC1. We use the FieldSplit preconditioner ca- pability in PETSc, which provides access to a wide variety Stefan Wild solver algorithms, including direct, block near direct, Schur Argonne National Laboratory complement, Gauss-Seidel, and additive and multiplicative [email protected] solver algorithms.

Mark Adams MS202 Lawrence Berkeley Laboratory Multigrid Preconditioning for Space-time Dis- [email protected] tributed Optimal Control Problems Constrained by Parabolic Equations Seung-Hoe Ku Princeton Plasma Physics Laboratory We present some recent results regarding multigrid pre- [email protected] conditioning of the linear systems arising in the solution process of space-time distributed optimal control problems constrained by parabolic equations. While the construction MS201 of the preconditioners is based on ideas extracted from op- timal control problems constrained by elliptic equations, in Algebraic Multigrid Solvers for Lattice QCD in the the parabolic-constrained case the multigrid precondition- Hypre Software Library ers exhibit a suboptimal behavior, namely they approxi- mate the operators to be inverted by half an order less Algebraic multigrid (AMG) has been instrumental in many than optimal. simulation codes for solving the requisite linear systems in a scalable manner. In quantum chromodynamics (QCD), Andrei Draganescu the development of effective AMG methods has been fairly Department of Mathematics and Statistics, UMBC recent so their use in QCD simulations has not yet become University of Maryland, Baltimore County commonplace. In this talk, we discuss work to develop a [email protected] variant of the bootstrap AMG method in the hypre library and efforts to interface it with the USQCD software stack. Mona Hajghassem Evan Berkowitz Department of Mathematics and Statistics Lawrence Livermore National Laboratory University of Maryland, Baltimore County [email protected] [email protected]

James Brannick MS202 Department of Mathematics Pennsylvania State University About Some Smoothers for Saddle-point Problems [email protected] In this work, we focus on the multigrid solution of saddle point problems. A key ingredient in designing an opti- Robert Falgout mal multigrid solver is the choice of the smoother. The Center for Applied Scientific Computing smoothers that we consider are mainly the obtained via Lawrence Livermore National Laboratory a coupled relaxation approach and they are tuned specifi- [email protected] cally for the indefinite matrices corresponding to the saddle point problems of interest. This is done guided by the lo- Chris Schroeder cal Fourier analysis (LFA), which allows us to estimate the Lawrence Livermore National Laboratory spectral radius of the k-grid operator in order to obtain [email protected] quantitative measures for the error reduction and to ac- curately predict the asymptotic convergence factor of the method. The LFA of such smoothers requires non-standard MS202 techniques, and they are used to adjust the parameters of Optimization Approach for Tomographic Inversion the underlying multigrid method and increase its efficiency. CS15 Abstracts 165

tions

Carmen Rodrigo,FranciscoJos´e Gaspar, Francisco The inverses and LR factors of stiffness matrices appearing Lisbona in the context of partial differential equations and integral University of Zaragoza equations are frequently rank-structured, i.e., they contain [email protected], [email protected], [email protected] submatrices that have low numerical rank. This property can be exploited to efficiently construct approximations of Ludmil Zikatanov these matrices and thereby find preconditioners for a wide Pennsylvania State University range of problems. This talk presents algorithms for carry- [email protected] ing out algebraic operations (matrix multiplication, factor- ization, inversion) approximately exploiting and preserving the low-rank structure. The algorithms rely on sequences 2 MS202 of low-rank updates applied to H -matrices, a relatively Multigrid in Chaos general class of rank-structured matrices that have efficient data-sparse representations. Dynamics of molecules, fluid flows, the climate, and other chaotic systems appear in many science and engineering Steffen B¨orm,KnutReimer applications. The long-time behavior of these dynamical Universitaet Kiel systems, and their sensitivity to perturbations, is interest- [email protected], [email protected] ing to both scientists and engineers. The multigrid method may be the key to finding such sensitivity. Sensitivity of MS203 chaotic dynamical systems can be computed using a new method known as Least Squares Shadowing, which requires A New Integral Formulation and Fast Direct Solver solving a space-time system of elliptic nature. Although for Periodic Stokes’ Flow multigrid shows great promise, this application also brings new challenges to multigrid methods. Many solution techniques have recently been developed to accurately and efficiently numerically model vesicle flow. Qiqi Wang The introduction of a periodic confining geometry adds fur- Massachusetts Institute of Technology ther complications to such simulations. This talk presents [email protected] a new integral formulation which avoids the use of the pe- riodic Green’s function. Additionally, a fast direct solver for the discretized confining geometry is presented. This Patrick Blonigan solver allows for efficient time stepping by decoupling the MIT static geometry from the moving vesicles. [email protected] Adrianna Gillman Dartmouth College MS203 Department of Mathematics Fast Solvers for Hierarchical Matrices [email protected] Recent years have seen the emergence of novel fast direct methods to solve linear systems with hierarchical matrices. Alex H. Barnett These methods are based on a type of direct elimination of Department of Mathematics the unknowns, in a manner similar to the LU factorization; Dartmouth College their accuracy is therefore less sensitive to the condition [email protected] number and distribution of eigenvalues of the matrix than with iterative solvers. We will present a novel class of fast Shravan Veerapaneni, Gary Marple direct solvers for sparse matrices. Department of Mathematics University of Michigan Amirhossein Aminfar [email protected], [email protected] Stanford University [email protected] MS203 Sivaram Ambikasaran Practical and Efficient Direct Solvers for BIEs Department of Mathematics Courant Institute of Mathematical Sciences The discretization of integral equations leads to dense lin- [email protected] ear systems. For large problems, these systems have tradi- tionally been solved using iterative solvers, often in combi- nation with accelerated techniques for the dense matrix- Mohammad Hadi Pour Ansari vector multiplication, such as, e.g., the Fast Multipole Stanford Method. However, in the last several years a number of [email protected] direct solvers with very high practical efficiency, and fa- vorable (often linear) asymptotic complexity have been de- Eric F. Darve veloped. This talk will describe techniques aimed at im- Stanford University proving performance and simplifying coding by using ran- Mechanical Engineering Department domized methods to accelerate certain structured matrix [email protected] computations. The direct solvers used will be based on the hierarchical merging of discrete analogs of scattering matrices. MS203 Rank-Structured Preconditioners for Two and Gunnar Martinsson Three-Dimensional Integral and Differential Equa- Univ. of Colorado at Boulder 166 CS15 Abstracts

[email protected] China Aerodynamics Research and Development Center China zhang [email protected] MS204 A One-Stage High-Resolution Constrained Trans- Chi-Wang Shu port Method for Magnetohydrodynamic Equations Brown University Div of Applied Mathematics Failure to maintain zero divergence of magnetic field has [email protected] been known to cause instability of numerical methods for solving magnetohydrodynamic equations. In this talk we will present a high-order conservative finite difference MS205 WENO method that uses constrained transport to enforce Constraint Aggregation Methods for PDE- a divergence free magnetic field. This method is based Constrained Optimization on the Picard Integral Formulation of the PDE, which al- lows us to construct a single-stage single-step scheme. This Many engineering design optimization problems are for- method is high-resolution, scalable to large clusters, and mulated with a bound on a physical quantity over a do- amenable to Adaptive Mesh Refinement (AMR). main of interest. Aggregation methods approximate this infinite-dimensional constraint in a differentiable manner. Xiao Feng However, many classical methods are non-conservative and Department of Mathematics it is often difficult to assess the error incurred through ag- Michigan State University gregation. To address these issues, we present a new class [email protected] of aggregation technique for PDE-constrained optimization and present a post-optimality method to assess the aggre- MS204 gation error. We present the results of these new techniques on large-scale structural optimization problems. A Hybrid Weno Reconstruction on Unstructured Mesh Graeme Kennedy Georgia Institute of Technology The weighted essentially non-oscillatory (WENO) schemes School of Aerospace Engineering are a popular class of high order numerical methods for hy- [email protected] perbolic partial differential equations (PDEs). In this talk, we will first talk about a hybrid approach for WENO recon- structions on the unstructured meshes and then discuss the Jason E. Hicken maximum-principle-preserving/positivity-preserving prop- Rensselaer Polytechnic Institute erties of the schemes. Numerical examples coupled with Assistant Professor third order Runge-Kutta time integrator are reported. [email protected]

Yuan Liu Department of Mathematics MS205 Michigan State University Large-Scale PDE-Constrained Fluid-Structure Op- [email protected] timization A multi-physics fluid-structure optimization problem with MS204 millions of state variables and thousands of design vari- A New RKDG Method with Conservation Con- ables is presented. The fluids domain is described by the straint to Improve CFL Condition for Solving Con- compressible Reynolds-Averaged Navier–Stokes equations servation Laws and the structural domain is described by the equations of linear elasticity. Parallel solution techniques for the cou- Abstract not available at time of publication. pled, non-linear multidisciplinary system and the linearized adjoint system are discussed. Zhiliang Xu University of Notre Dame Gaetan Kenway [email protected] University of Michigan Aerospace Engineering [email protected] MS204 High Order WENO Method for Steady State Prob- Joaquim R. R. A Martins lems University of Michigan [email protected] High order accurate shock capturing schemes such as WENO schemes often suffer from difficulties in their con- vergence towards steady state solutions. In this talk, I shall MS205 present our recent results on improving the convergence of A Krylov-Based Iterative Solver for Equality- fifth order WENO scheme for solving steady state hyper- Constrained Non-Convex Quadratic Subproblems bolic conservation laws by an explicit Gauss-Seidel sweep- ing framework combined with different new techniques. Conventional matrix-based constrained-optimization al- gorithms are not well suited to reduced-space PDE- Liang Wu, Yongtao Zhang constrained optimization, because, even for modest-sized University of Notre Dame primal and dual spaces, the cost of evaluating the Hessian [email protected], [email protected] and Jacobian can be prohibitive. This makes matrix-free optimization algorithms attractive for these applications. Shuhai Zhang Some challenges for reduced-space matrix-free algorithms CS15 Abstracts 167

include Hessians that are nonconvex in the null space of The Ohio State University the Jacobian, as well as finding effective matrix-free pre- [email protected] conditioners for the primal-dual system. Several matrix- free algorithms have been proposed to handle nonconvex- ity by adapting existing iterative solvers. In this work, MS206 we address nonconvexity within the primal-dual iterative Physically Based Assessment of Hurricane Surge method itself by modifying the subspace problem solved by Threat under Climate Change flexible GMRES. The approach is surprisingly simple and effective. We also present preliminary investigations of a Abstract not available at time of publication. multigrid matrix-free preconditioner. Ning Lin Jason E. Hicken Princeton University Rensselaer Polytechnic Institute [email protected] Assistant Professor [email protected] MS206 Pengfei Meng Understanding Coastal Hydrodynamic Processes Rensselaer Polytechnic University and Mitigating Risk Through High Fidelity Com- [email protected] puter Simulations

Abstract not available at time of publication. MS205 Aerodynamic Shape Optimization with Goal- Joannes Westerink Oriented Error Estimation and Control Department of Civil Engineering and Geological Sciences University of Notre Dame We investigate the control of discretization error in [email protected] gradient-based aerodynamic shape optimization through use of adaptive mesh refinement. The approach makes dual use of the adjoint method first in the computation of MS207 the objective function gradient and second in the estima- FinAT: A Mathematical Structure-Preserving Li- tion of discretization error. We focus on progressive opti- brary of Finite Elements mization, where the depth of mesh refinement is system- atically increased as the design improves. The approach Currently, automated finite element software generates is demonstrated on several challenging problems, including fairly traditional algorithms based on black box tabula- three-dimensional inverse design for sonic-boom minimiza- tion of basis functions. FInAT is a new project that will tion and the optimization of a flexible wing for transport exploit the algebraic structure of basis functions to gener- aircraft. This is an important step in our research toward ate more sophisticated algorithms that exploit tensor prod- dynamic error control to improve automation and minimize uct structure. It replaces arrays of tabulated values, with cost. specialized recipes for performing evaluation and integra- tion. This will create efficient implementations of product Marian Nemec elements, vector elements, Bernstein polynomials, and ele- Science & Technology Corp. ments such as Morley and Hermite with complicated pull- NASA Ames Research Center backs. [email protected] David Ham Michael Aftosmis Imperial College London NASA Ames Research Center [email protected] [email protected] Rob Kirby Baylor University MS206 robert [email protected] A Parallel Local Timestepping Runge-Kutta Dis- continuous Galerkin Method with Applications to MS207 Coastal Ocean Modeling Finite Element Geometric Multigrid Solvers from Abstract not available at time of publication. High-Level Problem Descriptions

Clint Dawson We present an implementation of geometric multigrid Institute for Computational Engineering and Sciences solvers in the Firedrake finite element framework. Our ap- University of Texas at Austin proach combines composable building blocks – appropriate [email protected] smoothers and intergrid transfer operators – with a sym- bolic representation of the PDE to simplify development of solvers for users: for many problems they need only pro- MS206 vide the fine grid discretisation. Our approach is agnostic Development and Validation of DG Wave: a Dis- to how the operators are applied, allowing simple switching continuous Galerkin-Based Numerical Wave Pre- between matrix-free and assembled operators. diction Model Lawrence Mitchell Abstract not available at time of publication. Department of Computing Imperial College London Ethan Kubatko [email protected] 168 CS15 Abstracts

Eike H. Mueller [email protected] University of Bath [email protected] MS208 David Ham Imperial College London Thermodynamically Consistent and Meta-Stable [email protected] Equation of State Models for Hydro and Solid Dy- namics Colin J. Cotter Simulations of real engineering interest require the use of Imperial College London thermodynamic and constitutive models that go beyond Department of Aeronautics simple analytic equations of state. In this talk we will dis- [email protected] cuss the complications that arise from using general equa- tions of states for fluids and solids. Issues that need to be addressed include equilibrium and non-equilibrium treat- MS207 ments for mixed and separated species and robust treat- ments for incompatible mixtures such as metals in tension Towards a Unified Framework for Automated a and gases. Posteriori Error Estimation and Adaptivity in Space-Time John W. Grove Computational Physics & Methods, CCS-2 Finite element systems that operate at a sufficiently high Los Alamos National Laboratory level of abstraction allow for efficient implementation of a [email protected] number of automated features. Here, we will discuss how to efficiency extend previous work on automated goal-oriented error control and adaptivity to space-time finite element MS208 methods. We’ll present a unified framework for automated derivation of problem-targeted error estimates and indica- Modelling of Fabric Surface for Parachute Inflation tors, and high level interfaces, efficient data structures and through Front Tracking algorithms for arbitrary dimension tensor product finite el- ement methods. We use the front tracking library on a triangulated spring system to model the dynamic evolution of parachute Marie E. Rognes canopy surface. The model is numerically convergent un- Simula Research Laboratory der the constraints that the summation of point masses is [email protected] constant and that both tensile and angular stiffness of the spring conform with the material’s Young modulus and Anders Logg Poisson ratio. This assembly is coupled with the fluid Chalmers University of Technology solver through the impulse method to compute parachute [email protected] inflation for comparison with experiments.

Benjamin Kehlet Xiaolin Li Simula Research Laboratory Department of Applied Math and Stat [email protected] SUNY at Stony Brook [email protected]

MS207 MS208 Multicore Parallelism for Common Finite Element Overlapping BEM on FEM computations Operations In this talk I will review some theoretical and computa- As the number of cores on a chip and in a node increases, tional work on how to deal with time-harmonic wave trans- the importance of multithreading increases. We identify a mission problems by superposing solutions of problems in design pattern where an embarrassingly parallel operation unbounded domains (discretized with BEM) and bounded on every cell is followed by a reduction. This design pattern domains with homogeneous properties (discretized with appears in finite element code through matrix assembly, FEM). estimating discretization errors, post-processing, etc. We also show a scalable implementation of this design pattern. Francisco J. J. Sayas Department of Mathematical Sciences University of Delaware Bruno Turcksin [email protected] Texas A&M University [email protected] Victor Dominguez Universidad Publica de Navarra Martin Kronbichler Spain Technische Universitat Munchen [email protected] [email protected] Matthew Hassell Wolfgang Bangerth Department of Mathematical Sciences Texas A&M University University of Delaware CS15 Abstracts 169

[email protected] DE-AC52-07NA27344.

Jean-Luc Fattebert MS208 Lawrence Livermore National Lab. [email protected] Fractional Schr¨odinger Dynamics Daniel Osei-Kuffuor We study the dynamics of the Schr¨odinger equation with α Lawrence Livermore National Laboratory a fractional Laplacian (Δ) . Analytically, we find equa- oseikuff[email protected] tions describing the dynamics of the expected position and expected momentum in the fractional Schr¨odinger equation, equations that are the fractional counterpart of MS209 the Newtonian equations of motion for the non-fractional Schr¨odingier equation (α = 1). We also propose a nu- Ab Initio Quantum Monte Carlo in Computational merical method for to study the dynamics of fractional Materials Science and Chemistry Schr¨odinger equation and find that the nonlocal interac- Ab initio Quantum Monte Carlo is an electronic structure tion from the fractional Laplacian introduces decoherence method that is highly accurate, well suited to large scale into the wave function. computation, and potentially systematically improvable in accuracy. The method has recently been applied to transi- Yanzhi Zhang tion metal oxides and to the prediction of defect properties Missouri University of Science and Technology and thermodynamics of materials, where established elec- [email protected] tronic structure methods have difficulty reaching the ac- curacies desired to inform experiment and the design and selection of materials. Nevertheless there remain signifi- MS209 cant challenges to achieving a methodology that is robust Towards Ab-Initio Simulations of Nanoelectronic and systematically improvable in practice, e.g., where the Devices statistical nature of the method precludes the use of algo- rithms developed for density functional theory or quantum To accurately simulate always smaller devices and predict chemical techniques. In this talk I will outline the cur- their ”current vs. voltage” characteristics prior to fabrica- rent state of the art and describe several opportunities for tion, the usage of a quantum transport (QT) solver has be- advances in the mathematical foundation and numerical come a must. Also, empirical models such as tight-binding implementation of key components of the method. cannot be considered as fully reliable when it comes to nanostructures so that in many applications they should Paul Kent be replaced by ab−initio solutions. Here, we will therefore Oak Ridge National Laboratory present the core algorithms of a DFT-based approach that [email protected] combines the CP2K community code with an existing QT simulator. As key feature the resulting tool can treat elec- tronic transport in 2-D and 3-D systems with more than MS209 10,000 atoms. Using Next-generation Architectures to Model Large and Complex Molecular Environments Mathieu Luisier, Mauro Calderara,SaschaBrueck Integrated Systems Laboratory Modelling large and complex molecular environments re- ETH Zurich quires fast, computationally scalable and efficient compu- [email protected], [email protected], tational tools utilizing novel algorithmic approaches on the [email protected] latest hardware technologies. Results of optimization ef- forts of the high-accuracy coupled cluster triples and the solid state planewave modules in the NWChem compu- Hossein Bani-Hashemian, Joost VandeVondele tational chemistry software for Intel Knights Corner and Nanoscale Simulations Landing multicore architectures combined with algorith- ETH Zurich mic advances will be discussed. [email protected], [email protected] Bert de Jong, Hongzhang Shan Lawrence Berkeley National Lab [email protected], [email protected] MS209 Truly Scalable O(N) Approach for First-Principles Leonid Oliker Molecular Dynamics (FPMD) of Non-Metallic Sys- Lawrence Berkeley National Laboratory tems [email protected]

We present a scalable O(N) FPMD algorithm based on a non-orthogonal localized orbitals formulation of DFT. A MS210 scalable strategy is used to approximately compute selected Segmental Refinement: A Multigrid Technique for elements of the inverse of the associated Gram matrix. The Data Locality algorithm exploits sparsity and uses nearest neighor com- munication only for excellent scalability. Accuracy is con- We investigate a technique, segmental refinement (SR), trolled by the mesh spacing of the discretization, the size proposed by Brandt in the 1970s as a low memory multigrid of the localization regions confining the orbitals, and a cut- method. The technique is attractive for modern computer off radius for the Gram matrix. This work was performed architectures because it provides high data locality, mini- under the auspices of the U.S. Department of Energy by mizes network communication, is amenable to loop fusion, Lawrence Livermore National Laboratory under Contract and is naturally highly parallel and asynchronous. The 170 CS15 Abstracts

network communication minimization property was rec- parallelizing Monte Carlo solvers for linear systems. Our ognized by Brandt and Diskin in 1994; we continue this work targets large, distributed memory systems by adapt- work by developing a segmental refinement method for a ing parallel algorithms developed in part by the radiation finite volume discretization of the 3D Laplacian on mas- transport community. sively parallel computers. An understanding of the asymp- totic complexities, required to maintain textbook multigrid Massimiliano Lupo Pasini efficiency, are explored experimentally with a simple SR Department of Mathematics and Computer Science method. A two-level memory model is developed to com- Emory University pare the asymptotic communication complexity of a pro- [email protected] posed SR method with traditional parallel multigrid. Per- formance and scalability are evaluated with a Cray XC30 with up to 64K cores. We achieve modest improvement in MS210 scalability from traditional parallel multigrid with a simple Parallel Algorithms for the Monte Carlo Synthetic SR implementation. Acceleration Linear Solver Method

Mark Adams Stochastic linear solvers based on Monte Carlo Synthetic Lawrence Berkeley Laboratory Acceleration are being studied as a potentially resilient al- [email protected] ternative to standard methods. Our work has shown that for certain classes of problems, these methods can also demonstrate performance competitive with modern tech- MS210 niques. In this talk we will review recent developments in Comparative Performance Analysis of an Algebraic parallelizing Monte Carlo solvers for linear systems. Our Multigrid Solver on Leading Multicore Architec- work targets large, distributed memory systems by adapt- tures ing parallel algorithms developed in part by the radiation transport community. We present a comparative performance analysis of a novel element-based algebraic multigrid method combined with Stuart Slattery a robust coarse-grid solution technique based on HSS low- Computer Science and Mathematics Division rank sparse factorization. Our test datasets come from the Oak Ridge National Laboratory SPE Comparative Solution Project for oil reservoir simu- [email protected] lations. We contrast the performance of the code on one 12-core CPU of a Cray XC30 with that on a 60-core Intel Tom Evans Xeon Phi. The steps we required to obtain top performance Oak Ridge National Laboratory are described in detail. [email protected]

Alex Druinsky Steven Hamilton Computational Research Division ORNL Lawrence Berkeley National Laboratory [email protected] [email protected]

Brian Austin MS211 NERSC Energy-based Inner Products for POD/Galerkin Lawrence Berkeley National Laboratory Model Reduction for Compressible Flows [email protected] The focus of this talk is the development of energy-based Xiaoye Sherry Li inner products for POD/Galerkin model reduction for com- Computational Research Division pressible flows. An energy stability analysis reveals that Lawrence Berkeley National Laboratory the inner product employed in the Galerkin projection step [email protected] of the model reduction dictates the ROMs stability. Fol- lowing the review of a symmetry inner product that gives rise to a stable formulation for linearized compressible flow, Osni A. Marques a new energy-based inner product for nonlinear compress- Lawrence Berkeley National Laboratory ible flow is derived and evaluated. Berkeley, CA [email protected] Jeffrey Fike, Irina K. Tezaur, Matthew Barone, Srinivasan Arunajatesan Eric Roman, Samuel Williams Sandia National Laboratories Lawrence Berkeley National Laboratory jafi[email protected], [email protected], [email protected], [email protected] [email protected], [email protected]

MS210 MS211 Iterative Performance of Monte Carlo Linear Data-driven Optimal Rational Approximation via Solver Methods Numerical Quadrature

Stochastic linear solvers based on Monte Carlo Synthetic Iterative Rational Krylov Algorithm (IRKA) has proved Acceleration are being studied as a potentially resilient al- very successful in producing optimal rational approxima- ternative to standard methods. Our work has shown that tions. The main cost for IRKA is the need to evaluate for certain classes of problems, these methods can also the underlying transfer function and its derivatives at new demonstrate performance competitive with modern tech- points at every step. In this talk, we present a quadrature- niques. In this talk we will review recent developments in based framework for IRKA that will remove this computa- CS15 Abstracts 171

tional cost. Transfer function will be evaluated only in an [email protected] off-line phase at selected quadrature nodes and iteration will not need new function evaluations. MS212 Christopher A. Beattie Optimal Explicit Strong Stability Preserving Virginia Polytechnic Institute and State University RungeKutta Methods with High Linear Order and [email protected] Optimal Nonlinear Order

Zlatko Drmac The search for high order strong stability time-stepping University of Zagreb methods with large allowable strong stability coefficient has Department of Mathematics been an active area ofresearch over the last two decades. [email protected] This research has shown that explicit SSP RungeKutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous prob- Serkan Gugercin lems, the order conditions simplify and this order barrier Virginia Tech. is lifted: explicit SSP RungeKutta methods of any linear Department of Mathematics order exist. These methods reduce to second order when [email protected] applied to nonlinear problems. In the current work we aim to find explicit SSP RungeKutta methods with large allow- able time-step, that feature high linear order and simul- MS211 taneously have the optimal fourth order nonlinear order. Reduced Order Modeling of Geophysical Flows These methods have strong stability coefficients that ap- proach those of the linear methods as the number of stages and the linear order is increased. This work shows that The reduced order models (ROMs) are frequently used in when a high linear order method is desired, it may be still the simulation of complex flows to overcome the high com- be worthwhile to use methods with higher nonlinear order. putational cost of direct numerical simulations. The proper orthogonal decomposition (POD), as one of the most com- Sigal Gottlieb monly used tools to generate ROMs, has been utilized in Department of Mathematics many engineering and scientific applications. For many University of Massachusetts Dartmouth complex flows, however, its original promise of computa- [email protected] tionally efficient, yet accurate approximation of coherent structures still remains to be fulfilled. To balance the low Zachary J. Grant computational cost required by ROMs and the complexity University of Massachusetts at Dartmouth of the targeted flows, appropriate closure modeling strate- [email protected] gies need to be employed. Several closure models for the POD-ROMs of structurally dominated flows are carefully derived and numerically investigated in the context of the Daniel L. Higgs quasi-geostrophic equations, which model the large scale University of Massachusetts, Dartmouth wind-driven ocean flows. [email protected]

Traian Iliescu MS212 Department of Mathematics Virginia Tech Strong Stability Preserving General Linear Meth- [email protected] ods We describe the construction of strong stability preserving (SSP) general linear methods (GLMs) for ordinary differ- MS211 ential equations. This construction is based on the mono- Efficient Reduced Basis Methods for Contact and tonicity criterion for SSP methods. This criterion can be Related Problems formulated as a minimization problem, where the objective function depends on the Courant-Friedrichs-Levy (CFL) We present online-efficient RB methods for contact and re- coefficient of the method, and the nonlinear constrains de- lated problems. Existing methods are inefficient since the pend on the unknown remaining parameters of the meth- online cost to compute the error estimates depends on the ods. The solution to this constrained minimization prob- dimension of the FE problem. Furthermore, the result- lem leads to new SSP GLMs of high order and stage order. ing error bounds are often pessimistic. We present two This is a joint work with Giuseppe Izzo from the University alternative, online-efficient approaches. The first approach of Naples. introduces an additional problem which enables the com- Zdzislaw Jackiewicz putation of sharp(er) error bounds. The second approach Arizona State University recasts the nonlinearity to allow treatment by the Empiri- [email protected] cal Interpolation Method (EIM).

Karen Veroy-Grepl, Zhenying Zhang, Eduard Bader MS212 Graduate School AICES Stability-Optimized Time Integrators for WENO RWTH Aachen University Discretizations [email protected], [email protected], [email protected] We present numerical time integrators designed for use with WENO and compact-WENO spatial discretizations of Mark Kaercher hyperbolic PDEs. These integrators have been optimized RWTH Aachen University for, in order of priority 172 CS15 Abstracts

1. Absolute stability with respect to the WENO semi- [email protected] discretizations (using the convex optimization tech- nique of Ketcheson & Ahmadia) 2. Strong stability preservation MS213 3. Accuracy Reweighted Minimization Method for Uncertainty Quantification of Microscopic Modeling We present theoretical and numerical evidence that these new methods allow the use of larger time steps without sacrificing accuracy. In this talk, reweighted minimization method for uncer- tainty quantification of microscopic modeling will be dis- David I. Ketcheson cussed. Fast and accurate surrogate model is very useful CEMSE Division in mescoscopic modeling. It helps to evaluate the quantity King Abdullah University of Science & Technology of interest, calibrate the model e?ciently (with Bayesian [email protected] framework), to study the uncertainty in the system quickly, etc. In this work, reweighted minimization method is em- Debojyoti Ghosh ployed for microscopic modeling when the system includes Mathematics and Computer Science Division i.i.d. uniform random variables. The proposed method en- Argonne National Laboratory hances our ability of exploiting information from limited [email protected] source of experiments or simulations. We employ the new method to practical problems in mesoscopic modeling in physical chemistry, electrochemistry, biophysics, biochem- MS212 istry, etc., to help to quantify the uncertainty, calibrate Implicit-Explicit General Linear Methods model, design experiments, etc. In conclusion, this work will provide a ?exible approach of e?ciently utilizing limited Implicit-explicit (IMEX) time stepping methods can effi- experimental or simulation results to construct an accurate ciently solve differential equations with both stiff and non- surrogate model. stiff components. In this work we study new implicit- explicit methods of general linear type. We develop an Guang Lin, Xiu Yang, Huan Lei order conditions theory for high stage order partitioned Pacific Northwest National Laboratory GLMs that share the same abscissae, and show that no [email protected], [email protected], additional coupling order conditions are needed. Conse- [email protected] quently, GLMs offer an excellent framework for the con- struction of multi-method integration algorithms. Next, we propose a family of IMEX schemes based on diagonally- implicit multi-stage integration methods and construct MS213 practical schemes of order up to five with numerically op- Least Square Methods for Low-Rank Approxima- timized stability regions. The new methods have similar tions with Sparsity Inducing Regularization stability properties as IMEX Runge-Kutta methods, but they do not suffer from order reduction, and are superior in terms of accuracy and efficiency. Numerical experiments Approximation of high dimensional stochastic functions us- with two and three dimensional test problems illustrate the ing functional approaches is often limited by the so called potential of the new schemes to speed up complex applica- curse of dimensionality. In literature, approximation meth- tions. ods often rely on exploiting particular structures of high di- mensional functions. One such structure which is increas- Hong Zhang ingly found to be applicable in these functions is sparsity Virginia Tech on suitable basis. Also, these functions exhibit optimal low [email protected] rank representation and can be approximated in suitable low rank tensor subsets. In this work, we exploit sparsity within low rank representation to approximate high dimen- MS213 sional stochastic functions in a non intrusive setting using Sampling Strategies for L1 Minimization few sample evaluations. The proposed method can also be combined with clustering and classification approaches to One of the biggest challenges of uncertainty quantification approximate high dimensional irregular and discontinuous is the inability to ‘densely’ sample the model input space functions. due to high-dimensionality and/or the immense compu- tational expense of a high-fidelity model. The need to Prashant Rai ‘densely’ sample can be often be alleviated by building LUNAM Universite, Ecole Centrale Nantes, CNRS, GeM a sparse Polynomial Chaos Expansion (PCE) using l1- [email protected] minimization. In this talk I will present sampling, pre- conditioning and basis adaptive strategies that allow one to accurately approximate high-dimensional compressible Mathilde Chevreuil functions from limited data using any orthonormal poly- LUNAM Universite, Universite de Nantes, CNRS, GeM nomial basis. [email protected]

John D. Jakeman Lo¨ıc Giraldi Sandia National Labs GeM, Ecole Centrale de Nantes [email protected] [email protected]

Akil Narayan Anthony Nouy University of Massachusetts Dartmouth LUNAM Universite, Ecole Centrale Nantes, CNRS, GeM CS15 Abstracts 173

[email protected] ditions using a matrix-free preconditioned Gauss-Newton- Krylov method for the Schur complement of the velocity field. We use a spectral Galerkin method in time to re- MS213 duce the number of unknowns. Also, we use a spectral Interpolation Via Weighted L1 Minimization discretization in space, which in turn allows for an efficient preconditioning of the Hessian. Functions of interest are often smooth and sparse in some sense. Classical linear interpolation methods are effective Andreas Mang under strong regularity assumptions, but cannot incorpo- The University of Texas at Austin rate nonlinear sparsity structure. At the same time, non- The Institute for Computational Engineering and Sciences linear methods such as L1 minimization can reconstruct [email protected] sparse functions from very few samples, but do not neces- sarily encourage smoothness. Here we show that weighted George Biros L1 minimization effectively merges the two approaches, University of Texas at Austin promoting both sparsity and smoothness in reconstruction. [email protected] We consider the implications of these results for spheri- cal harmonic and polynomial interpolation, in the univari- ate and multivariate setting. Along the way, we extend MS214 concepts from compressive sensing such as the restricted Efficient Algorithms for High-Resolution Diffusion- isometry property and null space property to accommodate Weighted MRI weighted sparse expansions; these developments should be of independent interest in the study of structured sparse Diffusion-weighted Magnetic Resonance Imaging (DW- approximations and continuous-time compressive sensing MRI) allows the acquisition of functional information in- problems. vivo and has important clinical applications, for instance, related to Ischemia and Alzheimer’s disease. In this talk, I Rachel Ward will present computational methods to overcome two lim- Department of Mathematics itations currently inherent in DW-MRI: Geometrical dis- University of Texas at Austin tortions due to measurement artifacts and low spatial res- [email protected] olution. The presented 3D correction and super-resolution method is based on a physical prior and employs a slice- Holger Rauhut wise parallelization to increase computational efficiency. Aachen University [email protected] Lars Ruthotto Department of Mathematics and Computer Science Emory University MS214 [email protected] Nonlinear Image Registration with a Sliding Mo- tion Deformation Model MS214 Common medical image registration approaches are enforc- Constrained Optimal Control Approaches in Large ing a global continuity of the estimated deformation field. Deformation Diffeomorphic Metric Mapping However, for deformations like e.g. the sliding of the lung along the ribcage a continuous deformation estimation is The large deformation diffeomorphic metric mapping (LD- not feasible. Therefore we present in this talk a registration DMM) algorithm, which addresses image or shape regis- framework that models discontinuities in the deformation tration, can be interpreted as an optimal control prob- field along organ boundaries described by arbitrary ori- lem in some suitable high-dimensional space of shapes. It entable submanifolds. The incorporated methods involve has led to a large number of applications in the domain constrained nonlinear registration in the Lagrange frame of computational anatomy, in which the focus is set on and a finite element discretization. the analysis of anatomical variations in relation with dis- ease. In some cases this algorithm can be invoked with Alexander Derksen additional constraints, which leads to interesting new ap- Institute of Mathematics and Image Computing plications and challenging implementation problems. We University of Luebeck will review some of these examples in this talk, including, [email protected] in particular, issues related to the combined registration of multiple shapes, and to the evaluation of deformations with atrophy constraints. MS214 Efficient Algorithms for Physically Constrained Laurent Younes Diffeomorphic Image Registration Center for Imaging Science , The Johns Hopkins University We treat image registration as a problem of optimal con- [email protected] trol. The deformation is represented by its velocity. This leads to a constrained variational optimization problem, where the constraints are partial differential equations MS215 1 2 (PDEs) . We augment standard H and H smoothing reg- Preconditioned MCMC and Adaptive Posterior ularization with differential constraints on the velocity that Refinement Leveraging Sparse PCE both encapsulate prior knowledge and explicitly control the determinant of the deformation gradient. The associated The process of performing Bayesian inference is frequently optimality conditions are a system of space-time non-linear hindered by expense and by a lack of reliability in the multi-component PDEs that is challenging to solve in an MCMC sampling used for computing the posterior dis- efficient way. We solve for the first-order optimality con- tribution. We present a recent prototype for adaptive 174 CS15 Abstracts

emulator-based inference that employs 1-regularized re- [email protected] gression for sparse polynomial chaos emulation, exploits analytic derivatives from the emulator to inform the pro- posal density, and then refines the emulator by performing MS215 new model evaluations for points with high posterior den- Quasi Optimal Sparse-Grid Approximation of Ran- sity. dom Elliptic PDEs

Michael S. Eldred Solutions of PDEs depending on parameters/random co- Sandia National Laboratories efficients can be conveniently approximated by polyno- Optimization and Uncertainty Quantification Dept. mial expansions over the parameter space. However, these [email protected] approximations suffer from a performance degradation as the number of random parameters increases (“curse of di- John D. Jakeman mensionality’ effect). In this talk we will propose an “a- Sandia National Labs priori/a-posteriori profit approach’ to minimize such effect [email protected] for sparse grids approximations. The efficiency of the pro- posed technique will be supported by theoretical conver- Laura Swiler gence results and numerical tests. Sandia National Laboratories Lorenzo Tamellini Albuquerque, New Mexico 87185 EPF-Lausanne, Switzerland, [email protected] lorenzo.tamellini@epfl.ch

MS215 Fabio Nobile Accelerated Bayesian Inference with Transport EPFL, Switzerland Maps fabio.nobile@epfl.ch

The essential challenge in Bayesian computation for UQ is Raul F. Tempone one of characterizing the posterior distribution, which of- Mathematics, Computational Sciences & Engineering ten is high-dimensional and non-Gaussian. We will show King Abdullah University of Science and Technology that the use of transport maps can dramatically accelerate [email protected] Bayesian inference in this setting. First, we use a combi- nation of optimal transport and the Metropolis-Hastings rule to yield a new adaptive MCMC approach for exact in- MS216 ference. Second, we develop new conditioning techniques, Approaches to Evaluate Interactions in Collabora- with tunable accuracy, that can utilize massively parallel tive Groundwater Management offline computation. Abstract not available at time of publication. Matthew Parno, Youssef M. Marzouk Massachusetts Institute of Technology Joseph Amaya [email protected], [email protected] Texas A&M University - Kingsville [email protected]

MS215 Sparse, Adaptive Smolyak Quadrature Algorithms MS216 for Stochastic Inverse Problems Managing Surface Water Resources in Data Sparse Regions Deterministic, dimension-adaptive quadrature methods for Bayesian inverse problems of parametric operator equa- Abstract not available at time of publication. tions with distributed uncertain inputs are proposed. For data from a sparsity class, the parametric, deterministic Felipe Estrada density of the Bayesian posterior belongs to the same spar- Texas Tech University sity class. Dimension-independent convergence rates for [email protected] dimension-adaptive Smolyak and QMC integration algo- rithms are shown. In the vanishing observation noise vari- MS216 ance limit the posterior concentrates near the MAP es- timate. We give asymptotic expansions of the Bayesian Climate Change and Water Scarcity estimate w.r. to observation noise variance. A “variable Abstract not available at time of publication. metric’ rescaling of the posterior near concentration points “preconditions’ quadrature for vanishing observation noise Donna Mitchell covariance. Numerical results in agreement with the the- Texas Tech University ory are presented. Supported by SNF and ERC under [email protected] AdG247277.

Christoph Schwab MS216 ETH Zuerich SAM Application of Simulation-Optimization for Water [email protected] Management in Hydraulic Fracturing Operations Abstract not available at time of publication. Claudia Schillings ETH Zurich Elma A. Uddameri SAM Texas Tech University CS15 Abstracts 175

[email protected] [email protected]

Nathaniel Trask MS217 Brown University Interface Resolved Numerical Method to Study Department of applied mathematics Electrokinetic Particle Assembly in Microdevices nathaniel [email protected]

A hybrid immersed interface-immersed boundary method MichaelL.Parks is developed to study electric field driven particle assembly Sandia National Laboratories where both electric and hydrodynamic forces are calculated [email protected] with interface-resolved approach instead of commonly used point-particle method. In this study, the Maxwell stress tensor is used to calculate the electric force acting on par- MS217 ticles by considering the physical effect of particles in the computational domain. Thus, this method eliminates the Meshless Methods for the Mesoscale - High Order approximations used in point dipole methods for calculat- Implicit ALE Schemes using Collocated MLS ing forces. A comparative study between Maxwell stress tensor and point dipole methods for computing electric Meshless methods are ideal for simulating flows occurring forces will be presented to elucidate the shortcoming of at the mesoscale, since they trivially handle both defor- the latter method. Next, electric field driven particle mo- mation of complex boundaries and interface tracking for tions and related fluid flow phenomena will be presented flows involving multispecies phenomena. Classical mesh- for charged, uncharged and bipolar particles. We will par- less methods tend to either be expensive or inconsistent ticularly demonstrate the particle chaining phenomena for and have mainly gained traction in the past as a low order similar and dissimilar type particles using applied electric technique. We present a collocation formulation of mov- fields. ing least squares (MLS) that allows high order discretiza- tion in space, and a fully implicit ALE projection scheme Prashanta Dutta that is demonstrated to provide up to third order accu- Washington State University racy in time. When the resulting system is solved using [email protected] algebraic multigrid preconditioners, the scheme provides a scalable, flexible framework for simulating multiphysics at the mesoscale. MS217 Classical Density Functional Theory of Charged Nathaniel Trask Fluids at Interfaces Brown University Department of applied mathematics Classical density functional theory (DFT) is a statistical nathaniel [email protected] mechanical theory for inhomogeneous fluids, based on the minimization of a free energy functional. Here I will de- scribe the application of DFT to charged systems and in Kyungjoo Kim particular the ionic correlations included by the DFT that Sandia National Laboratories go beyond the Poisson-Boltzmann treatment. I will present [email protected] results for macroion interactions in electrolyte solutions and the behavior of charged particles in nanochannels. Mauro Perego CSRI Sandia National Laboratories Amalie Frischknecht [email protected] Sandia National Laboratories [email protected] MS218 MS217 A Sampling Filter for Non-Gaussian Data Assimi- lation Efficient Parallel Implementation of Implicit SPH/MLS using LAMMPS and Trilinos Current operational ensemble-based filters like Ensemble We present an efficient parallel implementation of 3D im- Kalman Filter (EnKF), and Maximum Likelihood Ensem- plicit mesh-free particle methods for incompressible flows. ble Filter (MLEF), usually fail in case of non-linear obser- Mesh-free methods are widely used for solving complex vations or non-Gaussian distributions. We propose a gen- problems that mesh-based methods cannot handle easily. eral ensemble-based data assimilation method that works However, implicit time methods are rarely applied to large- by sampling directly from the posterior distribution fol- scale particle simulations due to the prohibitive computa- lowing a Hybrid Monte Carlo (HMC) ap- proach. The tional cost solving linear systems of equations. Our im- proposed filter was tested on Lorenz-96 model with several plementation is based on LAMMPS and adopts Trilinos observation operators. Results show that this filter is ca- packages for implicit time integration. Numerical experi- pable of handling non-linear as well as linear observations. ments are presented to demonstrate the parallel scalability.

Ahmed Attia Kyungjoo Kim Virginia Tech Sandia National Laboratories [email protected] [email protected] Adrian Sandu Mauro Perego Virginia Polytechnic Institute and CSRI Sandia National Laboratories State University 176 CS15 Abstracts

[email protected] state variables as well as on the underlying kinematics of the flow. In addition to describing the methodology we show comparisons of displacement data assimilation to MS218 more conventional assimilation in the context of pure ad- Bayesian Nonlinear Smoothing and Adaptive Sam- vection of a tracer in a flow constrained kinematically by pling area preserving maps. This comparison will demonstrate that our methodology minimizes phase errors and thus de- New schemes are presented for optimal Bayesian nonlinear livers better estimates of the topological features of ad- state estimation and adaptive sampling of large nonlinear vected tracers. fluid and ocean dynamical systems, both forward and back- ward in time. The Bayesian nonlinear smoothing com- Juan M. Restrepo bines reduced-order Dynamically-Orthogonal (DO) equa- Departments of Mathematics, Atmospheric Physics, and tions with Gaussian Mixture Models (GMMs), extending Physics linearized backward pass updates to a Bayesian nonlinear University of Arizona setting. Bayesian nonlinear adaptive sampling schemes are [email protected] then derived to predict the observations to be collected that maximize information about variables of interest. When Steven Rosenthal combined with rigorous time-optimal path planning, we University of Arizona obtain efficient coordinated swarms of autonomous ocean [email protected] sampling systems.

Pierre F.J Lermusiaux Shankar C. Venkataramani Massachusetts Institute of Technology University of Arizona [email protected] Department of Mathematics [email protected] Tapovan Lolla MIT Arthur Mariano [email protected] RSMAS/MPO University of Miami [email protected] MS218 An Information Theoretic Approach to Use High- Fidelity Codes to Calibrate Low-Fidelity Codes MS219 Statistical Metrics for Assessing Quality of Scenar- In this presentation, we discuss an information theoretic ios for Unit Commitment and Dispatch approach to employ high-fidelity codes to calibrate low- fidelity codes used for design optimization or control im- Wind power scenarios for use in stochastic unit commit- plementation. The objective is to employ a limited num- ment should accurately represent the stochastic process ber of high-fidelity code evaluations as data for Bayesian for available wind power. We employ statistical evalu- calibration of the low-fidelity code. We employ the mu- ation metrics to assess whether a scenario set possesses tual information between parameters and designs to deter- properties that are expected to minimize expected cost. A mine input values to the high-fidelity code, which maximize new mass transportation distance rank histogram assesses the available information. For computationally expensive calibration of unequally likely scenarios according to their codes, surrogate models are used to approximate the mu- bias, variability and autocorrelation. Energy scores, rank tual information. The framework is illustrated for exam- histograms, and Brier scores are applied to alternative sets ples arising in nuclear power plant design. of wind power scenarios.

Allison Lewis Sarah M. Ryan,DidemSari North Carolina State University Iowa State University [email protected] [email protected], [email protected]

Ralph C. Smith North Carolina State Univ MS219 Dept of Mathematics, CRSC Adaptive Robust Optimization with Dynamic Un- [email protected] certainty Sets for Power System Operations

Brian Williams In this talk, we present an adaptive robust optimization Los Alamos National Laboratory model with a new type of dynamic uncertainty sets for [email protected] power system operations under significant renewable gen- eration uncertainty. We introduce a data-driven frame- work that fuses statistical estimation with uncertainty set MS218 construction to model temporal and spatial correlations of Displacement Data Assimilation renewable generation. Computational results show the ad- vantages of the proposed robust model in terms of opera- We are developing a data assimilation methodology specif- tional cost and system reliability over existing deterministic ically geared to problems in which the preservation of fea- and robust models. tures and topological structures is crucial. The application of this methodology is aimed at improving estimates of Andy Sun such things as hurricane tracks and the Lagrangian tracks Georgia Tech of tracers in a flow. The basic strategy combines con- College of Engineering ventional nonlinear/non-Gaussian data assimilation on the [email protected] CS15 Abstracts 177

Alvaro Lorca Tokyo Institute of Technology Georgia Institute of Technology [email protected], [email protected], Industrial and Systems Engineering [email protected] [email protected]

MS220 MS220 A New Incompressibility Discretization for a Hy- Reconstructed Discontinuous Galerkin (RDG) brid Particle Mac Grid Representation with Sur- Method for Multi-Material Flows on Unstructured face Tension Meshes We take a particle based approach to incompressible free In this work, we discuss extension of the Reconstructed surface flow motivated by the fact that an explicit represen- Discontinuous Galerkin method, developed previously for tation of the interface geometry and internal deformations high-order spatio-temporal discretization of single-fluid gives precise feedback to an implicit solver for surface ten- flows on hybrid unstructured meshes, to fluid flow appli- sion. Methods that enforce incompressibility directly on cations with multi-material interfaces. The focus is placed the particles are typically numerically inefficient compared on challenging issues of hierarchical WENO based limit- to those that utilize a background grid. However, back- ing of discontinuous flow solutions, modal orthogonal basis ground grid discretizations suffer from inaccuracy near the functions, interface tracking using combination of volume free surface where they do not properly capture the inter- tracking and level set methods, sharp treatment of inter- face geometry. Therefore, our incompressibility discretiza- facial jump conditions, and combination with Arbitrary tion utilizes a particle based projection near the interface Lagrangian-Eulerian (ALE) techniques. and a background MAC grid based projection for efficiency in the vast interior of the liquid domain as well as a novel Robert Nourgaliev, Sam Schofield method for coupling these two disparate projections to- LLNL gether. We show that the overall coupled elliptic solver is [email protected], schofi[email protected] second order accurate, and remains second order accurate when used in conjunction with an appropriate temporal discretization for parabolic problems. A similar second or- MS220 der accurate discretization is derived when the MAC grid An Eulerian Projection Method for Quasi-Static unknowns are located on faces (as opposed to cell centers) Elastoplasticity so that Navier-Stokes viscosity can be solved for implicitly as well. Finally, we present a fully implicit approach to sur- A well-established numerical approach to solve the Navier– face tension that is robust enough to achieve a steady state Stokes equations for incompressible fluids is Chorin’s pro- solution in a single time step. Beyond stable implicit sur- jection method, whereby the fluid velocity is explicitly up- face tension for our novel hybrid discretization, we demon- dated, and then an elliptic problem for the pressure is strate preliminary results for both standard front tracking solved, which is used to project the velocity field to main- and the particle level set method. tain the incompressibility constraint. In this talk, a math- ematical correspondence between Newtonian fluids in the Wen Zheng,BoZhu incompressible limit and elastoplastic solids in the slow, Stanford University quasi-static limit will be presented. Using this correspon- [email protected], [email protected] dence, a new fixed-grid, Eulerian numerical method for simulating quasi-static elastoplastic solids will be devel- Byungmoon Kim oped, whereby the stress is explicitly updated, and then Adobe Systems Inc. an elliptic problem for the velocity is solved, which is used [email protected] to project the stress to maintain the quasi-staticity con- straint. Numerical tests of the method will be given, and a number of correspondences between incompressible fluid Ronald Fedkiw mechanics and quasi-static elastoplasticity will be shown, Stanford University creating possibilities for translating other numerical meth- [email protected] ods between the two classes of physical problems.

Chris H. Rycroft MS221 Harvard SEAS Applications of Distributed Methods to Non- [email protected] Traditional Linear Systems We investigate solutions to multi-dimensional linear sys- MS220 tems using single machine parallelization techniques. The A Robust and Efficient Solver for Interfacial Multi- tri-color-channel radioisty method is used as a test case phase Flows on Unstructured Grids where the Jacobi method is applied to solve the radiosity linear equation. The multi-dimensionality of the system is We present a robust, accurate and efficient numerical represented through a structure of arrays and an array of framework for multiphase interfacial fluid dynamics on un- structures, where the latter was found to be optimal. Work structured grids of arbitrary shapes of elements. The multi- distribution was implemented with CUDA and OpenMP moment finite volume method is used as a reliable and where OpenMP threading was found to be optimal. practical solver for complex flows in presence of complex geometries, which well balances numerical accuracy and Julian Gilyard computational cost. The free interfaces are computed by Department of Computer Science the THINC scheme which is an accurate algebraic VOF Wake Forest University method well-suited for unstructured grids. [email protected] Feng Xiao, Bin Xie, Sun Ziyao Thomas Stitt 178 CS15 Abstracts

Pennsylvania State University [email protected] Department of Electrical Engineering [email protected] Padma Raghavan The Pennsylvania State Univ. Oluwapelumi Adenikinju, Joshua Massey Dept of Computer Science Engr. University of Baltimore Maryland County [email protected] Department of Computer Science and Electrical Engineering [email protected], [email protected] MS221 General SpMV and SpMM for AMG on GPUs

MS221 Scientific computations on sparse graphs mainly require Multigrid Solvers on Heterogeneous Architectures two computational patterns: processing of neighbors (gen- eral SpMV) and processing of all neighbors of a set of HHG is a multigrid finite element solver that scales to a nodes, often all neighbors of neighbors (general SpMM). million threads and that can solve in excess of a trillion These two patterns have different properties and require- (1012) unknowns in about a minute compute time. This is ments for massively parallel implementations. The main achieved by a careful co-design of grid structure, discretiza- challenge for the former is the different number of neigh- tion, multigrid components, and the hybrid parallelization, bors and indirection in access, while the latter has the dom- all driven by a meticulous performance engineering process. inating problems of index matching and varying output HHG is now being extended to use GPU kernels and we sizes. Once these problems are solved in parallel an alge- will report on the acceleration achieved. braic multigrid solver (AMG) can be efficiently assembled on the GPU. Bj¨orn Gmeiner Computer Science 10 - System Simulation Robert Strzodka Friedrich-Alexander-University Erlangen-Nuremberg, NVIDIA Germany [email protected] [email protected]

Daniel Iuhasz MS222 FAU Erlangen Industrial Mathematics Education at Worcester [email protected] Polytechnic Institute

Sebastian Kuckuk Central to the philosophy of learning at Worcester Poly- Universit¨at Erlangen-N¨urnberg technic Institute (WPI) is the principle of project-based [email protected] learning. In the Department of Mathematical Sciences through our Center for Industrial Mathematics and Statis- tics (CIMS) we have a strong focus on industry-sponsored Markus Stuermer, Harald Koestler projects for students. These projects are based on real- University of Erlangen-Nuremberg world problems that come directly from business or gov- [email protected], ernment. Students work on these projects under the [email protected] guidance of a faculty advisor and an industrial liaison. These projects are used in many settings, including se- Ulrich J. Ruede nior projects for the Bachelor’s degree, Master’s degree University of Erlangen-Nuremberg projects, and summer Research Experience for Undergrad- Department of Computer Science (Simulation) uates (REU) projects. The focus of this talk will be about [email protected] the project process and its benefits to our WPI. Examples will be provided for illustration.

MS221 Marcel Blais Speeding Up Sparse Triangular Solution on Multi- Worcester Polytechnic Institute cores and GPUs [email protected]

Multicores have complex memory hierarchy and increased parallelism; GP-GPUs have tremendous amount of thread- MS222 based parallelism. We examine structures to expose the PIC Math: Preparation for Industrial Careers in underlying parallelism present in sparse-matrices to uti- Mathematical Sciences lize multicore NUMA architecture and GPU. Specifically we have developed CSR-k, a multilevel form of the tradi- PIC Math is a new program to prepare students in the tional compressed sparse row format that can be mapped mathematical sciences to succeed in careers in business, in- to NUMA hierarchy. We formulate sparse triangular solve dustry, and government (BIG). Funded by a 2 million dol- in terms of CSR-k with coloring and demonstrate how this lar NSF grant, this program (a) helps students be aware of perform with CPU and GPU. their choices for non-academic careers and opportunities for internships, (b) helps faculty be more fully aware of Humayun Kabir non-academic career options for their students, make con- Department of Computer Science and Engineering nections with people working for local BIG organizations, The Pennsylvania State University and develop internship opportunities for their students, (c) [email protected] offers students the opportunity to have a research expe- rience related to real-world problems from BIG during a Joshua D. Booth spring semester course, and (d) provide training to stu- The Pennsylvania State University dents and faculty in how to successfully work on problems CS15 Abstracts 179

from BIG and develop the needed communications skills. Discrete-Ordinates Radiation-Transport Cal- To accomplish these objectives, we are developing a set culations of educational and informative videos, conducting summer training workshops for faculty, and preparing materials for We present a multigrid method for discrete-ordinates a semester-long course in which students learn skills and radiation-transport calculations, in particular for the Self- work on research problems from BIG. Adjoint Angular Flux (SAAF) form of the transport equa- tion in two-dimensional Cartesian geometry. For smooth- Michael Dorff ing, we employ multistage cellwise block Jacobi iteration. Brigham Young University The use of the SAAF equation allows straightforward de- mdorff@math.byu.edu termination of optimal multistage parameters for small spatial cells; single-stage cellwise block Jacobi iteration is not effective in this regime. On coarse grids, we apply a MS222 Galerkin discretization based on bilinear interpolation. A New Curriculum in Applied and Computational Mathematics Jeffery D. Densmore, Daniel Gill, Justin Pounders Bettis Atomic Power Laboratory We present BYU’s new undergraduate curriculum in Ap- jeff[email protected], [email protected], plied and Computational Mathematics. We highlight the [email protected] main features of this program and discuss how we have been able to overcome numerous pedagogical, institutional, and cultural challenges, particularly as we’ve launched an MS223 applied math degree in a predominantly pure math de- A Conservative High-Order / Low-Order Method partment. We also show how we have been able to teach Based Upon a Non-Conservative High-Order Least a number of advanced topics to undergraduates, and we Squares Sn Formulation share our approach to recruiting and retaining students. We have developed a high-order/low-order (HO/LO) Jeffrey Humpherys scheme for neutronics eigenvalue calculations. The HO Brigham Young University equation is a second-order least-squares form of the Sn jeff[email protected] equations that contains scattering and fission sources from the LO equation. The LO equation is an angular moment equation in drift-diffusion form containing closure infor- MS222 mation from the HO equation. The HO equation generally A Student Perspective on Industrial Capstones at yields a non-conservative solution, while the LO equation Harvey Mudd College always yields a conservative solution adequate for reactor analysis. This talk will give a student’s perspective on Harvey Mudd’s Mathematics Clinic program, in which seniors ma- Jacob Peterson joring in mathematics work in teams to complete industrial Department of Nuclear Engineering projects. These projects give ample opportunity not only Texas A&M to hone mathematical skills, but also to practice effective [email protected] collaboration, communication, and project management. As a student, the combination of faculty mentorship and Jim E. Morel student-driven work provides an engaging transition into Texas A&M industrial careers in mathematics. [email protected] Elizabeth Schofield Harvey Mudd College MS223 eschofi[email protected] Multilevel Monte Carlo Methods for Kinetic Equa- tions

MS223 The adaptation of the Multilevel Monte Carlo (MLMC) Multilevel Projection Method for Nonlinear Radia- method - introduced by Giles for SDEs in finance - to ki- tive Transfer Problems netic equations will be presented. MLMC introduces multi- ple time-steps and uses correlations between them for vari- This talk presents a deterministic computational method ance reduction, thereby reducing the complexity of achiev- for solving coupled radiative transfer and energy balance ing RMS error ε from O(ε−3)toO(ε−2). Application to equations. It uses a multilevel system of equations con- the spatially homogeneous Landau-Fokker-Planck model of sisting of the high-order radiative transfer equation, multi- Coulomb collisions will be presented, as well as progress to- group low-order quasidiffusion (LOQD) and grey LOQD ward an MLMC-type scheme for the inhomogeneous Vlasov equations defined for moments of the specific intensity. The equation. energy balance equation is coupled to the grey LOQD equa- tions. Temperature is evaluated in a projected space of Lee F. Ricketson smallest dimensionality. We study discretization and lin- UCLA earization methods for coupled multiphysics equations. [email protected] Dmitriy Y. Anistratov North Carolina State University MS224 [email protected] Greedy Algorithms for Parametric Eigenvalue Problems MS223 Some greedy algorithms will be presented to compute the A Multigrid Method for Two-Dimensional solution of parametric eigenvalue problems. This work is 180 CS15 Abstracts

a continuation of the results presented in [1] where the au- grow exponentially with the number of dimensions, making thors presented algorithms for non-parametric eigenvalue classic approaches unfeasible. Approximation of the solu- problems. The principle of the method is to compute a tion by low-rank tensor formats often allows us to avoid reduced-order model for the solution of a parametric eigen- this curse of dimensionality by exploiting the underlying value problem as a sum of pure tensor-product functions, structure of the linear operator. We propose a new algo- each term being computed in an iterative way which will rithm that performs a preconditioned gradient method on be precised in the talk. Some theoretical results on the the manifold of tensors of fixed rank. In particular, we convergence of these algorithms will be presented and their focus on tensors represented in the Tensor Train (TT) / numerical behaviour will be illustrated on some simple test Matrix Product States (MPS) format. We demonstrate the cases. [1] E. Cancs, V. Ehrlacher and T. Lelivre. ”Greedy flexibility of our algorithm by comparing different approx- algorithms for high-dimensional eigenvalue problems”, ac- imations of the Riemannian Hessian as preconditioners for cepted for publication in Constructive Approximation. the gradient directions. Finally, we compare the efficiency of our algorithm with other tensor-based approaches such Virginie Ehrlacher as the Alternating Linear Scheme (ALS). This is joint work CERMICS - Ecole des Ponts Paristech / INRIA with Michael Steinlechner and Daniel Kressner (EPF Lau- [email protected] sanne).

Bart Vandereycken MS224 Department of Mathematics Semi-Supervised Robust Matrix Completion for Princeton University Dynamic Subspace Estimation and Tracking [email protected]

Recent SVD-free matrix factorization formulations have enabled rank minimization for systems with millions of MS225 rows and columns, paving the way for matrix completion Accurate Adaptive Loops for Finite Deformation for extremely high dimensional data. In this talk, we dis- Plasticity in Albany cuss a robust matrix completion and subspace tracking al- gorithm that uses factorized matrix decomposition with The Parallel Albany Adaptive Loop with Scorec software a pre-specified rank to detect and track a low rank sub- (PAALS) provides an automated framework for adap- space from incomplete measurements and in the presence tive finite element simulations on massively parallel ma- of sparse noise. We demonstrate the performance of our chines. Within the context of finite deformation plasticity algorithm for video background subtraction. in PAALS, remapping the material state during adapta- tion, maintaining high quality element shapes, and updat- Hassan Mansour ing the reference configuration are necessary to produce ac- Mitsubishi Electric Research Laboratories curate solution results. Methods to handle these situations [email protected] will be discussed and results will be shown that emphasize the interaction of these components.

MS224 Brian Granzow Low-rank Approximation of Matrices and Tensors Rensselaer Polytechnic Institute for Dynamical and Optimization Problems [email protected]

In this talk we will consider several topics that are con- Glen Hansen nected through the ideas of low-rank approximation. First, Sandia National Laboratories we propose a new method for the approximate solution of [email protected] the Lyapunov equation. Second, we will discuss how the low-rank methods help to solve reaction-diffusion equations Dan A. Ibanez with time-dependent potential. Third, we will describe the Rensselaer Polytechnic Institute ideas of efficient multidimensional sampling via cross ap- SCOREC proximation methods apply them to the problems of global [email protected] optimization. Mark S. Shephard Ivan Oseledets Rensselaer Polytechnic Institute Institute of Numerical Mathematics Scientific Computation Research Center Russian Academy of Sciences, Moscow [email protected] [email protected]

Denis Kolesnikov, Mikhail Litsarev MS225 Skolkovo Institute of Science and Technology Massively Parallel Flow Simulation using PETSc [email protected], [email protected] Implicit computational fluid dynamics solvers have recently been shown to scale to the full machine at several of the largest computer facilities using linear equation solvers that MS224 were coded to match the data structures of the equation Preconditioned Riemannian Optimization for Low- discretization. In this work, we describe efforts to apply Rank Tensor Equations PETSCs broad class of preconditioners to flow simulations at large core count to understand the tradeoff between im- The solution of very large linear systems is a challenging proved preconditioners and the cost of the required addi- task often encountered as a core ingredient when solving tional data structure translation. partial differential equations on high-dimensional domains. In these cases, the degrees of freedom in the linear system Michel Rasquin, Benjamin Matthews CS15 Abstracts 181

University of Colorado Boulder Mauro Perego [email protected], CSRI Sandia National Laboratories [email protected] [email protected]

Cameron Smith Ray S. Tuminaro Scientific Computation Research Center Sandia National Laboratories Rensselaer Polytechnic Institute Computational Mathematics and Algorithms [email protected] [email protected]

Kenneth Jansen University of Colorado at Boulder MS226 [email protected] Fast Algorithms for Shape Analysis of Planar Ob- jects

MS225 Effective computational tools for shape analysis are needed in many areas of science and engineering. We address this Variational Multiscale Analysis of Stochastic Par- problem and propose a fast iterative algorithm to com- tial Differential Equations in Albany pute the elastic geodesic distance between boundaries of We present the variational multiscale (VMS) method for planar objects. This algorithm is the most important com- stochastic PDEs to compute an accurate solution in a ponent for data mining of shapes, and a fast algorithm is coarse physical and stochastic space while accounting for essential for large-scale shape analyses.The key to our algo- the missing scales through a model term. The model term rithm is the decoupling of the optimization for the starting is based on an algebraic approximation of the fine-scale point and rotation and the optimization for the reparame- stochastic Green’s function and is rational in the random terization function in the distance formulation. Moreover, variables. We consider computationally efficient approxi- we develop a fast dynamic programming algorithm and a mations of this term and demonstrate their efficacy using nonlinear constrained optimization algorithm that work in the Albany code. tandem to compute optimal reparameterizations fast.

Onkar Sahni Gunay Dogan Rensselaer Polytechnic Institute Theiss Research, NIST [email protected] [email protected]

Jason Li, Jayanth Jagalur-Mohan MS226 Department of Mechanical, Aerospace and Nuclear Deflation-based Domain Decomposition Methods Engineering RPI Domain decomposition methods are widely used in ap- [email protected], [email protected] plied mathematics and regarded as highly scalable algo- rithms that can be seen as specific cases of multigrid meth- Assad Oberai ods. Projection operators are one of the essential tools for Department of Mechanical, Aerospace and Nuclear achieving scalability: they are used for building deflation Engineering preconditioners. A C++ framework will be presented ac- Rensselaer Polytechnic Institute companied by theoretical results to show how effective it [email protected] can be to solve problems arising from Darcy’s law, elastic- ity, or Helmholtz equation.

MS225 Pierre Jolivet Albany: A Trilinos-based code for Ice Sheet Simu- Laboratoire Jacques-Louis Lions lations and other Applications [email protected]

Albany is a finite element application code that incorpo- Frederic Nataf rates capabilities through interoperable software compo- Laboratoire J.L. Lions nents. By leveraging independently developed mathemat- [email protected] ical libraries, Albany-based applications have ready access to advanced technologies, spanning: discretizations, auto- Christophe Prud’homme matic differentiation, linear and nonlinear solvers, adjoint- University of Strasbourg based optimization and UQ, performance-portable kernels, France mesh adaptivity, and dynamic load balancing. This strat- [email protected] egy enables rapid development of sophisticated new codes, including the Albany/FELIX Ice Sheet application. Al- bany incorporates libraries from Trilinos, Dakota, and MS226 PUMI, some with FASTMath support. Multiscale Methods for Networks

Andrew Salinger Networks are a widely used type of abstraction for com- CSRI plex data. Optimization of different quantitative objectives Sandia National Labs on networks often plays a crucial role in network science, [email protected] not only when a practical solution is needed, but also for a general understanding of structural and statistical fea- Glen Hansen, Irina K. Tezaur tures of networks. We present multiscale approaches for Sandia National Laboratories two problems: optimal response to epidemics, and network [email protected], [email protected] generation. Both approaches are inspired by AMG scheme 182 CS15 Abstracts

reinforced by the algebraic distance connectivity strength. Gary Marple Department of Mathematics University of Michigan Ilya Safro [email protected] School of Computing Clemson University Leslie Greengard [email protected] Courant Institute New York University [email protected] MS226 The Auxiliary Space Solvers and Its Applications MS227 We talk about the mathematically optimal multigrid solvers for general unstructured grids which are robust Adaptive Boundary Element Methods and easy to use in practice based on the methodology of Fast Auxiliary Space Preconditioning. a new parallel One particular strength of the boundary element method is unsmoothed aggregation algebraic multigrid (UA-AMG) that it allows for a high-order pointwise approximation of method has also been developed based the idea of FASP. the solution of the related partial differential equation via It provides (nearly) optimal load balance and predictable the representation formula. We propose an adaptive mesh- communication patterns factors that make our new algo- refining algorithm and discuss recent results on its quasi- rithm suitable for parallel computing. optimal convergence behavior with respect to the point er- ror in the representation formula. Numerical examples for Lu Wang the weakly-singular integral equations for the Laplacian Penn State University underline our theoretical findings. wang [email protected] Michael Feischl, Thomas F¨uhrer, Gregor Ganter, MS227 Alexander Haberl, Dirk Praetorius Vienna University of Technology Robust Algorithms for Periodic Problems and [email protected], Evaluation of Layer Potentials [email protected], [email protected], I overview methods developed recently by our group for [email protected], solving time-harmonic acoustics and Maxwell scattering 3 [email protected] from media with 10 layers, doubly-periodic obstacles in 3D (with efficiency for axisymmetric obstacles), and Stokes flow in periodic pipes and doubly-periodic porous media. In each case we use only the free-space Greens function, MS227 an auxiliary field, and a small linear system, to circumvent Fast Algorithms for the Evaluation of Layer Poten- the traditional but problematic periodic Greens function. tials using ‘Quadrature by Expansion’ We also develop quadrature components such as 3D QBX and close evaluation for Stokes. Quadrature by Expansion, or ‘QBX’, is a systematic, high- Alex H. Barnett order approach to singular quadrature that applies to layer Department of Mathematics potential integrals with general kernels on curves and sur- Dartmouth College faces. Being based on a scheme for close evaluation due to [email protected] Barnett, the scheme provides a unified evaluation capabil- ity for layer potentials. This talk discusses algorithmic op- tions for using QBX within a variant of the Fast Multipole Shravan Veerapaneni Method. A method is presented that preserves accuracy, Department of Mathematics generality and close evaluation capability while only re- University of Michigan quiring a relatively modest increase in computational cost [email protected] in comparison to a point-to-point FMM. In addition, an optionally GPU-accelerated set of open-source software li- Adrianna Gillman braries is discussed that implements the proposed method. Dartmouth College Department of Mathematics [email protected] Andreas Kloeckner Department of Computer Science Min Hyung Cho University of Illinois at Urbana-Champaign Department of Mathematics [email protected] Dartmouth College [email protected] MS227 Lin Zhao, Yuxiang Liu Dartmouth College Title Not Available at Time of Publication [email protected], [email protected] Abstract not available at time of publication.

Bowei Wu Denis Zorin University of Michigan Computer Science Department [email protected] Courant Institute, New York University CS15 Abstracts 183

[email protected] Mathematics and Computer Science Division [email protected]

MS228 Compact-Reconstruction WENO on Non-uniform MS229 Meshes Parallel Preconditioning for Time-Dependent PDE-Constrained Optimization Compact-Reconstruction WENO (CRWENO) schemes use solution-dependent combinations of compact schemes to All-at-once schemes aim to solve all time-steps of time- produce a higher-order scheme that is non-oscillatory and dependent PDE-constrained optimization problems in one has the superior spectral resolution of compact schemes. coupled computation, leading to exceedingly large linear Previous work on these schemes has used uniform grids systems requiring efficient iterative methods. We present exclusively. In this talk we present a generalization of the a new block diagonal preconditioner which is both opti- fifth-order CRWENO scheme to non-uniform meshes in one mal with respect to the mesh parameter and parallelizable space dimension, with some results concerning the effects over time, thus can provide significant speed-up. We will of unequal spacing on the scheme’s accuracy and spectral present numerical results to demonstrate the effectiveness resolution. of this preconditioner.

Kilian Cooley Eleanor McDonald University of Maryland University of Oxford [email protected] [email protected]

James Baeder Andy Wathen Department of Aerospace Engineering Oxford University, UK University of Maryland [email protected] [email protected] MS229 MS228 Preconditioning of Active-Set Newton Methods for Superconvergence Properties of Discontinuous PDE-Constrained Optimal Control Problems Galerkin Methods Based on Upwind-Biased Fluxes for Linear Hyperbolic Equations We address the problem of preconditioning saddle point lin- ear systems arising in the solution of PDE-constrained opti- Superconvergence properties of discontinuous Galerkin mal control problems via active-set Newton methods, with (DG) methods using purely upwind fluxes under the as- control and (regularized) state constraints. We present two sumptions of periodic boundary conditions and a uniform preconditioners based on a full block matrix factorization mesh for solving linear hyperbolic equations with smooth of the Schur complement of the Jacobians matrices where solutions have been studied through various approaches: the active-set blocks are merged into the constraint blocks. pointwise a posteriori spacial discretization error estimates; The robustness of the new preconditioners is discussed and spectral analyses based on the Fourier approach; and the exhaustive numerical experiments are presented. smoothness increasing accuracy conserving (SIAC) filtered solution. We analyze via these approaches DG methods Margherita Porcelli using upwind-biased fluxes, illustrating the discussion with Dipartimento di Matematica numerical experiments. Universit`a di Bologna [email protected] Daniel Frean University of East Anglia Valeria Simoncini, Mattia Tani [email protected] Universita’ di Bologna [email protected], [email protected] MS228 A Compact-Reconstruction WENO Scheme with MS229 Semi-Implicit Time Integration HPC Methods for Structured Inverse Modeling in Diffusive Processes Weighted, nonlinear compact finite difference schemes are well suited for flows with a large range of length scales such In this talk we present a method which combines high per- as atmospheric flows. Semi-implicit time integration meth- formance computing and large scale applications with an ods allow for efficient solutions by treating the stiff compo- optimized, inverse shape identification procedure. We in- nents of the hyperbolic flux implicitly. We propose a high- troduce a limited memory BFGS approach for optimizing order finite-difference algorithm for atmospheric simula- the shape of the distribution of a jumping permeability in tions based on the CRWENO scheme and implicit-explicit diffusive flow processes. These techniques are utilized to time stepping. The performance and scalability of the al- fit a model of the human skin to data measurements and gorithm are evaluated for benchmark flow problems. not only estimate the permeability coefficients but also the shape of the cells. Debojyoti Ghosh Mathematics and Computer Science Division Martin Siebenborn Argonne National Laboratory University of Trier [email protected] [email protected]

Emil M. Constantinescu Volker H. Schulz Argonne National Laboratory University of Trier 184 CS15 Abstracts

Department of Mathematics hesive Sediment Transport Modeling in South San [email protected] Francisco Bay

Abstract not available at time of publication. MS229 Nonstandard Sobolev Spaces for Preconditioning Oliver Fringer Mixed Methods Environmental Fluid Mechanics Laboratory Stanford University In mixed methods for elliptic boundary value problems [email protected] auxiliary variables are used to reformulate the involved differential equation as a system of differential equations MS230 of lower order. These methods can often be written as PDE-constrained optimization problems, whose analysis Discontinuous Galerkin Methods for Spectral motivates the introduction of nonstandard Sobolev spaces Wave/Circulation Modeling for the auxiliary variables and leads to efficient solution techniques. The approach is exemplified for the Hellan- On large geographic scales, waves are represented in a spec- Herrmann-Johnson method applied to biharmonic bound- tral sense via the action balance equation. We present a ary value problems. computational spectral wave model developed using dis- continuous Galerkin (DG) methods. DG methods allow Walter Zulehner for the use of unstructured meshes and adaptive, higher- University of Linz, Austria order approximations, which we show leads to increased [email protected] accuracy and efficiency. We loosely couple the new DG spectral wave model to the DG-Shallow Water Equation Model (DG-SWEM), an existing circulation model. Wolfgang Krendl Johannes Kepler University Linz, Austria Jessica Meixner [email protected] University of Notre Dame [email protected] MS230 Strengthening the Hurricane Wave and Surge Fore- MS230 cast Guidance provided to Coastal Communities in Computational Modeling of Storm Surge in Galve- North Carolina ston Bay

North Carolina is sensitive to hurricane waves, storm surge Abstract not available at time of publication. and flooding. A computational modeling system is uti- lized operationally to provide daily forecast guidance for Jennifer Proft coastal waves and inundation (http://nc-cera.renci.org/). University of Texas at Austin This guidance has been expanded beyond Web-based de- [email protected] livery to include additional formats that are targeted to the needs of users within the state, are representative of the guidance at high levels of resolution, and are portable MS231 to widely-used geographic information systems. Simulating Coupled Pressure-Temperature Equa- tions for Trace Gas Sensors Using FEniCS and Rosemary Cyriac PETSc North Carolina State University Dept. of Civil, Construction and Environmental Trace gas sensors are currently used in many applications Engineering from leak detection to national security and may some day [email protected] help with disease diagnosis. These sensors are modelled by a coupled system of complex elliptic partial differen- J. Casey Dietrich tial equations for pressure and temperature. Solutions are University of Texas at Austin approximated using the finite element method which re- [email protected] quires the development of custom block preconditioners. Finite element solutions are approximated using FEniCS Jason Fleming and PETSc4py. Seahorse Coastal Consulting Morehead City, NC Brian W. Brennan jason.fl[email protected] Baylor University b [email protected] Brian Blanton University of North Carolina at Chapel Hill MS231 Renaissance Computing Institute Mesh-Independent Convergence for PDE- [email protected] Constrained Optimisation Solvers in Dolfin- Adjoint Rick Luettich University of North Carolina - Moorehead City A key feature of dolfin-adjoint is its high-level framework rick [email protected] for solving PDE-constrained optimisation problems using the finite element environment FEniCS. In this talk we dis- cuss the mesh-independent convergence of the optimisation MS230 framework. This is achieved by formulating standard opti- Three-Dimensional Coupled Wind-Wave and Co- misation algorithms in a Hilbert space setting. We discuss CS15 Abstracts 185

the implementation, show its effectiveness and compare it encouraging results. AgentSheets and AgentCubes are vi- to preconditioning approaches. Thanks to the high-level sual programming agent-based modeling applications that problem formulation in FEniCS the resulting framework are ideally suited to this projects goals. requires minimal user input, is fully parallel and scales to large problems. Fred Gluck AgentSheets, Inc. Simon W. Funke, Magne Nordaas [email protected] Center for Biomedical Computing Simula Research Laboratory [email protected], [email protected] MS232 Applying Run-Modify-Build Templates for Agent- MS231 Based Models Spectral/HP Element Modelling in Nektar++ Students can grow in competence and confidence in mod- eling and simulation through well-scaffolded templates of In this talk we will highlight the high-level aspects of working models. Instead of typing code or building struc- the Nektar++ high order finite element framework, which tures, students can learn any given syntax in the context enables rapid development of high-performance parallel of real models, focusing on learning the science and im- solvers. Using a straightforward linear PDE as an illus- proving the model. This is especially true for agent models trative example, we will demonstrate how the library can that require more detailed descriptions of behavior. Exam- be utilised at a variety of levels to fit the requirements ples of complex model templates across the computational of the end-user, and how simulation parameters such as sciences and for different tools will be shown. the time-stepping scheme can be changed without detailed technical knowledge of the underlying methods. Robert M. Panoff President and Executive Director David Moxey, Chris Cantwell, Spencer Sherwin Shodor Imperial College London rpanoff@shodor.org [email protected], [email protected], [email protected] MS232 Mike Kirby University of Utah Teaching Freshman Science Using Agent-Based School of Computing Computational Laboratories [email protected] With improved computational abilities and explosion of amounts of data, scientists routinely implement computa- MS231 tion to test hypotheses and guide their research. We have developed a course that employs computational approaches Supporting Modern HPC Hardware in the DUNE to investigate scientific questions. Students explore science Framework concepts, and using computational tools and algorithmic Upcoming exa-scale computers will exhibit multiple lev- thinking, implement the scientific method to understand els of concurrency. Specialized implementations, exploit- the natural world. Satisfying a science requirement, the ing all levels of parallelism, can gain a significant part of course is designed so faculty from any science or computer the peak performance. For high flexibility the C++ frame- science department can teach it. work DUNE [Bastian et.al., 2008] defines generic interface, which allow various different implementations. The EXA- George W. Shiflet DUNE project follows this approach to enable all levels of Wofford College concurrency for general DUNE applications. We present shifletgw@wofford.edu recent results and discuss implications on the interface de- sign. Angela B. Shiflet McCalla Professor of Math. & CS, Dir. of Computational Christian Engwer, Fahlke Jorrit Sci. INAM, University of M¨unster Wofford College [email protected], shifletab@wofford.edu [email protected]

Steffen M¨uthing MS232 Heidelberg University NetLogo in the Secondary Life Science Classroom steff[email protected] In response to the adoption of new middle school science textbooks which incorporated NetLogo models as well as MS232 other visualization software, NetLogo models were modi- Transitioning from Game Design to Simulation Us- fied or created for use in middle school life science and en- ing Agent-Based Modeling vironmental lessons as well as in high school biology class- rooms. Large group professional development, individual TheobjectiveoftheScalableGameDesignprojectisto instructional coaching and classroom co-teaching were used create a pipeline of people to work in computer-related to help teachers and students interact with the simulations fields by introducing them to game design. Hopefully, they successfully. will then transfer their interests and skills from game de- sign to science simulation. Over the past five years several Charlotte M. Trout thousand students have participated in the project, with WCPS-Retired 186 CS15 Abstracts

[email protected] cell motion in flow. This work is in collaboration with W. Hao, C. Liu and G. Lin.

MS233 Zhiliang Xu Microstructure for Free Surface Flows University of Notre Dame [email protected] Numerical simulations of turbulent mixing in the Large Eddy Simulation regime are nonunique, with the selection of solution microstructure regulated by subgrid turbulence MS233 models. Validation, ie comparison to experiments, is then Dissipation and Dispersion Errors of Discontinuous essential. We give examples of successfully validated Front Galerkin Method and Its Application to Level Set Trecking simulations with extrapolation to flows outside Equations of the experimental range. Appllcation to the selection of atomic vs. chunk mix for an inertial confinement fusion The discontinuous Galerkin (DG) method is known to pro- context will be given. vide high resolution properties, especially when applying after long time run. In this talk, we consider analysing the James G. Glimm error behaviour of the DG method for linear hyperbolic Stony Brook University equations. Through Fourier analysis we observe, with P2 Brookhaven National Laboratory quadratic polynomial approximations, the dissipation er- [email protected] or [email protected] ror is on the order of 5 and the dispersion error is on the order of 6. The part of the error that grows linearly in time is on the order of 6. When solving interface problems in MS233 a complex incompressible flow, the DG method is shown Volume-Preserving Adaptive Moment-of-Fluid to dramatically improve the mass conservation property Method for Interface Tracking of the level set method. Numerical examples demonstrate the high order accuracy of the scheme and the high resolu- We have developed a method to preserve the volume of a tion property especially when the interface undergoes large cell when the vertices of the cell move freely in a divergence- topological changes. free velocity field. An optimization procedure is proposed to minimize the total variation of the node positions of Jue Yan the vertices after they are advanced according to the ve- Dept. of Math. locity field. A matrix-free Newton Krylov method is used Iowa State University to solve the nonlinear system generated by the optimiza- [email protected] tion. The method has been applied to the multi-material moment-of-mluid interface tracking method with adaptive mesh refinement. Examples are provided to demonstrate MS234 the effectiveness of our numerical algorithm. Massively Parallel GW Calculations for Current and Next-generation HPC Shengtai Li Los Alamos National Laboratory The traditional GW-Bethe-Salpeter (BSE) approach has, [email protected] in practice, been prohibitively expensive on systems with large numbers of atoms. We show that through a com- Hyung T. Ahn bination of methodological and algorithmic improvements, University of Ulsan the standard GW-BSE approach can be applied to sys- [email protected] tems with thousands of atoms. We will discuss the mas- sively parallel GW-BSE implementation in the Berke- Mikhail Shashkov leyGW package (on-top of common DFT packages) includ- Los Alamos National Laboratory ing the importance of hybrid MPI-OpenMP parallelism, [email protected] parallel IO and library performance. We will discuss opti- mization strategies for and performance on many-core ar- chitectures. MS233 A Fictitious Domain Method with a Hybrid Cell Jack Deslippe Model for Simulating Motion of Cells in Fluid Flow National Energy Research Scientific Computing Center [email protected] In this work, we develop a hybrid model to represent membranes of biological cells and use the distributed- Lagrange multiplier/fictitious-domain (DLM/FD) formu- MS234 lation for simulating the fluid/cell interactions. The hybrid Recent Progress on Quantum Mechanics Embed- model representing the cellular structure consists of a con- ding Theory tinuum representation of the lipid bilayer, from which the bending force is calculated through energetic variational Abstract not available at time of publication. approach, a discrete cytoskeleton model utilizing the worm- like chain to represent network filament, and area/volume Chen Huang constraints. For our computational scheme, a formally Theoretical Division, T-1 second-order accurate fractional step scheme is employed Los Alamos National Laboratory to decouple the entire system into three sub-systems: a [email protected] fluid problem, a solid problem and a Lagrange multiplier problem. Numerical results compare favorably with pre- viously reported numerical and experimental results, and MS234 show that our method is suited to the simulation of the Towards Predictive Modeling of Correlation Effects CS15 Abstracts 187

in Many-electron Systems [email protected]

In this presentation we will discuss the development of scal- MS235 able and unique computational capabilities for modeling quasi-degenerate systems using implementations of multi- UsingPerformanceToolstoAssistPortingtoNew reference coupled-cluster (MRCC) methods in NWChem. Platforms We will discuss novel parallel algorithms for several MRCC methodologies, which are capable of taking advantage of Performance tool play a critical role in porting applications existing peta-scale architectures. In this context, the emer- to new platforms. They not only enable identifying hot gence of the heterogeneous computer architectures offers a spots; the first targets for acceleration, but can also show unique chance to advance accurate yet expensive MRCC the context of these hot spots. Tracing and profiling formalisms. We will also outline the recent development of tools can be used in combination to provide different coupled-cluster Green function formalism geared towards resolution of detail and amounts of runtime perturba- efficient inclusion of higher-order correlation effects. tion. Tools like Score-P can capture all parallel activity (MPI/OpenMP/pthreads/CUDA/OpenCL/OpenACC) and display it to the user using analysis engines like Karol Kowalski Vampir. Pacific Northwest National Laboratory [email protected] Guido Juckeland TU-Dresden [email protected] MS234 A Parallel Orbital-Updating Approach for Elec- MS235 tronic Structure Calculations Based on Singularity Algorithmic Selection, Autotuning, and Scheduling Decompositions for Accelerator-Based Codes for Numerical Linear Algebra In this presentation, we will introduce an orbital-based parallelization algorithm for electronic structure calcula- Often, a rewrite of the scientific software is unsustainable tions and demonstrate the efficiency of our algorithm by in the long run as the complexity increases to respond to numerical experiments. This algorithm is based on our the more parallel and heterogeneous hardware. In this talk, understanding of the single-particle approximation equa- I will give practical perspective on how algorithmic selec- tions of independent particles that move in an effective tion, software autotuning at installation time, and various potential and a singularity decomposition of the effective forms of dynamic runtime scheduling for multicore systems potential. With this algorithm, the solution to the single- with accelerators can alleviate the aforementioned prob- particle equation can be reduced to some solutions of sev- lems in the context of widely used numerical linear algebra eral independent linear algebraic systems and a small scale libraries. algebraic eigenvalue problem. This presentation is based Piotr Luszczek on some joint works with Xiaoying Dai, Xingao Gong, and Department of Electrical Engineering and Computer Xin Zhang. Science University of Tennessee, Knoxville Aihui Zhou [email protected] Chinese Academy of Sciences [email protected] MS235 Toward Heterogeneous Memory Systems for HPC MS235 Compute nodes equipped with a variety of memory tech- Algorithmic Adaptations for Scalable Community nologies such as scratchpad memory, on-chip 3D-stacked Detection on the Tilera Many-Core Architecture memory, or NVRAM-based memory, apart from traditional DRAM, are already a reality. Careful use of the different As power constraints and data movement costs become sig- memory subsystems is mandatory in order to exploit the nificant barriers for high-end computing, the Tilera many- potential of such supercomputers. I will present our view core architecture offers a low-power platform exhibiting on upcoming heterogeneous memory systems, which com- key characteristics of future systems: a large number of prises exposing the different memory subsystems as first- simple cores, a sophisticated network-on-chip, and fine- class citizens to efficiently exploit their capabilities. grained control over memory locality. We implemented a graph community detection application using platform- Antonio J. Pe˜na aware memory layouts and scheduling techniques resulting Argonne National Lab in speedups of up to 46x on the TileGX36 and comparable [email protected] result quality and performance to x86 platforms. MS236 Daniel Chavarria, Howard Lu, Mahantesh Halappanavar Reduced Order Models for Patient-Specific Pacific Northwest National Laboratory Haemodynamics of Coronary Artery Bypass [email protected], [email protected], Grafts [email protected] In this talk we present a POD-Galerkin reduced order Ananth Kalyanaraman model to simulate the haemodynamics of coronary artery Associate Professor bypass grafts. Clinically relevant physical (inlet flow rates) School of EECS, Washington State University and geometrical (stenoses severity, anastomoses geometry) 188 CS15 Abstracts

quantities are considered in a parametrized setting for un- by the example of our current work on the reduction of steady incompressible Navier-Stokes equations. The pro- microscale lithium-ion battery models. [1] B. Haasdonk, posed ROM is applied to some patient-specific cases. A M. Ohlberger, Reduced basis method for finite volume ap- presentation of a comparison, with respect to such param- proximations of parametrized linear evolution equations, eters, and a clinical discussion of the resulting flow patterns M2AN Math. Model. Numer. Anal., 42 (2008), 277–302. follows. [2] R. Milk, S. Rave, F. Schindler, pyMOR - Model Order Reduction with Python, http://pymor.org. Francesco Ballarin Politecnico di Milano, Italy Rene Milk [email protected] University of Muenster [email protected] Elena Faggiano Politecnico di Milano Mario Ohlberger Italy Universit¨at M¨unster [email protected] Institut f¨ur Numerische und Angewandte Mathematik [email protected] Sonia Ippolito Luigi Sacco Hospital Stephan Rave Milan, Italy University of Muenster [email protected] [email protected]

Andrea Manzoni Felix Schindler EPFL, MATHICSE-CMCS WWU Switzerland [email protected] andrea.manzoni@epfl.ch

Alfio Quarteroni MS236 Ecole Pol. Fed. de Lausanne Reduced Basis Methods for Option Pricing Alfio.Quarteroni@epfl.ch We present a reduced basis method for pricing European Gianluigi Rozza and American options based on the Black-Scholes and He- SISSA, International School for Advanced Studies ston model. To tackle each model numerically, we formu- Trieste, Italy late the problem in terms of a time dependent variational [email protected] equality or inequality and propose a method that combines POD-Greedy and Angle-Greedy procedures for the con- struction of the reduced spaces. In addition, we obtain a Roberto Scrofani posteriori error estimators. Numerical examples illustrate Luigi Sacco Hospital the efficiency of our approach. Milan, Italy [email protected] Julien Salomon CEREMADE, Universite Paris-Dauphine [email protected] MS236 pyMOR - A New Model Order Reduction Software Olena Burkovska Framework Technical University of Munich Over the past years, projection-based model order re- [email protected] duction (MOR) techniques, such as the reduced basis method (RB) ([1] and references therein), have become Bernard Haasdonk well-established tools for efficient numerical solution of University of Stuttgart partial differential equations. However despite the fact [email protected] that RB-methods are very generic in nature, most soft- ware solutions still provide only ad-hoc implementations Barbara Wohlmuth which are tailor-made for specific application problems and Technical University of Munich are tied to a given software ecosystem. In this talk we [email protected] present pyMOR [2], a new open source library for build- ing MOR-applications with the Python programming lan- guage. pyMOR’s main focus lies on the easy application of MS236 RB-methods to parameterized partial differential equations Adaptivity and Reduced Basis Methods solved by external high-dimensional discretization pack- ages. We give a brief overview of pyMOR’s main com- Usually, the computations in a Reduced Basis Method ponents and highlight the design philosophy and choices (RBM) are split into an offline and an online phase. In the that allow us to arrive at a set of completely generic re- offline phase, expensive computations are used to construct duction algorithms which can be readily incorporated with a Reduced Basis in terms of snapshots of a detailed model. any external solver connected to pyMOR via its lightweight This has a number of consequences that are also possible operator and vector interfaces. As a result of this abstrac- criticisms on the RBM itself: (1) The snapshots need to tion, well-proven MOR-algorithms can be easily applied based upon the same discretization (at least for parts of to new real-world problems. At the same time, different the parameter range); (2) If the problem itself is challeng- reduction algorithms can be compared for a given prob- ing, offline costs may be significant; (3) The separation lem without modification of the high-dimensional solver. into offline and online phase hides the overall complexity We conclude our presentation by illustrating these benefits of the problem. At an extreme, one could pre-compute CS15 Abstracts 189

‘everything’ offline and just pick the right data online. On may occur in non-embedded schemes. We demonstrate the other hand, several adaptive methods are known and that the lack of conservation in partitioned schemes can proven to be asymptotically optimal for a wide class of op- lead to non physical effects and propose conservative addi- erator equations. Asymptotically optimal means that the tive schemes based on partitioning the fluxes rather than rate of convergence is comparable to a best-possible bench- the ordinary differential equations. A variety of schemes mark and the computational cost is linear in the required are presented, including an embedded pair suitable for number of degrees of freedom. This is the motivation to the time evolution of fifth-order weighted non-oscillatory consider the combination of adaptive numerical methods (WENO) spatial discretizations. Numerical experiments and the RBM. We show some consequences of using adap- are provided. tive computations both for the snapshot generation as well as the evaluation of standard RB error estimates. The talk Steven Ruuth is based upon joint work with Kristina Steih (Ulm). Mathematics Simon Fraser University Karsten Urban [email protected] Institute of Numerical Mathematics, University of Ulm [email protected] David I. Ketcheson CEMSE Division MS237 King Abdullah University of Science & Technology An Accelerated Domain Decomposition Method [email protected] for Time Dependent Problems Colin B. Macdonald We consider the time integration of the system of ODEs Oxford University which results from the semi-discretization of PDEs. The [email protected] solution components are assumed to evolve on different time scales and hence some sort of multi-rate time integra- tion method which allows different time steps for different MS237 components may be suitable. Here we consider two algo- rithms for such problems: a multi-rate Schwarz Waveform A Massively Parallel Solver for the Incompressible relaxation hybrid algorithm and a multi-rate accelerated Navier–Stokes Equations Schwarz Waveform relaxation method. In 2011, Guermond and Minev proposed a massively par- Ronald Haynes allelizable directional splitting method for the time dis- Memorial University of Newfoundland cretization of the incompressible Navier–Stokes equations. St. John’s, NL, Canada It was shown to scale well in a distributed memory environ- [email protected] ment of up to 1024 CPUs. We modified this method to take advantage of the high computational throughput afforded MS237 by (multiple) GPUs as well as the efficiency of variable time steps. We demonstrate that the modified method exhibits Developing a Custom Time Integrator for the Non- substantial performance gains over the original. linear Schr¨odinger Equation for An Application in Paraxial Laser Propagation Raymond J. Spiteri I will report on the construction of a temporal inte- University of Saskatchewan, Canada gration scheme designed to be used with a higher-order Department of Computer Science finite-difference spatial approximation to the nonlinear [email protected] Schr¨odinger equation with perfectly matched layer bound- ary conditions. The temporal method is based on a semi- implicit spectral deferred corrections approach coupled MS238 with an alternating direction implicit (ADI) approximation to the (linear) implicit terms. The accuracy and efficiency Coherence Motivated Sampling of Polynomial of methods up to tenth-order in both time and space will be Chaos Expansions presented as well as some preliminary results on space-time parallelization of the method. We investigate solution recovery, particularly regarding methods for sampling basis functions associated with Her- Michael Minion mite and Legendre Polynomial Chaos Expansions. Recent Stanford University results have identified interesting quantities related to the [email protected] basis functions and their sampling which are computable, and analytically fruitful. Through these parameters we an- alyze asymptotically motivated samplings, and construct MS237 sampling methods with statistical optimality. We demon- Spatially Partitioned Embedded Runge-Kutta strate these methods on examples motivated from Uncer- Methods tainty Quantification. We study spatially partitioned embedded Runge-Kutta schemes for partial differential equations (PDEs), in which Jerrad Hampton each of the component schemes is applied over a different University of Colorado, Boulder part of the spatial domain. Such methods may be conve- [email protected] nient for problems in which the smoothness of the solution or the magnitudes of the PDE coefficients vary strongly in Alireza Doostan space. We focus on embedded partitioned methods as they Department of Aerospace Engineering Sciences offer greater efficiency and avoid the order reduction that University of Colorado, Boulder 190 CS15 Abstracts

[email protected] tems. The advantage of those methods is that they pro- vide not only statistics, but give a direct representation of the measure of the solution as a so-called surrogate model, MS238 which can be used for very fast sampling. Especially at- Sparse Solutions to Large-Scale Nonlinear Subsur- tractive for elliptic stochastic partial differential equations face Flow Inverse Problems is the stochastic Galerkin method, since it preserves essen- tial properties of the differential operator. One drawback We present sparse inversion formulations for nonlinear sub- of the method is, however, that it requires huge amounts of surface flow model calibration problems. By promoting memory, as the solution is represented in a tensor product sparsity, the inversion is transformed into a feature selec- space of spatial and stochastic basis functions. Different tion problem that is flexible and robust against prior uncer- approaches have been investigated to reduce the memory tainty. Specifically, in addition to effective low-rank repre- requirements, for example, model reduction techniques us- sentation, the formulation allows for discriminating against ing subspace iterations to reduce the approximation space alternative plausible prior geologic scenarios based on non- or methods of approximating the solution from successive linear multiphase flow data from scattered well locations. rank-1 updates. See more in my dissertation [1]. [1] Elmar Using several case studies, we demonstrate the advantages K. Zander, Tensor Approximation Methods for Stochastic of sparse nonlinear inversion for geoscience application. Problems, Dissertation, TU Braunschweig, 2013.

Benham Jafarpour Elmar Zander ViterbiSchoolofEngineering TU Braunschweig University of Southern California Inst. of Scientific Computing [email protected] [email protected]

Reza Khaninezhad Electrical Engineering MS239 University of Southern California Novel Priors and Algorithms for 4d Tracking and [email protected] Classification of Cells

In biomedical imaging efficient reconstruction and tracking MS238 methods play a fundamental role. Particularly in cell bi- An Efficient Method for the Computation of the ology and medical tomography innovative spatio-temporal Stochastic Galerkin Projections by Means of Ten- imaging models are of strongly growing interest. The aim sor Format Representations of this talk is to highlight novel priors and related convex optimization for reconstruction and flow quantification in The stationary diffusion problem with an uncertain per- 4D image sequences. Motivated by the success of L1 and meability coefficient is solvedin a low-rank tensor repre- higher-order (e.g. TGV) regularization for static imag- sentation without changes of the available deterministic ing we will focus on spatio-temporal priors for the optimal code. The presented uncertainty is modeled by a random transportation of cells. field, which is discretized by KLE as well as by PCE. It was shown in previous works [Espig et al 2012, 2013] un- Christoph Brune der which conditions the stochastic Galerkin operator can Department of Applied Mathematics be approximated/represented in a low-rank tensor format. University of Twente The obtained symmetrical and positive defined linear sys- [email protected] tem is solved by the new iterative method. The iteration matrix as well as the whole computations are done also in that low-rank tensor format. The choice of the tensor MS239 format is not crucial here. The computational cost and Parameter Estimation for Malignant Brain Tumors storage (independent on the tested tensor formats) are lin- ear in the stochastic dimension. Determining patient specific tumor parameters is impor- tant in choosing optimal treatment plans. We present an Alexander Litvinenko inverse problem formulation to approximate the parame- SRI-UQ Center, King Abdullah University of Science and ters of interest using PDE-constrained optimization algo- Techn rithms. The choice of the optimization method is impor- [email protected] tant as solving this problem has a high computational cost. We will present a reduced space formulation, novel precon- Mike Espig ditioners to speed up the solution process, and numerical Max Planck Institute for Mathematics in the Sciences experiments on a synthetic dataset for preliminary evalua- [email protected] tion of the method. Amir Gholaminejad Matthies HERMANN G. PhD Student, Institute for Computational Engineering Instiute of Scientific Computing and Sciences, University of Texas at Austin TU Braunschweig [email protected] [email protected] George Biros MS238 University of Texas at Austin Tensor Approximation Methods for Stochastic [email protected] Problems

Spectral stochastic methods have gained wide acceptance MS239 as a tool for efficient modelling of uncertain stochastic sys- Incorporating Uncertainty in MR Images of CS15 Abstracts 191

Glioblastoma when Leveraging Models to Interpret [email protected], [email protected] Therapeutic Efficacy

MS240 There is a lack of response metrics that can quickly and ac- curately predict the therapeutic efficacy for glioblastoma. QoI Basis Adaptation Recently, a mathematical model of glioma growth has been used to define a response metric based on patient-specific We demonstrate the efficiency and scope of the basis adap- parameters of proliferation and invasion calibrated from tation methodology developed for Gaussian polynomial pre-treatment imaging which was shown to be prognostic chaos. The approach is based on adapting the basis in for overall survival. This talk will focus on how data un- L2 by applying an isometry to its Gaussian base. We dis- certainty affects the calibrated parameters, the response cuss error estimates associated with this approach, and the metric, and the implications for clinical translation. the concept of an optimal isometry. We also present imple- mentation details and applications to large scale problems from across science and engineering. We also explore the Andrea Hawkins-Daarud importance of specific quantities of interest to the adapta- Department of Neurological Surgery tion process, and extend the approach to situations defined Northwestern University by multiple quantities of interest. [email protected] Roger Ghanem Kristin R. Swanson University of Southern California Northwestern University Aerospace and Mechanical Engineering and Civil [email protected] Engineering [email protected]

MS239 Kenny Chowdhary Sandia National Laboratories Platform-independent Description of Image Regis- [email protected] tration Algorithms Habib N. Najm In the last years real-time imaging and more complex mod- Sandia National Laboratories els for the various imaging applications like image registra- Livermore, CA, USA tion became feasible mostly because of the progress made [email protected] in parallel computer architectures like found in GPUs and modern multi-core CPUs. However, the implementation effort increases, if one wants to achieve good performance. MS240 A solution to this problem is to formulate the image regis- Numerical Methods for SPDEs with Levy Jump tration algorithms in an abstract way in a domain-specific Processes SPDES: Stochastic and Deterministic language (DSL) and then automatically generate efficient Approaches C++ or CUDA code. A multi-layered approach is sketched that allows users to describe applications in a natural way We present numerical results on SPDEs with multiple Levy from the mathematical model down to the program speci- jump processes of various depen- dence structures by gPC fication. (stochastic approach) and by joint PDF from the general- ized Fokker- Planck equations for spatial modes to decom- Harald Koestler pose the SPDEs into SODEs (deterministic ap- proach). University of Erlangen-Nuremberg As examples, we solve SPDEs with TaS jump processes, [email protected] with tempered fractional PDEs as joint density functions. We will demonstrate that we largely improve the accuracy and efficiency of the traditional MC method!

MS240 Mengdi Zheng Computational Complexity of Stochastic Galerkin applied math, brown university and Collocation Methods for PDEs with Random mengdi [email protected] Coefficients George E. Karniadakis We will present a rigorous cost metric, used to compare Brown University the computational complexity of a general class of stochas- Division of Applied Mathematics tic Galerkin methods and stochastic collocation methods, george [email protected] when solving high-dimensional stochastic PDEs. Our ap- proach allows us to calculate the cost of preconditioning MS240 both the Galerkin and collocation systems, as well as ac- count for the sparsity of the Galerkin projection. The- Optimal Least-Squares Projection: Applications to oretical complexity estimates will also be presented and Uq validated with use of several computational examples. In this talk, we discuss the problem of approximating a multivariate function by discrete least-squares projection Nick Dexter onto a general polynomial space, using a random chosen University of Tennessee sub-grid of the tensor grid of Gaussian points. The inde- [email protected] pendent variables of the function are assumed to be random variables, and thus, the framework provides a non-intrusive Clayton G. Webster, Guannan Zhang way to construct the generalized polynomial chaos expan- Oak Ridge National Laboratory sions, stemming from the motivating application of Un- 192 CS15 Abstracts

certainty Quantification (UQ). We prove the stability and [email protected] an optimal convergence estimate, provided the number of points scales linearly (up to a logarithmic factor) with the dimension of the polynomial space. The framework in- MS241 cludes both the bounded measures such as the uniform Parallel Randomized Structured Multifrontal and the Chebyshev measure, and the unbounded measures Method for Sparse Direct Solutions which include the Gaussian measure. Several numerical examples are given to confirm the theoretical results. We present a fast parallel direct solver for general sparse matrices based on a fully structured randomized multi- Tao Zhou frontal method. Distributed memory is used. A sequence Institute of Computational Mathematics, AMSS of innovative parallel strategies are designed for random- Chinese Academy of Sciences ized compression, hierarchical structures, and structured [email protected] multifrontal solution. Multilevel parallelism is built upon two hierarchical tree layers. This gives a significant new Akil Narayan direction for designing fast scalable sparse direct solvers. University of Massachusetts Dartmouth Zixing Xin, Jianlin Xia [email protected] Department of Mathematics Purdue University Dongbin Xiu [email protected], [email protected] University of Utah [email protected] MS242 Fluctuating Hydrodynamics Methods for Elec- MS241 trokinetics and Capillary Electrophoresis of N-Body Algorithms for Matrices with Decay: Mul- Charged Colloids tiplication, Projection, Inverse Factorization & Fock-Exchange Motivated by problems in the design and operation of re- cent microfluidic and nanofluidic devices, we present fluctu- We report on several fast algorithms for operations on ating hydrodynamic methods for confined electrokinetics. dense matrices with decay. Based on the SpAMM algo- We investigate the capillary electrophoresis of charged col- rithm [arXiv:1203.1692 and 1403.7458] for matrix-matrix loids. We show that the colloid counter-ion layers exhibit multiplication, we develop methods for spectral projection deviations from Poisson-Boltzmann theory and interesting and inverse factorization with reduced, O(N) complexity phenomena arising from discrete ion effects, hydrodynamic as well as error control in accordance with estimates. We interactions, and overlap with ion layers near the channel further demonstrate the generalization of these methods walls. to the higher dimensional problem of Fock-exchange, in- volving multi-level multipole approximation with nested Paul J. Atzberger SpAMM contraction. University of California-Santa Barbara [email protected] Matt Challacombe Los Alamos National Laboratory Theoretical Division MS242 [email protected] Mesoscale Models for Molecular Solvation: Funny Business at the Solute-Solvent Interface Nicolas Bock Electrostatic interactions between biomolecules (proteins) Los Alamos National Laboratory and the surrounding aqueous environment are crucial for [email protected] correct function. Continuum electrostatic models are sig- nificantly faster than atomistic molecular-dynamics sim- Terry Haut ulations, but trade off realism: e.g., at protein surfaces, University of Colorado, Boulder solvent is not a bulk material. Although multiscale mod- [email protected] els resembling gradient-elasticity theories improve accuracy somewhat, non-standard boundary conditions capture rele- vant interfacial-solvent effects much better. These findings MS241 motivate the development of rigorous methods for obtain- Linear-Cost Storage and Computation with Kernel ing boundary conditions between multiscale materials. Matrices Jaydeep Bardhan Kernel matrices embrace a rich structure that enables more Northeastern University efficient storage and computation than does a usual dense [email protected] matrix. The FMM and tree code methods are prominent examples exploiting such a structure: far-field low-rank Matthew G. Knepley interaction. In this talk, we lay the fundamental O(n) University of Chicago data structure in the context of linear algebra and present [email protected] O(n) algorithms for performing matrix operations, includ- ing matrix-vector multiplication, matrix inversion, and de- terminant calculation. We demonstrate numerical stability, MS242 linear scaling, and applications in statistical data analysis. Mesoscopic Modeling of Temperature-dependent Properties in Non-isothermal Fluid Systems Jie Chen Argonne National Laboratory We develop an energy conserved dissipative particle CS15 Abstracts 193

dynamics model to capture the correct temperature- [email protected] dependent properties of fluids. We demonstrate that the proposed model can predict correctly the temperature de- pendence of the diffusivity, viscosity and thermal conduc- MS243 tivity of liquid water, which is consistent with available ex- Multi-Scale Data Assimilation for Fine-Resolution perimental data of water at various temperatures. Subse- Models quently, this mesoscopic model is applied to investigations of the nonisothermal hydrodynamic flows and the phase The commonly used data assimilation algorithms are based transition of thermoresponsive polymers. on optimal estimation theory, in which error covariance is of fundamental importance. It is shown that the stan- Zhen Li dard optimal estimation algorithm is inherently ineffective Brown University when it is applied to fine resolution models, and the inef- Brown University fectiveness arises from its filtering nature. We propose a Zhen [email protected] multi-scale data assimilation algorithm, in which the cost function is decomposed for a set of distinct spatial scales. Yu-Hang Tang, Bruce Caswell Data assimilation is implemented sequentially from large Brown University to fine scales. Results are presented to demonstrate the yuhang [email protected], bruce [email protected] algorithm.

George E. Karniadakis Zhijin Li Division of Applied Mathematics Jet Propulsion Laboratory Brown University California Institute of Technology george [email protected] [email protected]

MS243 MS243 Ensemble Kalman Filters Without Tuning for Unified Ensemble-Variational Data Assimilation Large Applications System

Ensemble Kalman filters are widely used for large geophys- In this presentation we present a development of a unified ical data assimilation problems but generally require signif- ensemble-variational data assimilation system that com- icant tuning of inflation and localization to produce good bines best properties of ensemble and variational DA meth- results in the presence of sampling error from small ensem- ods, as well as filter and smoother methodologies. The bles. Methods to reduce the tuning required by estimating main idea is to create a practical, yet theoretically ad- and correcting for errors in ensemble sample covariances vanced system for general data assimilation applications. are presented. The feasibility of treating ensemble filters The new system has a complete feedback in terms of un- as a black box for general applications is discussed. certainties and optimal states. Recent progress and results will be presented. Jeffrey Anderson National Center for Atmospheric Research Milija Zupanski Institute for Math Applied to Geophysics Cooperative Institute for Research in the Atmosphere [email protected] Colorado State University [email protected]

MS243 Orthogonal Transformations for the Ensemble MS244 Kalman Filter An Adaptive Augmented Lagrangian Method for Large-Scale Constrained Optimization Data assimilation of complex physical systems is common- place in many areas of science in order to predict phenom- We present augmented Lagrangian (AL) methods for solv- ena of interest. In this talk we use orthogonal transforma- ing nonlinear optimization problems. AL methods are ad- tions in the ensemble Kalman filter to capture the domi- vantageous as they can be implemented matrix-free, and nant correlations within a model and reduce noise. A series so are scalable for solving large scale problems. However, of assimilation experiments are presented for a ionosphere- they often suffer from poor initial choices of the penalty thermosphere model using real observational data. The parameter and Lagrange multipliers. Our methods over- results show a reduction in forecast error using orthogonal come this disadvantage by incorporating dynamic updates transformation compared with assimilation without trans- for the penalty parameter while minimizing the AL func- formation. tion. Numerical experiments with LANCELOT software illustrate the benefits of our proposed methods. Humberto C. Godinez Los Alamos National Laboratory Frank E. Curtis Applied Mathematics and Plasma Physics Industrial and Systems Engineering [email protected] Lehigh University [email protected] Earl Lawrence Los Alamos National Laboratory Nicholas I.M. Gould [email protected] Rutherford Appleton Laboratory UK Dave Higdon [email protected] Los Alamos National Laboratory Statistical Sciences Hao Jiang 194 CS15 Abstracts

Department of Applied Mathematics and Statistics tic Two-Phase Flows Johns Hopkins University [email protected] We present computational schemes for the study of vis- coelastic two-phase flows. A new formulation that trans- Daniel Robinson forms the constitutive equation for viscoelastic stress into a Northwestern University conservative form is developed and combined with a finite- [email protected] volume discretization of the Navier-Stokes equations. The numerical method is based on a volume of fluid algorithm for tracking the interface. Numerical examples are pre- MS244 sented to demonstrate the higher order accuracy of devel- A Data-Driven Approach to PDE-Constrained Op- oped schemes. timization Under Uncertainty Shahriar Afkhami I present an approach for incorporating data in PDE- Department of Mathematical Sciences constrained optimization. First, I develop a data-driven New Jersey Institute of Technology discretization for probability measures of uncertain PDE [email protected] parameters and prove rigorous error bounds. I then for- mulate a robust optimization problem that accounts for MS245 the uncertainty in the estimated probability measures. Fi- nally, I propose an algorithm to solve the resulting semidis- A Moment-of-Fluid Method for Computing Solu- cretized minimax problem. This algorithm employs trust tions to Multi-Phase Flows regions and permits inexact derivative computations. I The Moment-of-Fluid (MOF) reconstruction algorithm is conclude with preliminary numerical results. volume preserving, generalizable to arbitrary number of Drew P. Kouri materials, and uses only information local to the compu- Optimization and Uncertainty Quantification tational cell. These properties enable one to develop a Sandia National Laboratories multiphase flow algorithm that accurately computes com- [email protected] pressible or incompressible multiphase flows consisting of any number of materials without the aid of Riemann solvers and no acoustic time step constraint required. An outline MS244 of the MOF multiphase flow algorithm will be explained, PDE-Constrained Optimization Under Uncer- and example multiphase flow simulations with applications tainty for Convection-Diffusion-Reaction Systems in energy and medicine will be shown.

We present an overview of algorithms for large-scale opti- Mark Sussman mization of partial differential equations (PDEs) with un- Department of Mathematics certain coefficients. Our algorithms minimize risk-based Florida State University objective functions using sparse-grid discretizations. We [email protected] demonstrate our approach on large scale source inversion for multi-spieces convection-diffusion-reaction dynamics. MS245 Bart G. Van Bloemen Waanders A Time Splitting Projection Scheme for Compress- Sandia National Laboratories ible Two-Phase Flows : Application to the Inter- [email protected] action of Bubbles and Droplets with Ultrasound Waves

Harriet Li We will present a time-splitting scheme for pressure and MIT velocity in order to account with surface tension effects in [email protected] the framework of projection method for compressible two- phase flows. Several benchmarks, based on the Rayleigh- Drew P. Kouri Plesset theory (volume oscillation of a bubble), will be pre- Optimization and Uncertainty Quantification sented in order to demonstrate the efficiency of this new Sandia National Laboratories time-splitting scheme in comparisons with others existing [email protected] methods (HLLC solver, Turkel preconditionning) in situa- tions involving a low Mach number. Denis Ridzal Sandia National Laboratories Sebastien Tanguy [email protected] Universite de Toulouse [email protected]

MS244 Inexact Primal-Dual Interior Point Filter Method MS245 Fourth-Order Interface Tracking and Curvature Abstract not available at time of publication. Estimation for An Arbitrary Number of Materials in Two Dimensions Victor Zavala Argonne National Laboratory We present the iPAM method as the first fourth-order in- [email protected] terface tracking method in two dimensions, prove its con- vergence rates by mapping and adjusting regular semi- algebraic sets, and propose fourth-order algorithms for es- MS245 timating the unit normal and the curvature. Exploiting al- A Finite-Volume Based Formulation for Viscoelas- gorithms and theories in computational geometry, general CS15 Abstracts 195

topology, and algebraic geometry, iPAM directly applies to guage, it is easily extendable and yet fast as will be outlined both structured and unstructured grids, both incompress- for a large electromagnetic test problem. ible and compressible flows, and an arbitrary number of phases without any algorithmic modifications. Lars Ruthotto Department of Mathematics and Computer Science Qinghai Zhang, Aaron L. Fogelson Emory University University of Utah [email protected] [email protected], [email protected]

MS246 MS246 An Extensible Test Matrix Collection for Julia Large-Scale 3D Electromagnetic Imaging Using Ju- lia Matrix Depot is an open source project aiming to provide a rich collection of test matrices. This software can be easily In this talk we discuss the implementation of large scale extended and therefore facilitate exchange of matrices be- electromagnetic inverse problems with multiple sources and tween researchers in numerical linear algebra community. frequency using Julia. We discuss how asynchronous opti- We will describe the design and implementation of this mization and regularization techniques can be implemented software. Matrix Depot supports a variety of languages, in an efficient way and propose a paradigm for general data including Fortran and Python, but in this talk, we will rich inverse problems that invoke with nontrivial simula- focus on how to use Matrix Depot in Julia. tions. Weijian Zhang, Nicholas Higham Eldad Haber School of Mathematics Department of Mathematics The University of Manchester The University of British Columbia [email protected], [email protected] [email protected]

MS246 MS247 JuMP: Algebraic Modeling of Optimization Prob- lems in Julia Meet Informally with the CSE15 Co-Chairs and Several Invited Speakers We present JuMP, an open-source algebraic modeling lan- guage for mathematical optimization (cf. AMPL, GAMS, Meet Informally with the CSE15 Co-Chairs and Several CVX, YALMIP). We describe how JuMP takes advantage Invited Speakers. of Julia’s advanced technical features like just-in-time com- pilation and metaprogramming to achieve competitive per- Hans De Sterck formance with commercial tools, including a reimagined University of Waterloo implementation of Automatic Differentiation (AD) tech- Applied Mathematics niques for computing exact Hessian matrices for nonlinear [email protected] optimization. JuMP supports a number of commercial and open-source solvers for linear, mixed-integer, quadratic, Christopher Johnson conic, and nonlinear optimization. University of Utah Department of Computer Science Miles Lubin [email protected] Operations Research Center Massachusetts Institute of Technology Lois Curfman McInnes [email protected] Mathematics and Computer Science Division Argonne National Laboratory Iain Dunning [email protected] Operations Research Center Massachusetts Insitute of Technology [email protected] MS248 Approximation of the Boltzmann Equation with Joey Huchette the Method of Moments for Low Speed Gas Flow Operations Research Center Massachusetts Institute of Technology Gas flows in micro-electro-mechanical systems (MEMS) are [email protected] usually at a low speed and in the transition regime. The Navier-Stokes-Fourier equations are no longer adequate to capture the non-equilibrium phenomena in MEMS and the MS246 Boltzmann equation is necessary to describe the flow field Distributed and Parallel Computing for Pde Con- correctly. However, the full solution of the Boltzmann strained Optimization in Julia equation is complicated and expensive. Approximation of the Boltzmann equation with the moment method is intro- This talk presents a Julia framework for the solution of duced and the accuracy and validity range of the method large-scale PDE constrained optimization problems. It will be discussed. is based on a discretize-then-optimize approach, uses a (projected) Gauss-Newton method, and provides interfaces Xiaojun Gu state-of-the-art linear solvers (both explicit and iterative). Scientific Computing Department The framework uses Julia’s potential for parallel and dis- STFC Daresbury Laboratory tributed computation. Being written in a dynamic lan- [email protected] 196 CS15 Abstracts

David Emerson, Jianping Meng [email protected] Scientific Computing Department STFC Daresbury Laboratory [email protected], [email protected] MS248 Theoretical and Computational Investigations of the Non-linear Coupled Constitutive Relations MS248 (NCCR) A Framework on Moment Model Reduction for Ki- In a classical framework, the Navier-Stokes-Fourier (NSF) netic Equation equations can be obtained via linear uncoupled thermo- dynamic flux-force relations which guarantee the non- Model reduction of kinetic equation turns a high dimen- negativity of the entropy production. It is commonly ac- sional problem to a low dimensional quasi-linear system, cepted that the conventional thermodynamic description which not only provides further understanding of the prob- is only valid when the Knudsen number is sufficiently lem, but also essentially improves the efficiency of the nu- small. Here, we will show that the range of validity of merical simulation. As a quasi-linear system with Cauchy the NSF equations may be extended further by consider- data, the well-posedness of the model deduced is required ing the nonlinear coupling between thermodynamic fluxes to be hyperbolic. In the existed models, some of them and forces. The resulted Nonlinear Coupled Constitutive are hyperbolic, and some of them may be regularized to Relations (NCCR) can capture many interesting rarefac- be hyperbolic, while there are seldom progress on the else tion effects, such as Knudsen paradox, transpiration flows, models. Studies indicate that the hyperbolicity is possibly thermal stress, heat flux without temperature gradients, related with H-theorem, preserving of certain physics, etc. etc. We will also derive a set of phenomenological bound- In this talk, I will reveal the underlying reason why some ary conditions for NCCR which respect the second law of existed models are hyperbolic and the others are not, and thermodynamics. We will explore some boundary value how the hyperbolic regularization works. It is pointed out problems by comparing the NCCR and the DSMC simula- that the hyperbolicity is not related to H-theorem, con- tions. servation, etc, at all. The even fascinating point is, with only routine calculation, symmetric hyperbolic models can Anirudh Singh Rana always be deduced with any ansatz for generic kinetic equa- GNU Building 404 Room 305 tion by the framework we proposed. By this framework, Dept: ACML, GNU, South Korea existing models are re-presented and brand new models are [email protected] discovered. Even if the study is restricted in the scope of the classical Grad’s 13-moment system, a new model with Rho Shin Myong global hyperbolicity can be deduced. School of Mechanical and Aerospace Engineering Gyeongsang National University, South Korea Ruo Li [email protected] School of Mathematical Science Peking University [email protected] MS249 Exploiting Active Subspaces for Nonlinear Pro- gramming MS248 m The active subspace of function f : R → R is the span Numerical Solution of a Fourteen-Moment Closure of n

Boone Tensuda Large-scale higher-order datasets pose many challenges in University of Toronto terms of computational and storage costs. As these tensors Institute for Aerospace Studies may not fit into the computer’s memory, most canonical [email protected] polyadic decomposition algorithms cannot be used. In this talk, we propose to use stochastic optimization methods, Clinton P. Groth as these kind of algorithms require only a small amount of University of Toronto Institute for Aerospace Studies entries in memory in every iteration. The power of these Canada methods will be illustrated on both synthetic and real life CS15 Abstracts 197

data. level Scotch partitioner that take into account these mul- tiple criteria. We illustrate the results on graphs used for Nico Vervliet numerical scientific applications. Department of Electrical Engineering (ESAT) KU Leuven Astrid Casadei [email protected] INRIA Bordeaux Sud-Ouest & CNRS (LaBRI UMR 5800) Lieven De Lathauwer Bordeaux University Katholieke Universiteit Leuven [email protected] [email protected] Pierre Ramet LaBRI, Univ Bordeaux, France MS249 701868 Non-Convex Low-Rank Matrix and Tensor Recov- ery Jean Roman INRIA In this talk, I will present algorithms for solving non- [email protected] convex low-rank matrix and also tensor recovery models. Global convergence to stationary point or in terms of first- order optimality condition is given. Although we cannot MS250 guarantee global optimal solutions, numerical experiments demonstrate that our algorithms can give more faithful so- Handling Multiple Communication Metrics for Hy- lutions than those for solving convex models on both syn- pergraph Partitioning thetic and real-world data. We investigate connectivity-based partitioning methods, Yangyang Xu specifically hypergraph partitioning-based methods, for Rice University task mapping problem in order to efficiently parallelize the [email protected] communicating tasks. A good partitioning method should divide the load among the processors as evenly as possible and minimize the inter-processor communication overhead. MS249 The total communication volume is the most popular com- Towards an Optimal Scalability in Computing Ex- munication overhead metric which is reduced by the ex- treme Eigenpairs of Large Matrices isting state-of-the-art hypergraph partitioners. However, other metrics such as the total number of messages, the SVD and/or eigen-decomposition are fundamental prob- maximum amount of data transferred by a processor, or lems in scientific and engineering computing. For large- a combination of them are equally, if not more, impor- scale data and on modern computers, classic algorithms tant. We propose a directed hypergraph model to capture have encountered scalability bottlenecks. In this work, multiple communication metrics and a one-phase approach we study two block methods that are based on, respec- where all the communication cost metrics can be effectively tively, the Gauss-Newton and the power methods. We minimized in a multi-objective setting. We wrapped the present theoretical and numerical results to demonstrate proposed model and methods in a multi-objective, multi- their promises. In particular, we show that the proposed level hypergraph partitioner called UMPa. The partitioner multi-power method can frequently achieve an optimal takes various prioritized communication metrics into ac- scalability. count, and optimizes all of them together. Compared to the state-of-the-art methods which only minimize the to- Yin Zhang tal communication volume, we show on a large number of Rice University problem instances that UMPa produces better partitions Computational and Applied Mathematics in terms of several communication metrics. [email protected] Mehmet Deveci Zaiwen Wen The Ohio State University Peking University [email protected] Beijing International Center For Mathematical Research [email protected] Kamer Kaya The Ohio State University Xin Liu Department of Biomedical Informatics Academy of Mathematics and Systems Science [email protected] Chinese Academy of Sciences [email protected] Bora Ucar LIP, ENS-Lyon, France. [email protected] MS250 Towards a Recursive Graph Bipartitioning Algo- Umit V. Catalyurek rithm for Well Balanced Domain Decomposition The Ohio State University In the context of hybrid sparse linear parallel solvers based Department of Biomedical Informatics on Schur complement approaches, getting a domain decom- [email protected] position tool leading to a good balancing of both internal and interface nodes for all the domains is a critical point for parallel efficiency. In this presentation, we introduce MS250 several variations of the existing algorithms in the multi- Complex Objective Partitioning of Small-World 198 CS15 Abstracts

Networks Using Label Propagation oped methods will be presented as well.

We present PULP, a parallel and memory-efficient graph Yekaterina Epshteyn partitioning method specifically designed to partition low- Department of mathematics diameter networks with skewed degree distributions. Par- University of Utah titioning determines the in-memory layout of a graph, [email protected] which affects locality, inter-task load balance, communi- cation time, and overall memory utilization of graph ana- lytics. A novel feature of our method PULP (Partitioning MS251 using Label Propagation) is that it optimizes for multiple A High-Order Adaptive Finite Volume Solver for objective metrics simultaneously, while satisfying multiple Steady Euler Equations graph constraints. Using our method, we are able to parti- tion a web crawl with billions of edges on a single compute In this talk, we will present our work on high-order adap- server in under a minute. For a collection of test graphs, tive finite volume methods for steady Euler equations. we show that PULP uses 8-39x less memory than state-of- There are two main components in our solver. The first the-art partitioners, and is up to 14.5x faster, on average, one is a high-order finite volume solver for steady Euler than alternate approaches (with 16-way parallelism). We equations. To reach the high-order accuracy, the k-exact also achieve better partitioning quality results for both the reconstruction is used. The Newton iteration is applied multi-constraint as well as multi-objective scenarios. to linearize the equations, then the linear system is solved by a geometrical multigrid method. In the second compo- George Slota, Kamesh Madduri nent, we use the framework of the goal oriented a posteriori Pennsylvania State University error estimation, and develop some new and efficient tech- [email protected], [email protected] niques to generate the error indicator. Then a h-adaptive method will be introduced to optimize the distribution of Siva Rajamanickam the mesh grids, and the improvement of the efficiency on Sandia National Laboratories the algorithm implementation can be expected. The nu- [email protected] merical results verify our theoretical results, and the high- order behavior of our method will be demonstrated by the benchmark examples. MS250 Load Balancing Multiscale Simulations Guanghui Hu University of Macau Adaptive procedures and associated load-balancing opera- [email protected] tions are requirements for a high-performance parallel sim- ulations to take full advantage of computational resources. Multiscale simulations introduce additional sensitivities MS251 and costs into adaptive processes which are not present in A Seventh Order Hybrid Weighted Compact the standard single-program multiple-data (SIMD) parallel Scheme Based on WENO Stencil for Hyperbolic model used by the overwhelming majority of single-scale Conservation Laws codes. The Adaptive Multiscale Simulation Infrastruc- ture (AMSI) supports the implementation and execution In this paper, we propose a hybrid seventh order weighted of general multiscale simulations, and provides methods for compact scheme for shock capturing. In smooth region, global and local scale-sensitive load balancing and adaptive present scheme recovers a seventh linear compact scheme. operations. An implementation of a multiscale simulation Near discontinuities, fifth order weighted compact scheme of soft-tissue mechanics using AMSI is discussed along with is used. To guarantee convergence condition, the sev- its usage of the scale-sensitive adaptive and load-balancing enth order scheme and fifth order scheme are coupled by procedures provided by AMSI. a new smooth indicator based on WENO weights. Present scheme only uses five points which is the same as fifth order William R. Tobin, Daniel Fovargue WENO scheme. Rensselaer Polytechnic Institute [email protected], [email protected] Jun Peng, Yiqing Shen State Key Laboratory of High Temperature Gas Mark S. Shephard Dynamics Rensselaer Polytechnic Institute Institute of Mechanics, Chinese Academy of Science Scientific Computation Research Center [email protected], [email protected] [email protected] MS251 MS251 Maximum Principle and Positivity Preserving Flux High-Order Accurate Numerical Methods for El- Limiters for High Order Schemes liptic and Parabolic Interface Models Abstract not available at time of publication. Designing numerical methods with high-order accuracy for problems with interfaces (for example, models for compos- Zhengfu Xu ite materials or fluids, etc), as well as models in irregular Michigan Technological University domains is crucial to many physical and biological appli- Dept. of Mathematical Sciences cations. In this talk we will discuss recently developed [email protected] efficient numerical schemes based on the idea of the Dif- ference Potentials for elliptic and parabolic composite do- main/interface problems. Numerical experiments to illus- MS252 trate high-order accuracy and the robustness of the devel- PDE-constrained Optimization with Local Control CS15 Abstracts 199

and Boundary Observations: Robust Precondition- we illustrate the effectiveness of our solvers with numerical ers experiments.

We consider PDE-constrained optimization problems with Akwum Onwunta, Peter Benner control functions defined on a subregion of the domain of Max Planck Institute, Magdeburg, Germany the state equation. The main purpose of this paper is to [email protected], define and analyze robust preconditioners for KKT systems [email protected] associated with such optimization tasks. That is, precon- ditioners that lead to iteration bounds, for the MINRES Martin Stoll scheme, that are independent of the regularization param- Max Planck Institute, Magdeburg eter α and the mesh size h. Our analysis addresses elliptic [email protected] control problems, subject to Tikhonov regularization, and covers cases with boundary observations only and locally defined control functions. A number of numerical experi- MS252 ments are presented Accelerated Source-Encoding Full-Waveform Seis- Ole Løseth Elvetun mic Inversion with Additional Constraints Department of Mathematical Sciences and Technology Norwegian University of Life Sciences We present a semismooth Newton-PCG method for full- [email protected] waveform inversion governed by the elastic wave equation that can handle additional constraints on the material. Bjørn F. Nielsen Source-encoding substantially reduces the computational Simula Research Laboratory costs compared to conventional approaches that consider [email protected] every source individually. In particular, we accelerate the minimization of a sample average approximation model by using inexact Hessian information based on mini-batches MS252 of the samples. Furthermore, we compare the performance Robust Preconditioners for PDE-Constrained Op- with preconditioned stochastic descent schemes. timization with Limited Observation Data Michael Ulbrich Regularization robust preconditioners have been success- Technische Universitaet Muenchen fully developed for some PDE-constrained optimization Chair of Mathematical Optimization problems. These methods, however, typically assume that [email protected] observation data is available throughout the entire domain of the state equation. For many inverse problems, this is an Christian Boehm unrealistic assumption. We propose and analyze precondi- Technische Universit¨at M¨unchen tioners for PDE-constrained optimization problems with [email protected] limited observation data, e.g. observations are only avail- able at the boundary of the computational domain. Our methods are robust with respect to both the regularization parameter and the mesh size. MS253 Improved Understanding of Atmospheric Stability Magne Nordaas Effects on Wind Farm Performance Using Large- Center for Biomedical Computing Eddy Simulation Simula Research Laboratory [email protected] Recent evidence from operational wind farms has shown that atmospheric stability, especially heat fluxes at the Kent-Andre Mardal surface, can have a profound effect on turbine-atmosphere Simula Research Laboratory and Department of interactions. We use two LES codes to study atmo- Informatics spheric stability effects in wind farms: the Simulator for University of Oslo Offshore/Onshore Wind Farm Applications (SOWFA), a [email protected] publicly-available, finite-volume code developed in C++ by the National Renewable Energy Laboratory, and the Bjørn F. Nielsen Wind Turbine and Turbulence Simulator (WiTTS), a new, Simula Research Laboratory finite-difference, Fortran code developed in-house. Com- [email protected] prehensive results will be presented for both single- and multiple-turbine cases under a variety of initial conditions.

MS252 All-at-once Approach to Optimal Control Problems Cristina L. Archer Constrained by PDEs with Uncertain Inputs University of Deleware [email protected] We present an efficient approach to simulate optimization problems governed by partial differential equations involv- Shengbai Xie, Niranjan Ghaisas ing random coefficients. This class of problems leads to University of Delaware prohibitively high dimensional saddle point systems with [email protected], [email protected] Kronecker product structure, especially when discretized with the stochastic Galerkin finite element method. Here, we derive robust Schur complement-based block diago- MS253 nal preconditioners for solving the resulting stochastic Galerkin systems with all-at-once low-rank solvers. Finally, Characterizing Turbulence in Wind Turbine Wake: 200 CS15 Abstracts

Role of Stratification Bergische Universit¨at Wuppertal Department of Mathematics Abstract not available at time of publication. [email protected] Kiran Bhaganagar University of TExas, San Antonio MS254 [email protected] Root-Node Based Algebraic Multigrid

MS253 Recent approaches to improving multigrid convergence Les Study of a Large Wind Farm Within a Diurnal through modified coarsening and enhanced interpolation Atmospheric Boundary Layer have shown to be effective in a general setting (e.g. com- plex, non-Hermitian, and indefinite). Yet, the the resulting Abstract not available at time of publication. multigrid hierarchies may exhibit higher complexities than necessary. In this talk we outline a root-node based ap- Marc Calaf proach to multigrid, which can be viewed as a hybrid of University of Utah classical and aggregation based multigrid methods. This [email protected] allows both point-wise decisions in the setup while retain- ing the framework of aggregation. We give an overview MS254 of root-node multigrid using interpolation based on energy minimization and show how the complexity of the multi- Bootstrap and Adaptive Methods grid cycle is controlled through selective filtering by utiliz- In this talk, I will highlight several recent advances in the ing a root-node. The method yields improved interpolation development and analysis of AMG coarsening algorithms. (and convergence), while limiting the total work of the cy- I will discuss various strategies for selecting the coarse vari- cle with minimal tuning of parameters. We present some ables and defining interpolation, in both the adaptive AMG numerical results in support and discuss directions for fur- and Bootstrap AMG settings. Numerical experiments of ther theoretical and numerical development. the proposed techniques applied to various applications will also be provided. Luke Olson Department of Computer Science James Brannick University of Illinois at Urbana-Champaign Department of Mathematics [email protected] Pennsylvania State University [email protected] Jacob B. Schroder Lawrence Livermore National Laboratory [email protected] MS254 Algebraic Multigrid for H-hermitian Matrices MS254 We develop an algebraic multigrid method for solving linear systems of equation Ax = b with non-Hermitian matrices A Algebraic Multigrid Method for Implicit Smoothed that possess a simple symmetrizing operator, e.g., Saddle- Particle Hydrodynamics point problems, Hamiltonian matrices. That is there ex- ists a simple matrix H such that HA is hermitian. We Recently, a Lagrangian particle model based on smoothed observe that by carefully constructing the intergrid trans- particle hydrodynamics (SPH) is proposed to numerically fer operators it is possible not only to transfer this non- solve the coupled system that describes the electrokinetic standard symmetry to coarse scales, but also to reduce a phenomena. We generalize the aggregation based Alege- general Petrov-Galerkin to a Galerkin coarse grid construc- braic multigrid (AMG) method to solve the large-scale tion, namely for HA. We show that by using this con- linear system of equations discretized from implicit SPH. struction and a Kaczmarz smoother we obtain a method Auxiliary grid approach is used to improve the efficiency that yields the same iterates when applied to Ax = b or and reduce the computational complexity. Numerical ex- HAx = Hb. To demonstrate the applicability of this ap- periments for modeling electroosmotic flow in microchan- proach we develop a method for the Wilson discretization nels and flow throgh charged membranes are presented of the 2-dimensional Dirac equation. The proposed ap- to demonstrate the effectiveness of the proposed AMG proach uses a bootstrap setup algorithm based on a multi- method. grid eigensolver. It computes test vectors which define the least squares interpolation operators by working mainly Xiaozhe Hu on coarse grids, leading to an efficient and integrated self The Pennsylvania State University learning process for defining algebraic multigrid interpola- [email protected] tion. The algorithm is motivated by the γ5-symmetry of the Dirac equation, which carries over to the Wilson dis- Wenxiao Pan cretization. This discrete γ5-symmetry is used to reduce Pacific Northwest National Laboratory a general Petrov Galerkin bootstrap setup algorithm to a [email protected] Galerkin method for the Hermitian and indefinite formu- lation of the Wilson matrix. Kaczmarz relaxation is used as the multigrid smoothing scheme in both the setup and Jinchao Xu solve phases of the resulting Galerkin algorithm. Extensive Pennsylvania State University numerical results are presented to motivate the design and [email protected] demonstrate the effectiveness of the proposed approach. Hongxuan Zhang Karsten Kahl Penn State University CS15 Abstracts 201

[email protected] [email protected]

MS255 MS255 Designing Visualizations for Biological Research Exploring Big Urban Data Advances in measurement devices in the last decade have given rise to an explosion of scientific data. In biology, For the first time in history, more than half of the world’s access to massive amounts of quantitative data has fun- population lives in urban areas. Given the growing volume damentally changed how discoveries are made, and now of data that is being captured by cities, the exploration an important component of the scientific process is mak- of urban data will be essential to inform both policy and ing sense of this data using visualization methods. For administration, and enable cities to deliver services effec- most biologists, however, their toolbox is made up of only tively, efficiently, and sustainably while keeping their cit- broadly-available tools that were designed for over-arching izens safe, healthy, prosperous, and well-informed. Urban problems, often leaving them without answers to their spe- data analysis is a growing research field that will not only cific questions. A growing trend in the visualization com- push computer science research in new directions, but will munity is to develop tools that focus on specific, real-world also enable many others, including urban planners, social problems. Called a design study, the process of developing scientists, transportation experts. We have been working these tools relies on a close collaboration with end-users on methods and systems that support urban data analy- as well as the use of methods from design. In this talk sis, with a focus on spatio-temporal aspects. We will de- I’ll present several design studies that target complex, bio- scribe these efforts, in particular our work on analyzing the logical data analysis, from discovering trends in molecular NYC taxi dataset, which contains information about over networks to understanding the results of comparative ge- 850 million yellow cab trips. Supported by NSF, Google, nomics algorithms. Moore-Sloan Data Science Environment, IBM, and CUSP. Miriah Meyer University of Utah Claudio T. Silva [email protected] NYU [email protected]

MS255 Block-Based Analysis of Scientific Data MS256 Block-based analysis is the division of an analysis problem Probability Density Methods for the Analysis of into blocks (not processes) that communicate. By allow- Power Grids Under Uncertainty ing blocks to be configurable size and number, flexibly as- signing blocks to processes, and migrating blocks among We present the probability density function (PDF) method different levels of memory/storage hierarchy, an analysis for the analysis of power grids under uncertainty due to infrastructure can scale and adapt to current and future random renewable energy inputs. We derive determinis- science applications and HPC platforms. We will discuss tic equations for the evolution of the PDF of the power these fundamental concepts and their implementation in a systems using various closures. The resulting PDEs are reusable data movement library designed for block-based solved numerically, and results are compared against refer- scientific data analysis. ence Monte Carlo simulations to assess the accuracy of the Tom Peterka proposed closures. Argonne National Laboratory [email protected] David A. Barajas-Solano Pacific Northwest National Lab [email protected] MS255 Exascale Scientific Data Analytics and Visualiza- Alexander Tartakovsky tion Pacific Northwest National Laboratory [email protected] Among many existing feature descriptors, statistical infor- mation derived from data samples is a promising approach Debojyoti Ghosh to taming the big data avalanche because data distribu- Mathematics and Computer Science Division tions computed from a population can compactly describe Argonne National Laboratory the presence and characteristics of salient data features [email protected] with minimal data movement. The ability to computa- tionally summarize and process data using distributions Emil M. Constantinescu also provides an efficient and representative capture of in- Argonne National Laboratory formation that can adjust to size and resource constraints, Mathematics and Computer Science Division with the added benefit that uncertainty associated with re- [email protected] sults can be quantified and communicated. In this talk, I will discuss applying distribution-based approaches for vi- sualization and data analytics, including multivariate anal- Shrirang Abhyankar ysis, vector/scalar field analysis, and histogram compres- Argonne National Laboratory sion and query. [email protected]

Han-Wei Shen Zhenyu Huang The Ohio State University Pacific Northwest National Laboratory 202 CS15 Abstracts

[email protected] [email protected], [email protected], [email protected], [email protected]

MS256 Distributed Optimization Algorithms for Wide- MS257 Area Oscillation Monitoring in Power Systems A multi-physics Domain Decomposition Method for Navier-Stokes-Darcy Model In this talk we will present three distributed optimiza- tion algorithms based on Alternating Directions Multiplier This presentation discusses a multi-physics domain de- Method (ADMM) for estimating the electro-mechanical os- composition method for solving the coupled steady-state cillation modes of large power system networks using Syn- Navier-Stokes-Darcy system with the Beavers-Joseph in- chrophasors. Both synchronous and asynchronous commu- terface condition. The wellposedness is first showed by nications will be considered. Each architecture integrates a using a branch of singular solutions. Robin boundary con- centralized Prony-based algorithm with several variants of ditions on the interface are constructed based on the phys- ADMM. We will discuss convergence and resiliency prop- ical interface conditions to decouple the Navier-Stokes and erties of each architecture using analytical results as well Darcy parts. Then a domain decomposition method is de- as simulations of IEEE prototype power system models. veloped and analyzed. Numerical examples are presented to validate this method. Aranya Chakrabortty North Carolina State University Xiaoming He [email protected] Department of Mathematics and Statistics Missouri University of Science and Technology Seyedbehzad Nabavi [email protected] NC State University [email protected] MS257 Improvements in the Level Set Method with a Fo- MS256 cus on Curvature-Dependent Forcing Exploiting Network Laplacian Structure in Power Grid Dynamics One particular subset of moving interface problems is when the interface exerts a curvature-dependent force on the sur- The electromechanical dynamics of the power grid possess rounding material. Such a force can arise, for example, a structure that is ”nearly” Hamiltonian, with the gradient when the interface is resistant to bending or has surface an underlying scalar function capturing much of the infor- tension. Stable numerical computation of the interface cur- mation needed to reconstruct the vector field. This work vature can be difficult as it is often expressed as high-order will go further to exploit added structure in this scalar derivatives of either marker particle positions or of a level potential function, demonstrating that its network related set function. Focusing on the latter, the level set method portion can be written as a Hermitian form in the com- is modified to track not only the interface position, but the plex variables of the voltage phasors (i.e., the fundamental curvature as well. The definition of the signed-distance component for a windowed Fourier transform of the nearly function that is used in this approach is also used to de- sinusoidal bus voltages of the power grid). Moreover, the velop an interpolation-free, closest-point method for solv- defining matrix of this Hermitian from is a weighted Lapla- ing surface PDEs. cian, defined by the topology and electrical characteristics of the transmission grid. We show how this structure can Chris Vogl be exploited to build tractable dynamic models of cascad- University of Washington ing failure phenomena, in which overload and protective [email protected] disconnection of one transmission line may induce subse- quent overloads and disconnects of further links, with the risk of cascade into system-wide failure. MS257 Optimal Energy Conserving Discontinuous Christopher DeMarco, Honghao Zheng Galerkin Methods for the Wave Propagation University of Wisconsin-Madison Problems in Heterogeneous Media [email protected], [email protected] Solving wave propagation problems within heterogeneous media has been of great interest and has a wide range of MS256 applications in physics and engineering. The design of nu- Fast Algorithms for Synchrophasor Computations merical methods for such general wave propagation prob- lems is challenging because the energy conserving property There is an urgent need to develop fast real-time algorithms has to be incorporated in the numerical algorithms in or- that can extract operator friendly information out of large- der to minimize the phase or shape errors after long time scale high speed synchronized measurement devices being integration. In this talk, we will discuss multi-dimensional implemented in power systems all over the world. This wave problems and consider linear second-order wave equa- talk will highlight the stability monitoring algorithms de- tion in heterogeneous media. We will present an LDG veloped recently in this context while emphasizing the com- method, in which numerical fluxes are carefully designed putational challenges in realizing the theoretical methods. to maintain the energy preserving property and accuracy. Distributed algorithms as well as centralized formulations We propose compatible high order energy conserving time will be compared. integrators and prove the optimal error estimates and the energy conserving property for the semi-discrete methods. Vaithianathan Venkatasubramanian, Tianying Wu, Seyed Our numerical experiments demonstrate optimal rates of Arash Sarmadi, Ebrahim Rezaei convergence, and show that the errors of the numerical so- Washington State University lution do not grow significantly in time due to the energy CS15 Abstracts 203

conserving property. ecution conditions at run-time, such as problem sizes and hybrid MPI/OpenMP. In this talk, we introduce FIBER Yulong Xing framework of Auto-tuning (AT) to optimize codes for the Department of Mathematics many-core processors. We also show effect of the AT with Univeristy of Tennessee / Oak Ridge National Lab multi nodes of the Xeon Phi with an application of Finite [email protected] Difference Method.

Takahiro Katagiri MS257 Information Technology Center, The University of Tokyo Surface Phase Separation Mediated by Nonlocal [email protected] Interactions Satoshi Ohshima Motivated by the lipid phase separation on membrane me- The University of Tokyo diated by electrostatic interactions, we propose here a gen- Information Technology Center eral Cahn-Hilliard equation with nonlocal electrostatic in- [email protected] teractions. A C-0 interior penalty discontinuous Galerkin method is adapted to solve the coupled system of PDEs on Masaharu Matsumoto arbitrary surfaces. Phase separation of smaller scales are Information Technology Center found compared to scenario without nonlocal interaction, The University of Tokyo indicating that the nonlocal interaction may generate lipid [email protected] rafts.

Yongcheng Zhou MS258 Department of Mathematics Colorado State University A Framework for Separation of Concerns Between [email protected] Application Requirements and System Require- ments

MS258 An HPC application is usually optimized for a particu- lar platform and unable to run efficiently on other plat- The Role of Autotuning Compiler Technology forms. The Xevolver framework is designed to sepa- Autotuning empirically evaluates a search space of possible rate such platform-specific optimizations from application implementations of a computation to identify the imple- codes. In Xevolver, a code portion that needs to be modi- mentation that best meets its optimization criteria (e.g., fied for system-specific code optimization is just annotated performance, power, or both). Autotuning compilers gen- for user-defined code transformations to prevent messing erate this search space of different implementations either up the original code. The usefulness and practicality of automatically or with programmer guidance. This talk will Xevolver are discussed on the basis of some case studies. explore the role of compiler technology in achieving very Hiroyuki Takizawa, Shoichi Hirasawa high levels of performance, comparable to what is obtained manually by experts. It will focus on the optimizations re- Tohoku University/JST CREST quired for specific domains: geometric multigrid, stencils, [email protected], [email protected] and tensor contraction computations. Hiroaki Kobayashi Mary Hall Tohoku University, Japan School of Computing [email protected] University of Utah [email protected] MS259 Microstructural Modeling of Fracture in Uranium MS258 dioxide Using a Phase-Field Based Approach Active Harmony: Making Autotuning Easy A phase-field model is implemented in MOOSE to inves- Active Harmony is an auto-tuning framework for paral- tigate the effect of porosity and grain size on the inter- lel programs. In this talk, I will describe how the system granular brittle fracture in UO2. The grain boundary frac- makes it easy (sometime even automatic) to create pro- ture parameters are obtained from the results of molecu- grams that can be auto-tuned. I will present example from lar dynamics simulations. A numerical sensitivity study a few applications and programming languages. is then performed to obtain a microstructurally informed stress-based fracture model usable at the engineering scale. Jeffery Hollingsworth Computer Science Department University of Maryland Pritam Chakraborty, Michael Tonks [email protected] Idaho National Laboratory [email protected], [email protected]

MS258 Towards Auto-tuning in the Era of 200+ Thread MS259 Parallelisms — FIBER Framework and Minimizing Computational Microstructure Science Using the Software Stack — Moose Framework

Currently, parallelism of 200+ threads is pervasive by Mesoscale modeling and simulation provide a bridge be- many-core processors, such as the Xeon Phi. In the pro- tween atomistic data and engineering scale computation. cessors, we need careful optimizations with respect to ex- However, mesoscale modeling can be complicated due to 204 CS15 Abstracts

the multiphysics nature of the problems, and the typically solution of the original system. The reduced model size high computation costs. The open source Multiphysics is problem dependent and could be smaller than the full Object-Oriented Simulation Environment (MOOSE) pro- problem, but large enough to make direct solution costly. vides a number of physics modules that are aimed specif- In this scenario, the iterative solution of the ROM can be ically at mesoscale simulation. These tools model the more effecient. coevolution of microstructure and properties due to ap- plied load, temperature, and radiation damage. The Phase Virginia Forstall Field Module provides all the necessary tools to predict mi- University of Maryland at College Park crostructure evolution using the phase field method and the [email protected] Tensor Mechanics Module provides the tools for finite de- formation mechanics simulations at the level of microstruc- Howard C. Elman ture. Also, effective mechanical and thermal properties can University of Maryland, College Park be calculated as the microstructure evolves. Since these [email protected] tools are based on MOOSE, they are massively parallel, work in 1D, 2D, and 3D and can use mesh and time step adaptivity. We have also developed the capability to re- MS260 construct experimental microstructures directly into the simulations, to set the initial condition for simulations, to Model Reduction in Physics-Based Sound Synthe- simplify validation and to facilitate virtual property mea- sis surement. Synthesizing physics-based sounds by time-stepping com- Bradley Fromm, Daniel Schwen, Michael Tonks putational models of coupled solid and fluid systems is ex- Idaho National Laboratory tremely time consuming due to long-time integration and [email protected], [email protected], the desire for real-time auditory feedback. This talk will [email protected] highlight some of our recent work on reduced-order mod- eling of vibration and acoustic radiation: (1) basis com- pression to reduce the memory footprint of modal sound MS259 models, and (2) reduced-order modeling of bubble-based Fission Bubble Modeling in Uranium Carbide liquid sounds.

Fission gas bubble behavior is a complex microscopic effect Doug L. James, Timothy Langlois that leads to macroscopic changes in nuclear fuel. The in- Cornell University terplay between thermal diffusion causing bubble growth, [email protected], [email protected] pitted against physical knock-outs from fission fragments causing bubble shrinkage, creates a non-linear problem that is not easily solved. MOOSE allows for character- MS260 ization of this behavior within the code BISON by using Online Adaptive Model Reduction lower-length scale effects to estimate the large bubble struc- ture and swelling of irradiated uranium carbide. Model reduction approximates the nonlinear manifold in- Christopher Matthews, Andrew Klein duced by full-order solutions with a (linear) reduced space. Oregon State University We present a nonlinear approximation of the manifold [email protected], [email protected] based on adapting the reduced space online. The adap- tation relies on low-rank basis updates derived from sparse data of the full-order model. In particular in the presence MS259 of nonlinearities, our nonlinear approximation achieves a Grizzly: A Simulation Tool for Nuclear Power higher accuracy than the classical linear approximation. Plant Component Aging The sparsity of the data ensures computational efficiency.

To determine the risk associated with extending the life of Benjamin Peherstorfer nuclear power plants, the effects of age-related degradation ACDL, Department of Aeronautics & Astronautics of critical components in those plants must be understood. Massachusetts Institute of Technology Grizzly is a MOOSE-based tool being developed to simu- [email protected] late aging processes and understand the effects that age- related degradation will have on those components. An Karen E. Willcox initial application of Grizzly is for coupled physics simula- Massachusetts Institute of Technology tions to assess the susceptibility of aged reactor pressure [email protected] vessels to fracture under accident conditions.

Benjamin Spencer MS260 Idaho National Laboratory [email protected] Reduced-order Models using Dynamic Mode De- composition

MS260 Dynamic mode decomposition (DMD) is a technique that Iterative Solution Techniques in Reduced-order uses data to express “black-box” dynamics in terms of the Modeling eigenvalues, eigenfunctions, and modes of the correspond- ing Koopman operator. For a linear system, these modes Reduced-order models (ROMs) efficiently solve related lin- are the eigenvectors, and they have a similar role in non- ear systems arising in many-query applications. The full linear settings. We describe Extended DMD, an exten- linear system is projected onto a smaller dimensional sub- sion that uses a richer set of functions to approximate the space resulting in a ROM whose solution approximates the Koopman eigenfunctions, and demonstrate the method on CS15 Abstracts 205

several examples, including flow past a cylinder. permeation through human skin.

Clarence Rowley Andreas Kreienbuehl Princeton University University of Lugano Department of Mechanical and Aerospace Engineering [email protected] [email protected] Arne Naegel Matthew O. Williams Goethe University Frankfurt Applied Mathematics [email protected] University of Washington [email protected] Daniel Ruprecht Institute of Computational Science Maziar S. Hemati, Scott Dawson Universita della Svizzera italiana Princeton University [email protected] [email protected], [email protected] Robert Speck MS261 Juelich Supercomputing Centre Forschungszentrum Juelich A Posteriori Analysis of the Parareal Algorithm: [email protected] Efficient Resource Allocation and Convergence Cri- teria Gabriel Wittum We carry out a posteriori analysis of the parareal algorithm Goethe Center for Scientific Computing using adjoint based methods. The analysis is carried out Goethe University Frankfurt relatively cheaply and allows for quantification of error in [email protected] a quantity of interest. Furthermore, the analysis provides guidance in choosing discretization parameters so as to en- Rolf Krause hance load balancing in the parallel stage of the algorithm Institute of Computational Science and by quantifying different sources of error, suggests ap- University of Lugano propriate strategies to accelerate convergence. [email protected]

Jehanzeb H. Chaudhry Florida State University MS261 [email protected] Multigrid Reduction in Time (MGRIT): A Flexible Don Estep, Simon Tavener and Non-Intrusive Method Colorado State University [email protected], [email protected] This talk highlights practical aspects of the parallel-in- time method, multigrid-reduction-in-time (MGRIT). The algorithm is non-intrusive and wraps existing time step- MS261 ping codes. MGRIT is versatile by allowing for various An Overview of the Multigrid Reduction in Time time discretizations (e.g., Runge-Kutta and multistep) and (MGRIT) Method for adaptive refinement and coarsening in time and space. Non-linear problems are handled through full approxima- The multigrid-reduction-in-time (MGRIT) method is a tion scheme (FAS) multigrid. Details of the software phi- scalable, truly multilevel approach to parallel time integra- losophy and practical experience and results (e.g., from a tion, derived based on multigrid reduction principles. In nonlinear compressible Navier-Stokes code), will also be this talk, we present the algorithm and demonstrate that given. MGRIT offers excellent strong and weak parallel scaling up to thousands of processors. Complementary convergence Jacob B. Schroder analysis methodologies such as a semi-algebraic approach Lawrence Livermore National Laboratory to mode analysis, which provides a predictive analysis tool [email protected] for MGRIT and related algorithms on space-time grids, will also be discussed. Robert Falgout Center for Applied Scientific Computing Stephanie Friedhoff Lawrence Livermore National Laboratory KU Lueven [email protected] stephanie.friedhoff@cs.kuleuven.be Ulrike Meier Yang MS261 Lawrence Livermore National Laboratory [email protected] Parareal Library for Time-Dependent PDEs in Medical Applications Tzanio V. Kolev The parallel-in-time integration method Parareal provides Center for Applied Scientific Computing an additional direction for concurrency when solving time- Lawrence Livermore National Laboratory dependent PDEs numerically. Thus, it can extend the [email protected] strong scaling limit of a purely space-parallel approach. In this talk, we present a new C++ ‘Library for the Parareal Veselin Dobrev Method’ (Lib4PrM). To illustrate its performance, a cou- Lawrence Livermore National Laboratory pling with the ug4 package is used to solve a PDE modeling [email protected] 206 CS15 Abstracts

Stephanie Friedhoff [email protected] KU Lueven stephanie.friedhoff@cs.kuleuven.be MS262 Scott Maclachlan Process Mapping onto Complex Architectures and Department of Mathematics Partitions Thereof Tufts University [email protected] The Scotch software computes process-processor mappings by assigning recursively parts of the process graphs to parts of the target graphs. To date, while regular target archi- MS262 tectures can be described using pre-coded routines, irreg- 2 Demonstrating Improved Application Performance ular architectures or parts of regular ones require P data Using Dynamic Monitoring and Task Mapping structures, which makes them unpractical for very big ma- chines. We will present a new, multilevel description of We present a framework enabling dynamic application target architectures that alleviates this problem, trading- mapping based on run-time analysis of system-wide net- off memory for run time. work data, architecture-specific routing algorithms, and Francois Pellegrini application communication patterns. We demonstrate dy- University of Bordeaux namic remapping of MPI tasks based on route-length, [email protected] bandwidth, and credit-stalls metrics for a parallel sparse matrix-vector multiplication kernel. Remapping based on dynamic network information in a congested environment MS263 in a shared network topology recovers up to 50% of the time lost to congestion, reducing matrix-vector multiplica- Fluctuating Hydrodynamics of Reactive Multi- tion time by 8%. species Mixtures

Ann Gentile, James Brandt, Karen D. Devine, Kevin This paper describes the extension of the fluctuating Pedretti Navier-Stokes (FNS) equations to multispecies, reactive Sandia National Laboratories mixtures. In FNS, hydrodynamic effects of thermal fluc- [email protected], [email protected], kd- tuations are represented by adding stochastic flux terms, [email protected], [email protected] whose magnitude are set by fluctuation dissipation bal- ance, to the Navier Stokes equations. Incorporating re- actions into the system introduces a number of additional MS262 complexities. We discuss approaches to addressing these is- sues and present numerical results illustrating the impact Topology Aware Process Placement and Data Man- of fluctuations in reacting systems. agement John B. Bell Programming multicore or manycore architectures effi- CCSE ciently is a challenge because numerous hardware char- Lawrence Berkeley Laboratory acteristics have to be taken into account, especially the [email protected] memory hierarchy. In this talk we will show how we can efficiently manage data and reduce communication cost by taking into account the topology of the machine and the MS263 affinity of the application processes in different contexts: Modeling Multi-Phase Flow Using Fluctuating Hy- process placement, load-balancing, resource allocation. drodynamics

Emmanuel Jeannot Incorporating thermal fluctuations in continuum Navier- INRIA Stokes equations requires the development of numerical [email protected] methods that solve the complex stochastic partial differen- tial equations of fluctuating hydrodynamics. The situation becomes more complex when more than one fluid phase MS262 is involved as in a liquid-vapor system. These stochas- Local Search to Improve Geometric Task Mapping tic PDE’s require a special spatio-temporal discretization so that the correct Gibbs-Boltzmann equilibrium distribu- We present a local search strategy to improve the mapping tion is achieved at long times and the correct fluctuation- of a parallel job’s tasks to the MPI ranks of its parallel allo- dissipation balance is preserved at each time step. We de- cation in order to reduce network congestion and the job’s scribe a stochastic method of lines discretization of the communication time. The goal is to reduce the number fully compressible Landau-Lifshitz-Navier-Stokes (fluctu- of network hops between communicating pairs of ranks. ating hydrodynamics) equations with the van der Waals Using the miniGhost mini-app, which models the shock equation of state. The diffuse interface method is used to physics application CTH, we demonstrate that our strat- model the order parameter (density) as a smooth variation egy reduces application running time while also reducing across the interface. The surface tension effects give rise to the runtime variability. Korteweg type stresses that show up as additional terms in the momentum and energy equations. The numerical Vitus Leung scheme is validated by comparison of measured structure Sandia National Laboratories factors and capillary wave spectra with equilibrium theory. [email protected] We also present several non-equilibrium examples to illus- trate the capability of the algorithm to model multi-phase David Bunde fluid phenomena in a neighborhood of the critical point. Knox College These examples include a study of the impact of fluctu- CS15 Abstracts 207

ations on the spinodal decomposition following a rapid University of Colorado, Boulder quench, as well as the piston effect in a cavity with super- [email protected] cooled walls. The conclusion in both cases is that thermal fluctuations affect the size and growth of the domains in off-critical quenches. MS264 Bayesian Compressive Sensing Framework for Anuj Chaudhri,JohnB.Bell High-Dimensional Surrogate Construction CCSE Lawrence Berkeley Laboratory Surrogate construction for high-dimensional models is chal- [email protected], [email protected] lenged in two major ways: obtaining sufficient train- ing model simulations becomes prohibitively expensive, Alejandro Garcia and non-adaptive basis selection rules lead to excessively San Jose State University large basis sets. We enhanced select state-of-the-art tools [email protected] from statistical learning to build efficient sparse surro- gate representations, with quantified uncertainty, for high- Aleksandar Donev dimensional complex models. Specifically, Bayesian com- Courant Institute of Mathematical Sciences pressive sensing techniques are supplemented by iterative New York University basis growth and weighted regularization. Application to [email protected] a 70-dimensional climate land model shows promising re- sults.

Khachik Sargsyan, Cosmin Safta MS263 Sandia National Laboratories The Long-time Tail of the Velocity Autocorrelation [email protected], [email protected] Function of a Particle in a Molecular Fluid Bert J. Debusschere Through large-sized-ensemble runs of molecular dynamics Energy Transportation Center simulation for a tracer particle suspended in a molecular Sandia National Laboratories, Livermore CA fluid, its velocity autocorrelation function and diffusion co- [email protected] efficient are very accurately determined. The finite-system- size effects of molecular dynamics simulation and the effects of molecular character of the surrounding fluid are investi- Habib N. Najm gated. In addition, our results are compared with theoret- Sandia National Laboratories ical results obtained from the fluctuating hydrodynamics Livermore, CA, USA and computational results obtained from the smoothed- [email protected] particle hydrodynamics.

Changho Kim, George E. Karniadakis MS264 Brown University Inverse Subspace Iteration for Spectral Stochastic Division of Applied Mathematics Finite Element Methods changho [email protected], george [email protected] We study random eigenvalue problems in the context of spectral stochastic finite elements. We assume that the MS264 matrix operator is given in the form of a polynomial chaos expansion, and we search for the coefficients of the polyno- A Low-Rank Approximation Method for High- mial chaos expansions of the eigenvectors and eigenvalues. Dimensional Uncertainty Quantification We formulate a version of stochastic inverse subspace iter- This work introduces a model reduction technique that ex- ation, which is based on stochastic Galerkin finite element ploits the low-rank structure of the solution of interest, method, and we compare its accuracy with that of Monte when exists, for fast propagation of high-dimensional un- Carlo and stochastic collocation methods. certainties. To construct this low-rank approximation, the Bedrich Sousedik proposed method utilizes a hierarchy of models with lower University of Maryland fidelities, than the intended model, which can be simulated [email protected] cheaply. Several numerical experiments will be provided to demonstrate the efficiency of the proposed approach. Howard C. Elman Alireza Doostan University of Maryland, College Park Department of Aerospace Engineering Sciences [email protected] University of Colorado, Boulder [email protected] MS264 Dongbin Xiu Preconditioner for Parameter-dependent Linear University of Utah Systems Based on an Empirical Interpolation of the [email protected] Matrix Inverse We consider parameter-dependent linear systems of equa- Akil Narayan tions, e.g. arising from the discretization of a parameter- University of Massachusetts Dartmouth dependent or stochastic PDE. We propose a parameter de- [email protected] pendent preconditioner defined as an interpolation of the matrix inverse based on a Frobenius norm projection. We Hillary Fairbanks then show how such preconditioner can be used for projec- Department of Applied Mathematics tion based model reduction methods such as the reduced 208 CS15 Abstracts

basis method. We propose constructions of interpolation The Weak Galerkin method is an extension of the standard points that are dedicated either to the improvement of Galerkin finite element method where classical derivatives Galerkin projections or to the estimation of projection er- were substituted by weakly defined derivatives on functions rors. with discontinuity. Recent development of weak Galerkin methods will be discussed in the presentation. Lo¨ıc Giraldi GeM, Ecole Centrale de Nantes Xiu Ye [email protected] University of Arkansas, Little Rock [email protected] Anthony Nouy, Olivier Zahm LUNAM Universite, Ecole Centrale Nantes, CNRS, GeM [email protected], [email protected] MS265 A Divergence-free Weak Galerkin Finite Element

MS265 A weak Galerkin finite element is designed so that the com- Numerical Applications of Weak Galerkin Finite puted velocity is divergence-free. The significance of such Element Methods a method is shown by solving a low-viscosity Stokes prob- lem. The traditional finite elements, weak Galerkin finite Weak Galerkin finite element methods are new numerical elements and discontinous Galerkin finite flements fail to methods for solving partial differential equations that were produce a meaningful solution in solving such a test prob- first introduced by Wang and Ye for solving general second lem. order elliptic partial differential equations (PDEs). The differential operators in PDEs are replaced by their weak Shangyou Zhang forms through the integration by parts, which endows high University of Delaware flexibility for handling complex geometries, interface dis- [email protected] continuities, and solution singularities. This new method is a discontinuous finite element algorithm, which is param- MS266 eter free, symmetric, and absolutely stable. Furthermore, through the Schur-complement technique, an effective im- Implementation of a Fast Multifrontal Solver Using plementation of the weak Galerkin is developed a linear Randomized HSS Compression system involving unknowns only associated with element We present an efficient code for solving large sparse linear boundaries. In this talk, several numerical applications of systems using the multifrontal method with hierarchically weak Galerkin methods will be discussed. semi-separable (HSS) matrices. The low rank compression Lin Mu in HSS limits fill-in and reduces complexity of the solver. Michigan State State University The HSS matrices are constructed using randomized sam- [email protected] pling and rank-revealing QR. ULV decomposition replaces the traditional dense LU. The factorization acts as solver or preconditioner. Shared and distributed memory parallel MS265 results are presented for a range of applications. BPX Preconditioner for Nonstandard Finite Ele- Pieter Ghysels ment Methods for Diffusion Problems Lawrence Berkeley National Laboratory Computational Research Division We propose and analyze an optimal preconditioner for [email protected] a general linear symmetric positive definite (SPD) sys- tem by following the basic idea of the well-known BPX framework. The SPD system arises from a large num- Francois-Henry Rouet ber of nonstandard finite element methods for diffusion Lawrence Berkeley National Laboratory problems, including the well-known hybridized Raviart- [email protected] Thomas and Brezzi-Douglas-Marini mixed element meth- ods, the hybridized discontinuous Galerkin method, the Xiaoye Sherry Li Weak Galerkin method, and the nonconforming Crouzeix- Computational Research Division Raviart element method. We prove that the presented Lawrence Berkeley National Laboratory preconditioner is optimal, in the sense that the condition [email protected] number of the preconditioned system is independent of the mesh size. Numerical experiments provided confirm the theoretical result. MS266 Deterministic and Randomized CUR and Nystrom Xiaoping Xie Approximations Sichuan University, China [email protected] The goal is to improve the accuracy and efficiency of CUR and Nystr¨om approximations, by exploiting traditional ma- trix decompositions. To this end we establish connections MS265 between CUR approximations and LU decompositions, and Recent Development of Weak Galerkin Methods derive conditions for the optimality of CUR decomposi- tions. Furthermore, we express the standard Nystr¨oap- Newly developed weak Galerkin finite element methods proximation as an incomplete Cholesky decomposition, the will be introduced for solving partial differential equations. modified Nystr¨om approximation as a CUR approxima- Weak Galerkin methods have the flexibility of employing tion, and derive residual bounds for deterministic approxi- discontinuous elements and share the simple formulations mations based on rank revealing QR decompositions. The of continuous finite element methods at the same time. results for the deterministic approximations are used to CS15 Abstracts 209

guide and calibrate the randomized algorithms, and we de- plication experts. rive new bounds for uniform and leverage score sampling. Ichitaro Yamazaki UTK Ilse Ipsen [email protected] North Carolina State University Department of Mathematics Theo Mary [email protected] Universite de Toulouse, INPT ENSEEIHT [email protected]

MS266 Jakub Kurzak, Stanimire Tomov Fast Generation of Random Orthogonal Matrices University of Tennessee, Knoxville [email protected], [email protected] Random orthogonal matrices have a wide variety of appli- cations. They are used in the generation of various kinds Jack J. Dongarra of random matrices and random matrix polynomials. The Department of Computer Science random orthogonal matrix (ROM) simulation method uses The University of Tennessee random orthogonal matrices to generate multivariate ran- [email protected] dom samples with the same mean and covariance as an observed sample. The natural distribution over the space of orthogonal matrices is the Haar distribution. One way MS267 to generate a random orthogonal matrix from the Haar Optimized Reduced Order Modeling and Data As- distribution is to generate a random matrix A with ele- similation for Hydrodynamics with Large Time ments from the standard normal distribution and compute Step Observations its QR factorization A = QR,whereR is chosen to have nonnegative diagonal elements; the orthogonal factor Q is This presentation focuses on the theoretical development then the required matrix. Stewart develops a more effi- of numerical methods for problems originating from me- cient algorithm that directly generates an n×n orthogonal teorology and application of two complementary methods matrix from the Haar distribution as a product of House- of decomposing the flow field from experimental measure- holder transformations built from Householder vectors of ments into coherent structures namely: the Proper Or- dimensions 1, 2,...,n− 1 chosen from the standard nor- thogonal Decomposition (POD) and the Dynamic Mode mal distribution. The goal of this work is to design an Decomposition (DMD). Additionally, we aim to apply the algorithm that reduces the computational cost of Stew- four-dimensional variational approach of data assimilation art’s algorithm by giving up the property that Q is exactly (4D-Var) to seek for the model coefficients such that the Haar distributed. We generate orthogonal random Q using derived ROM will inherit good dynamical properties. k Householder transformations. We will argue that for the purpose of test matrix generation we can take k much less Diana Bistrian than the matrix dimension and still obtain an acceptable Dept. of Electrical Engineering and Industrial matrix. We will give performance results on a variety of Information architectures to show the benefits of the new algorithm. University ”Politehnica” of Timisoara diana.bistrian@fih.upt.ro Amal Khabou NRIA Saclay, 4 Rue Jacques Monod 91893 Ionel M. Navon [email protected] Florida State University Department of Scientific Computing Francoise Tisseur [email protected] University of Manchester Department of Mathematics [email protected] MS267 Model Reduction and Sensor Placement in a Feed- Nicholas J. Higham back Flow Control Problem University of Manchester We consider the flow control problem of stabilizing the School of Mathematics wake behind a circular cylinder through the cylinder’s rota- [email protected] tion. Model reduction methods are applied for computing the optimal linear feedback control as well as for choosing the location of a number of velocity measurements that can MS266 be used to practically implement the control law. Numer- Performance of Computing Low-Rank Approxima- ical results demonstrate the effectiveness of the controller tion on Hybrid CPU/GPU Architectures reduction when compared to the full-state linear feedback control. Low-rank matrix approximations play important roles in many statistical, scientific, and engineering applications. Jeff Borggaard In this talk, we study the performance of various algo- Virginia Tech rithms (including random projection/sampling) to com- Department of Mathematics pute such approximation of large sparse matrices on a hy- [email protected] brid CPU/GPU architecture. Ultimately, we would like to develop robust, efficient, and flexible software that com- Serkan Gugercin putes such approximation for a wide range of applications. Virginia Tech. One objective for this talk is to seek inputs from such ap- Department of Mathematics 210 CS15 Abstracts

[email protected] Fangxin Fang Department of Earth Science and Engineering Lizette Zietsman Imperial College London, U.K. Virginia Tech [email protected] Interdisciplinary Center for Applied Mathematics [email protected] Christopher Pain Imperial College [email protected] MS267 Goal-Based Rom Adjoint for Optimal Sensor Loca- Andrew G. Buchan tions and Data Assimilation Department of Earth Science & Engineering Imperial College An goal-based reduced order modelling (ROM) adjoint ap- [email protected] proach is developed for optimising sensor locations. An adjoint (or sensitivity) based error measure is formulated Ionel M. Navon which measures the error contribution of each solution vari- Florida State University able to an overall goal (defined as a measure of what is Department of Scientific Computing deemed important in a problem). It provides importance [email protected] maps for determining where best to place the monitoring devices. The expensive data resources will be efficiently used for data assimilation. MS268 Fangxin Fang Higher Order Finite Volume Approximations of the Department of Earth Science and Engineering Inviscid Primitive Equations in a Complex Domain Imperial College London, U.K. [email protected] We construct the cell-centered finite volume discretization of the two-dimensional inviscid primitive equations in a do- Christopher Pain main with topography. To compute the numerical fluxes, Imperial College the so-called (first order) upwind scheme and the (second [email protected] order) central-upwind scheme are introduced. Numerical simulations verify that the upwind and central-upwind are robust schemes regardless of the shape or size of the topog- Ionel M. Navon raphy. Florida State University Department of Scientific Computing [email protected] Gung-Min Gie Indiana University USA Zhizhao Che [email protected] Chemical Engineering, Imperial College London [email protected] Arthur Bousquet, YoungJoon Hong Indiana University Andrew G. Buchan, Pavlidis Dimitrios [email protected], [email protected] Department of Earth Science & Engineering Imperial College [email protected], Roger M. Temam [email protected] Inst. for Scientific Comput. and Appl. Math. Indiana University [email protected] Dunhui Xiao Department of Earth Science and Engineering Imperial Colleg London [email protected] MS268 A New Atmospheric Dynamic Core using 4th Or- der Flux Reconstruction Method with WENO Lim- MS267 iting Reduced Order Modelling (rom) of the Navier- Stokes Equations for 3D Free Surface Flows In this talk, we present a dynamic core for compress- ible non-hydrostatic atmosphere by using a newly devised This article presents a reduced order modelling method for high-resolution scheme, so-called FR4-CD-WENO (4th or- Navier-Stokes Equations for 3D free surface flows. This der Flux-Reconstruction with Constrained Derivative us- work is the first to introduce ROM into 3D free surface ing WENO limiting). Compared to the existing WENO- flows. This newly ROM reduced CPU time for solving 3D DG paradigm, the FR4-CD-WENO method shows supe- free surface problems by orders of magnitude while keeping riorities in at least three aspects. 1) It makes use of the a high accuracy. This ROM has significant potential ad- sub-cell information of the local reconstruction instead of vantages in : interactive use, emergency response, control the cell-averaged values, which results in a compact stencil and uncertainty analysis. for reconstruction, 2) It is more accurate than the WENO- DG scheme using the same degrees of freedom, and 3) It Dunhui Xiao is algorithmically simpler and more computationally effi- Department of Earth Science and Engineering cient. We have developed the FR4-CD-WENO dynamic Imperial Colleg London core for atmospheric flows and shown it as a very promis- [email protected] ing framework for high-performance atmospheric models. CS15 Abstracts 211

University of California, Los Angeles Department of Atmospheric and Oceanic Sciences Xingliang Li [email protected] Center of Numerical Weather Predication, China Meteorological Administration YoungJoon Hong [email protected] Indiana University [email protected] Ziyao Sun Department of Energy Sciences Joseph J. Tribbia Tokyo Institute of Technology Nat’l Center for Atmospheric [email protected] Research [email protected] Feng Xiao Tokyo Institute of Technology [email protected] MS268 Title Not Available at Time of Publication Chungang Chen Xi’an Jiaotong Unversity Abstract not available at time of publication. [email protected] Yau Shu Wong Xueshun Shen University of Alberta Center of Numerical Weather Predication, [email protected] China Meteorological Administration [email protected] MS269 Ming Xue Towards Efficient N-x Contingency Selection Using Center for Analysis and Prediction of Storms Group Betweenness Centrality University of Oklahoma [email protected] The goal of N - x contingency selection is to pick a sub- set of critical cases to assess their potential to initiate a severe crippling of an electric power grid. Even for a mod- MS268 erate sized system there can be an overwhelmingly large Numerical Weather Prediction in Two Dimensions number of contingency cases that need to be studied. The with Topography, using a Finite Volume Method number grows exponentially with x. This combinatorial explosion renders any exhaustive search strategy computa- We aim to study a finite volume scheme to solve the two tionally infeasible, even for small to medium sized systems. dimensional inviscid primitive equations of the atmosphere We propose a novel method for N - x contingency selection with humidity and saturation, in presence of topography for x ¿ 1 using group betweenness centrality and show that and subject to physically plausible boundary conditions to computation can be relatively decoupled from the prob- the system of equations. The equations are a nonlinear lem size. Thus, making contingency analysis feasible for system of equations close to the Euler equations (the in- large systems with x ¿ 1. Consequently, it may be that N viscid Primitive Equations), which are coupled with the - x (for x ¿ 1) contingency selection can be effectively de- equation for the content of water vapor. These equations ployed despite the combinatorial explosion of the number form a nonlinear system of partial differential equations, of potential N - x contingencies. with discontinuities due to the change of phase. A version of the projection method is introduced to enforce the com- Mahantesh Halappanavar patibility condition on the horizontal velocity field, which Pacific Northwest National Laboratory comes from the boundary conditions. The resulting scheme [email protected] allows for a significant reduction of the errors near the to- pography when compared to more standard finite volume Yousu Chen schemes. In the numerical simulations, we first present the Pacific Northwest National Lab convergence results that are satisfied by the solutions simu- [email protected] lated by our scheme when compared to particular analytic solutions. We then report on numerical experiments using Zhenyu Huang realistic parameters. Finally, the effects of a random small- Pacific Northwest National Laboratory scale forcing on the velocity equation is numerically inves- [email protected] tigated. The numerical results show that such a forcing is responsible for recurrent large-scale patterns to emerge in the temperature and velocity fields. MS269 Computational Study of Security-Constrained Eco- Roger M. Temam nomic Dispatch with Multi-Stage Rescheduling Inst. for Scientific Comput. and Appl. Math. Indiana University Security-constrained economic dispatch with multiple [email protected] stages of rescheduling gives rise to a linear program that is not solvable by traditional LP methods due to its large Arthur Bousquet size. We devise a series of algorithmic enhancements based Indiana University on the Benders’ decomposition method to ameliorate the [email protected] computational difficulty. We also propose a set of online measures to correct infeasibility encountered in the solu- Mickael Chekroun tion process. The approach, coded in GAMS, is able to 212 CS15 Abstracts

process large network cases. Hybrid Shared/distributed Memory Computing

Yanchao Liu Task-based parallelism is a well-known paradigm for effi- University of Wisconsin cient and scalable shared-memory parallel computing. In [email protected] this talk, we will present QuickSched, a library for task- based parallelism which extends the usual model of tasks MichaelC.Ferris and dependencies by conflicts between tasks, and by speci- University of Wisconsin fying explicitly which resources are used by which task. We Department of Computer Science show how this approach allows us to provide good scaling [email protected] for problems with complex task hierarchies. We also show how QuickSched extends task-based parallelism to CUDA- Feng Zhao based GPUs. The task/resource decomposition is also use- ISO New England ful for hybrid shared/distributed-memory computations, [email protected] e.g. on clusters of multicores. The task graph can be used to equitably partition the work involved in a compu- tation over a set of distributed-memory nodes, as opposed MS269 to simply partitioning the data. Furthermore, the task- based system can be used to implement fully asynchronous Moment-Based Relaxations of the Optimal Power communication between distributed-memory nodes on top Flow Problem of MPI.

The optimal power flow (OPF) problem seeks an optimal Pedro Gonnet operating point for an electric power system subject to con- University of Oxford straints from both the network physics and engineering lim- [email protected] its. We present a hierarchy of moment-based convex relax- ations that globally solve many non-convex OPF problems for which existing relaxations fail. This talk demonstrates MS270 the capabilities of the moment relaxations using illustra- Parallelization Techniques for Tsunami Simulation tions of the feasible spaces of small example OPF problems. Using Space-Fillig-Curve Orders We also describe recent work on computational improve- ments for the moment relaxations, including the exploita- Samo(oa)2 is a parallel code for element-oriented numer- tion of sparsity, which enable global solution of larger OPF ical solution of PDEs based on space-filling curve traver- problems. sals. Heuristics and methods for adaptive, parallel grids are gained by sequential element orders induced by the Daniel Molzahn,IanHiskens Sierpinski curve, which provide an efficient approach that University of Michigan we use as basis for an application framework. We imple- [email protected], [email protected] mented a model that simulates tsunamis originating from time-dependent sea-floor displacements computed from an MS269 earthquake simulation (Galvez et al.). Parallel perfor- mance was studied with hybrid OpenMP/MPI paralleliza- Decomposition Algorithms for Transmission and tion and several load balancing techniques that exploit in- Generation Investment Planning herent properties of the space-filling curve.

Stochastic transmission and generation expansion plan- Michael Bader, Oliver Meister ning models are receiving increasing attention among re- Technische Universit¨at M¨unchen searchers today. They are being used to explicitly model [email protected], [email protected] uncertainties that result from the increasing penetration of renewable energy technologies, as well as from long- term market and regulatory conditions. However, existing MS270 commercial planning tools still lack stochastic capabilities. A Patchwork Family - Task Distribution Patterns We propose a two-stage investment-planning model that for Shallow Water Equations on Patch-structured takes into account the aforementioned uncertainties, and AMR Grids we describe a scalable decomposition algorithm to solve real-sized problems. An application of our algorithm is Spacetrees holding regular Cartesian patches are a powerful illustrated using a 240-bus network representation of the formalism to describe dynamically adaptive Cartesian grids Western Electricity Coordinating Council. We discuss its that scale on manycores. In previous work, we successfully performance when implemented in both the Red Mesa/Sky used this formalism to solve shallow water equations. The supercomputer and a commodity multi-core workstation. choice of a proper block size here is delicate. While large block sizes foster loop parallelism and vectorisation, they Francisco Munoz restrict the adaptivity’s granularity. They increase the to- Sandia National Laboratories tal memory footprint and lower the numerical accuracy per [email protected] invested byte. Though small patches exhibit a high inter- block concurrency they are surprisingly outperformed by Jean-Paul Watson huge blocks processed by a plain parallel-for on Xeon Phis. Sandia National Laboratories This insight from our previous work has motivated us to Discrete Math and Complex Systems introduce algorithms that automatically detect assemblies [email protected] of patches that can be fused into one big patch and then to replace the assemblies by such a regular data structure. The present talk rolls back to a small-patch formulation MS270 and studies the patch performance, in particular the con- QuickSched - Using Tasks for Massively Parallel currency, en detail. We propose to formalise inter-block CS15 Abstracts 213

parallelism as tasks each representing one patch update. approximately or exactly divergence-free discrete magnetic These tasks then are fired into a scheduler to be deployed field values, including hyperbolic divergence-cleaning, con- among the cores. We study the arising distribution pat- strained transport, and elliptic projection techniques. In terns and try to put the best-case data and task assign- this work we develop a high-order discontinuous Galerkin ment into relation to the data access patterns of the fused version of the elliptic projection method that produces a patches. globally divergence-free magnetic field. After developing it, we show how to efficiently implement this method both Tobias Weinzierl on Cartesian and unstructured grids. The resulting scheme Durham University is applied to several standard test cases. [email protected] James A. Rossmanith MS270 Iowa State University Deparment of Mathematics Understanding Tsunami and Hurricane Deposits [email protected] with a Mess-Scale Model for Sediment Dynamics A meaningful event history for storms and tsunamis does not only include the number of events, but also contains MS271 information of the magnitude of each event. Conventional methods to simulate the sediment dynamics in tsunamis Multi-Fluid Plasma Modeling Through the Colli- and storms have so far failed to reproduce the fine de- sional Transition Regime tail that real deposits feature. We employ a meso-scale approach to do this with some success. Our model runs Plasmas consist of charged particles that interact through on HPC platforms containing multi-CPU and multi-GPU electromagnetic fields and collisions. Neutral particles achitectures. when present interact only through collisions. For low col- lisionality, a multi-species kinetic model must be used. For Robert Weiss, Wei Cheng high collisionality, a fluid model with lower dimensional- Virginia Tech ity can be used. Multi-fluid plasma models approximate Department of Geosciences the velocity distribution function by a limited number of [email protected], [email protected] moments for each species. Models with higher moments extend the region of validity and relax the assumption of local thermodynamic equilibrium. MS271 Block Adaptive MHD Simulations for Solar Coro- Uri Shumlak, Andrew Ho nal Dynamics Aerospace and Energetics Research Program University of Washington I will present the open source MPI-AMRVAC simulation [email protected], [email protected] toolkit [Keppens et al., 2012, JCP 231, 718-744], with a focus on solar physical applications modeled by its mag- netohydrodynamic module. Spatial discretizations avail- Robert Lilly able cover standard shock-capturing finite volume algo- University of Washington rithms, but also extensions to conservative high-order fi- [email protected] nite difference schemes, both employing many flavors of limited reconstruction strategies. Multi-step explicit time Sean Miller stepping includes strong stability preserving high order Aerospace and Energetics Research Program Runge-Kutta steppers to obtain stable evolutions in multi- University of Washington dimensional applications realizing up to fourth order accu- [email protected] racy in space and time. The parallel scaling of the code is discussed and we obtain excellent weak scaling up to 30000 Noah F. Reddell, Eder Sousa processors allowing to exploit modern peta-scale infrastruc- University of Washington ture. Solar physics applications target the formation of flux [email protected], [email protected] rope topologies through boundary-driven shearing of mag- netic arcades, following the in situ condensation of promi- nences in radiatively controlled evolutions of arcades and MS271 fluxropes, and the enigmatic phenomenon of coronal rain, where small-scale condensations repeatedly form and rain Positivity-Preserving Weno Schemes with Con- down in thermodynamically structured magnetic arcades. strained Transport for Ideal MHD Rony Keppens We will present a novel positivity-preserving flux limiting KU Leuven technique developed for WENO schemes to solve idea mag- Centre for Mathematical Plasma-Astrophysics netohydrodynamic (MHD) equations. There are two main [email protected] steps in our MHD solver: first updating conservative quan- tities by WENO scheme with positivity-preserving limiter MS271 and then correcting the magnetic field and total energy by a high-order constrained transport approach. Several ex- Globally Divergence-Free Projection Methods for amples are presented to verify the order of accuracy and to Ideal Magnetohydrodynamics demonstrate the efficiency of positivity-preserving limiter. It has been long established in the literature that control- ling magnetic field divergence errors in compressible mag- Qi Tang netohydrodynamic (MHD) simulations is necessary for nu- Department of Mathematics merical stability. Many approaches exist to achieve either Michigan State University 214 CS15 Abstracts

[email protected] ments and present our progress to date in their implemen- tation.

MS272 David M. Hall A High-Order Global Discontinuous Galerkin Non- University of Colorado at Boulder Hydrostatic Atmospheric Model Using Hevi Time Department of Computer Science Integration Scheme [email protected]

Availability of peta-scale computing resources facilitate de- Henry Tufo velopment of high-resolution non-hydrostatic (NH) atmo- NCAR spheric model at a global scale. Discontinuous Galerkin University of Colorado at Boulder (DG) method is an ideal candidate for such model de- [email protected] velopment because of its inherent conservation property, geometric flexibility and excellent parallel efficiency. We consider a NH atmospheric model based on DG spatial MS272 discretization on cubed-sphere grid. The model uses the Tempest: Efficient Computation of Atmospheric horizontally-explicit and vertical-implicit (HEVI) operator- Flows Using High-Order Local Discretization split time integration method to overcome the CFL limi- Methods tation resulting from the small vertical grid-spacing, and is constrained only by the minimum horizontal resolution. The Tempest Framework composes several numerical The performance of the DG-HEVI model will be evaluated methods to easily facilitate intercomparison of non- through a suite of benchmark test cases. hydrostatic atmospheric flow calculations on the sphere. This framework includes the implementations of Spec- Ram Nair tral Elements, Discontinuous Galerkin, Flux Reconstruc- NCAR tion, and Hybrid Finite Element methods with the goal of Institute for Mathematics Applied to Geosciences achieving optimal accuracy and efficiency in computing the [email protected] solution of atmospheric problems. Several advantages of this approach are discussed such as: improved pressure gra- Lei Bao dient calculation, numerical stability by vertical/horizontal University of Colorado at Boulder splitting, arbitrary order of accuracy, etc. The local nu- Dept. of Applied Mathematics merical discretization allows for high performance parallel [email protected] computation and efficient inclusion of parameterizations. Paul Ullrich MS272 University of California, Davis Vertical Discretization of Geophysical Flows with [email protected] the Hybrid Finite Element Method - Normal Mode and Wave Dispersion Properties MS273 The Hybrid Finite Element Method is a new technique Ongoing Developments in BigDFT towards the ab- that takes advantage of the arbitrary order of accuracy of initio Computation of Resonant States the discontinuous Galerkin and Spectral Element methods Siegert’s resonant states provide a convenient description of and provides a combined, natural setting for the imple- unoccupied electronic states of atoms and molecules, since mentation of grid staggering. We present a discrete nor- few (discrete) resonant states carry as much information mal mode analysis of this method for the vertical direction as many (in principle infinite) continuum states. The com- using the linearized Euler equations. 2-D simulations will plex scaling method, and generalizations thereof, allows be shown demonstrating atmospheric waves reproduced by one to compute resonant states as particular eigenstates of the HFEM compared to traditional methods. complex-symmetric Hamiltonians. In my presentation, I Jorge E. Guerra will discuss the application of Polizzi’s FEAST eigensolver Department of Land, Air and Water Resources to the iterative, matrix-free extraction of resonant states University of California, Davis from complex-scaled Kohn-Sham Hamiltonians. [email protected] Alessandro Cerioni Institute of Nanosciences and Cryogeny Paul Ullrich CEA - Grenoble University of California, Davis [email protected] [email protected] Luigi Genovese MS272 Institut Nanosciences et Cryog´enie, CEA [email protected] Toward Exa-Scale Computing in CAM-SE

Supercomputers are projected to achieve exa-flop scales Thierry Deutsch within the next fire years, providing enough computa- Institute of Nanosciences and Cryogeny tional power to perform climate simulations with lateral CEA resolutions approaching or exceeding the hydrostatic bar- [email protected] rier. To perform accurate simulations at these resolutions, CAM-SE will require new technologies including: nonhy- Ivan Duchemin drostatic dynamical solvers, increased vertical accuracy, Institute of Nanosciences and Cryogeny improved variable-resolution grids, and scale-aware param- CEA France eterizations. We will discuss the need for these improve- [email protected] CS15 Abstracts 215

Maxime Moriniere [email protected], [email protected] Institute of Nanosciences and Cryogeny CEA - Grenoble [email protected] MS274 Scalable Algorithms for Optimal Control of Sys- MS273 tems Governed by PDEs under Uncertainty

Planning the Next Generation of Electronic Struc- We focus on optimal control of systems governed by PDEs ture Codes with random coefficient functions. We seek controls that minimize an objective function that incorporates mean and Pseudopotential density functional theory implemented in variance of the control objective. To enable applications real space provides a means for computing the properties of to problems with infinite-dimensional (high-dimensional materials in many different forms, including liquids, solids, when discretized) parameters, we consider linearization of and nanoscale structures. Current approaches yield self- the control objective at the mean of the uncertain param- consistent solutions for systems with thousands of atoms. eters. As application, we consider optimal control of a However, there remain systems where quantum mechani- porous medium flow model with a random permeability cal accuracy is desired, but scalability proves to be a hin- field. drance. We will present an overview of our work on algo- rithms for this problem, which performs spectrum slicing in the eigensolver. Alen Alexanderian University of Texas at Austin [email protected] James R. Chelikowsky Institute for Computational Engineering and Sciences University of Texas at AUstin Noemi Petra [email protected] University of California, Merced [email protected]

MS273 Georg Stadler Courant Institute for Mathematical Sciences A Projected Preconditioned Conjugate Gradient New York University Algorithm for Eigenvalue Calculation [email protected]

We examine a projected gradient algorithm for computing Omar Ghattas a relatively large number of lowest eigenvalues of a Hermi- The University of Texas at Austin tian matrix. The algorithm performs fewer Rayleigh-Ritz [email protected] calculations than some of the existing algorithms, thus has better parallel scalability. It is relatively easy to imple- ment (for example in the Quantum Espresso package). We MS274 will discuss a number of practical issues for implementing this algorithm, and demonstrate its performance in Kohn- A Scalable Compositional Approach to Uncertainty Sham density functional theory based electronic structure Quantification for the Optimization under Uncer- calculations. tainty of Multi-physics Systems

Chao Yang, Eugene Vecharynski Complex multi-physics systems often exhibit a great deal Lawrence Berkeley National Lab of uncertainty due to unexpected interactions. To ensure [email protected], [email protected] a sufficiently reliable and robust system, rigorous design under uncertainty must be carried out with models ca- John Pask pable of precisely representing multi-physics interactions. Lawrence Livemore National Lab We propose a compositional approach to uncertainty quan- [email protected] tification based on importance sampling that enables an offline/online approach to optimization under uncertainty with high-fidelity physics-based models. Our approach is MS273 demonstrated on the design of a gas turbine blade. Updating Strategies for Efficient Large-Scale Elec- tronic Structure Calculations Doug Allaire Texas A&M [email protected] We give an introduction to our recently published Blocked Householder-CholeskyQR algorithm which has been devel- oped for the dense symmetric eigensolver ELPA, whereat Sergio Amaral the QR-decomposition of tall and skinny matrices repre- Department of Aeronautics & Astronautics sents an important substep. Further, we show the benefits Massachusetts Institute of Technology of this algorithm on today’s HPC systems in terms of par- [email protected] allel efficiency. Finally, we give an outlook on modifying the classical ELPA solver,e.g. for updating the eigenspace Kaiyu Li information in case of small changes. Texas A&M [email protected] Roland Wittmann, Thomas K. Huckle Institut fuer Informatik Karen E. Willcox Technische Universitaet Muenchen Massachusetts Institute of Technology 216 CS15 Abstracts

[email protected] algorithms to preprocess the matrix structure and to max- imize sparsity in the approximate inverse factors. We de- scribe the preordering, analysis and factorization phase MS274 of the construction, we assess their performance, consider Stochastic Reduced-Order Models in Optimization strategies for automatic parameter selection, and we dis- and Inverse Problems cuss applications to preconditioning least-squares prob- lems. This work presents a novel approach for inverse problems in the presence of uncertainty using stochastic reduced or- Yiming Bu der models (SROMs). Given the statistics of an uncertain University of Groningen observed quantity, the statistics of unknown system pa- [email protected] rameters are estimated through the solution of a stochastic optimization problem. The proposed framework is based Bruno Carpentieri on the representation of a random quantity using a SROM Insitute for Mathematics and Computation an optimal discrete approximation to a continuous random University of Gronengin element that permits efficient and non-intrusive stochastic [email protected] computations.

Wilkins Aquino MS275 Associate Professor A Recursive Multilevel Approximate Inverse- Dept. of Civil and Environmental Engineering, Duke Based Preconditioner for Solving General Linear Univ. Systems [email protected] Abstract not available at time of publication. James Warner Nasa Langley Research Center Bruno Carpentieri [email protected] Insitute for Mathematics and Computation University of Gronengin Mircea Grigoriu [email protected] Cornell University [email protected] MS275 Krylov Subspace Methods Preconditioned by Inner MS274 Iterations for Rank-Deficient Least Squares Prob- Integration of Approximate Schur Preconditioners lems and SQP Algorithms for Nonlinear PDE Optimiza- tion under Uncertainty Inner-iteration preconditioning performed by several iter- ations of stationary iterative methods including the SOR- We study the integration of Schur preconditioners for opti- type method is applied to Krylov subspace methods such mality systems and matrix-free composite-step sequential as the CG-, MINRES-, and GMRES-type methods for solv- quadratic programming (SQP) algorithms in the context of ing rank-deficient least squares problems. We present the- partial differential equation (PDE) constrained optimiza- oretical justifications for using these methods. Numerical tion under uncertainty. Our approach extends the recently experiments on large sparse problems show that the pro- introduced optimal solvers for PDE-constrained optimiza- posed methods are more robust and efficient compared to tion to a wide range of problems in optimal engineering previous methods for some problems. design, including those governed by PDEs with random inputs. We present numerical examples in thermal-fluid Keiichi Morikuni control, acoustic design and topology optimization. Instiute of Computer Science Academy of Sciences of the Czech Republic Denis Ridzal [email protected] Sandia National Laboratories [email protected] Miroslav Rozloznik Institute of Computer Science Drew P. Kouri Czech Academy of Sciences Optimization and Uncertainty Quantification [email protected] Sandia National Laboratories [email protected] Ken Hayami National Institute of Informatics Bart G. Van Bloemen Waanders [email protected] Sandia National Laboratories [email protected] MS275 Global Adaptive Dropping in Incomplete Factor- MS275 izations Recursive Multilevel Approximate Inverse-Based Preconditioning Incomplete factorizations represent an important compo- nent in solving large sparse systems of equations and linear We present an algebraic recursive multilevel approximate least squares problems. A new approach for SPD matrices inverse preconditioner based on a distributed Schur com- is described. It is based on the factorized approximate in- plement formulation, for solving systems of linear equa- verse that links together the inverse and direct factors. The tions. The proposed solver uses recursive combinatorial strategy is motivated by the floating-point behavior of the CS15 Abstracts 217

decomposition that implies an algorithm where dropping drawn from a Gaussian mixture model (GMM) with sparse of the incomplete decomposition mimicks propagation of precision matrices. Previous work has shown: (i) a signal the rounding errors. Numerical experiments demonstrate drawn from a given GMM can be perfectly reconstructed its efficiency. from r noise-free measurements if the (dominant) rank of each covariance matrix is less than r; (ii) a sparse Gaus- Miroslav Tuma sian graphical model can be efficiently estimated from fully- Academy of Sciences of the Czech Republic observed training signals using graphical lasso. This paper Institute of Computer Science addresses a problem more challenging than both (i) and [email protected] (ii), by assuming that the GMM is unknown and each sig- nal is only partially observed through incomplete linear Jiri Kopal measurements. Under these challenging assumptions, we Technical University in Liberec develop a hierarchical Bayesian method to simultaneously [email protected] estimate the GMM and recover the signals using solely the incomplete measurements and a Bayesian shrinkage prior Miro Rozloznik that promotes sparsity of the Gaussian precision matrices. Czech Academy of Sciences In addition, we provide theoretical performance bounds to Prague, Czech Republic relate the reconstruction error to the number of signals for [email protected] which measurements are available, the sparsity level of pre- cision matrices, and the incompleteness of measurements. Theproposedmethodisdemonstratedextensivelyoncom- MS276 pressive sensing of imagery and video, and the results with Model-Based Sketching and Recovery with Ex- simulated and hardware-acquired real measurements show panders significant performance improvement over state-of-the-art methods. Linear sketching and recovery of sparse vectors with ran- domly constructed sparse matrices has numerous appli- Larry Carin cations in several areas, including compressive sensing, Electrical & Computer Engineering data stream computing, graph sketching, and combinato- Duke University rial group testing. This work considers the same prob- [email protected] lem with the added twist that the sparse coefficients of the unknown vector exhibit further correlations as deter- mined by a known sparsity model. We prove that exploit- MS276 ing model-based sparsity in recovery provably reduces the sketch size without sacrificing recovery quality. We also Practical Compressed Sensing: On Asymptotic present the model-expander iterative hard thresholding al- Structure gorithm for efficient recovery of model sparse signals from linear sketches. Compressed Sensing allows recovery from undersampled data, a desirable feat in many applications, e.g. MRI, mi- Luca Baldassarre croscopy, tomography, imaging, interferometry etc. How- Ecole´ Polytechnique F´ed´erale de Lausanne ever, a wide gap exists between practice and traditional luca.baldassarre@epfl.ch CS theory as some of its principles such as sparsity and incoherence are unsuitable. This talk shows how new CS Volkan Cevher principles, namely asymptotic sparsity, asymptotic inco- EPFL herence and multilevel sampling, provide a better fit for volkan.cevher@epfl.ch practical problems and help to better understand under- lying phenomena and significantly improve results in real- world applications. MS276 Performance Limits of Ideal Decoders in Linear In- Bogdan Roman verse Problems University of Cambridge [email protected] In this talk, we focus on the fundamental performance lim- its that can be expected from an ideal decoder given a general model in a linear inverse problem. We link the MS277 existence of an instance optimal decoder and the Null Space Property of the measurement operator in very gen- Optimal Energy Conserving Local Discontinuous eral cases. We prove that in this general setting, the lower- Galerkin Methods for Second-Order Wave Equa- RIP yields instance optimality with an operator-dependent tion in Heterogeneous Media norm called the M-norm while the upper-RIP allows to up- per bound this M-norm by an operator-independent norm. Abstract not available at time of publication.

Anthony Bourrier Ching-Shan Chou IRISA Department of Mathematics [email protected] Ohio State University [email protected] MS276 Statistical Methods in Compressive Sensing: The- MS277 ory and Experiment Performance Analysis of High-Order Discontinuous This talk is concerned with compressive sensing of signals Galerkin Methods for First and Second Order For- 218 CS15 Abstracts

mulation of the Wave Equation approach and some numerical results.

Abstract not available at time of publication. Peter B. Monk Department of Mathematical Sciences Julien Diaz University of Delaware Team-Project Magique-3D [email protected] INRIA Bordeaux Sud-Ouest [email protected] MS278 MS277 An Exponentially Convergent Convolution The Double Absorbing Boundary Formulation of Quadrature Method for Time-Domain Bound- Complete Radiation Boundary Conditions ary Integral Equations

Complete radiation boundary conditions are local se- The Convolution Quadrature method is a recent method quences implementing optimal rational approximations to to solve time-domain wave problems with Boundary Ele- the exact time-domain DtN map. Our original implemen- ment Methods. We present new results on the exponen- tation of CRBCs was for first order systems and was not tially convergence of the CQ solution to the exact solution directly generalizable to second order formulations. The of the underlying time-stepping scheme. These results rely double absorbing boundary method provides an easy al- on the analyticity of the frequency-domain solution and on ternative formulation which can be directly applied to sec- the location of the resonant poles. We study the influence ond order equations. We will outline the stability theory of on the convergence of the scheme used for the time dis- double absorbing boundaries, and demonstrate implemen- cretisation, the contour involved in the inverse transform, tations for a variety of volume discretizations. and the number of frequency problems solved. Thomas M. Hagstrom Southern Methodist University Nicolas Salles,TimoBetcke Department of Mathematics University College London [email protected] [email protected], [email protected]

MS277 MS278 Second-Order Wave Equation with Uncertain Pa- Fast Galerkin Method for Parabolic Space-Time rameters: Analysis and Computation Boundary Integral Equations Abstract not available at time of publication. Layer potentials of the heat equation are coercive in appro- Mohammed Motamed priate anisotropic Sobolev spaces. This fact implies stabil- Department of Mathematics and Statistics ity and error estimates for Galerkin methods. The resulting The University of New Mexico linear systems are block-lower triangular and can be solved [email protected] by block-forward elimination. To handle the cost of dense matrix calculation a space-time version of the fast multi- pole method can be used, which allows the computation MS278 a matrix vector product with nearly optimal cost. Fur- ≤ 2 Adaptive Time Domain Boundary Element Meth- ther, if the space-time meshwidths satisfy ht Chx the ods (TD-BEM) for Scattering Problems conditioning of the linear system in each time step does not grow with mesh refinements. We will also discuss the We investigate a generalized version of the MOT method application of the methodology to three-dimensional tran- for TD-BEM, which allows variable time-steps in an adap- sient Stokes flow. Perhaps surprisingly, this is not straight tive algorithm. The residual error estimator is based on forward, because of different properties of the fundamental new regularity results. We also discuss numerical quadra- solutions of the heat and Stokes equations. ture schemes for the evaluation of the time-dependent Galerkin elements. Our theoretical results are underlined Johannes Tausch by several numerical examples. Southern Methodist University Department of Mathematics Matthias Maischak, Matthias Gl¨afke [email protected] Brunel University [email protected], m [email protected] MS279 MS278 Overview Co-Design at the DOE NNSA Trilabs Convolution Quadrature Discretization of Volume Integral Equations Los Alamos, Lawrence Livermore, and Sandia National laboratories, collectively know as the Department of En- Time domain scattering from an inhomogeneous penetra- ergy NNSA Trilabs, have been conducting a variety of code- ble medium can be formulated as a time domain volume sign studies. In this presentation we give an overview of a integral equation. This equation can be discretized in time recently completed trilab milestone that focused on an ex- using convolution quadrature. Using a Fourier basis in ploration of the capabilities and characteristics of emerging space, the resulting integral operators can be diagonalized and expected future architectures. to allow fast operator evaluation. The fully discrete system can then be solved by marching on in time and an itera- Richard Barrett tive two grid procedure. We provide an analysis of this Sandia National Laboratories CS15 Abstracts 219

[email protected] jeff[email protected]

MS279 MS280 Mathematical Modeling in the Early Grades The ∇-Nabla Time-Composite Approach for Multi- Physics Applications Productivity The common core state standards for mathematics specif- ically name modeling with mathematics as a mathemati- The numerical-analysis specific ∇ language provides a cal practice. Applied mathematicians, especially those en- new approach for integrating next generation multi- gaged in mathematical modeling are in a great position physics large-scale scientific applications. Reflection to work with mathematics education specialists, teachers, and hierarchical-logical-time composition are combined to curriculum developers and students to decide how students demonstrate productive practices and abilities for agile will enact this standard in the classroom. I will share production at extreme-scale. The gain in abstraction with the conclusions of such a group, describe a new three year ∇ during design improves portability, allowing composable project and solicit feedback from the audience about the software integration for continually changing hardware ar- potential for mathematical modeling in the early grades. chitectures. This presentation will illustrate these new pos- sibilities on several proxies to build a multi-physics appli- Rachel Levy cation within the above-cited codesign space. Harvey Mudd College [email protected] Jean-Sylvain Camier CEA, DAM, DIF [email protected] MS280 Applied and Computational Mathematics at the High School Level MS279 Secondary schools in the US offer their students a varying Multi-Material ALE in the Blast Code level of access to rich mathematical modeling topics. Some schools offer entire courses centered on mathematical mod- The goal of the BLAST project is to develop a new multi- eling practices while others offer very little. Our working physics ALE code based on higher-order finite elements. In group has developed a set of recommendations for ques- this talk I will explain how we handle multi-material mixed tions to investigate and tasks to carry out that might help cells during the Lagrangian and remap phases. The main infuse models and modeling across the curriculum. Please topics will include the application of higher-order finite ele- join us to explore these ideas further in a constructive con- ments to multi-material closure models, remap approaches versation. that preserve monotonicity, conservation and synchroniza- tion between different fields and materials, elimination of Katherine Socha artificial mixing during remap. Math for America [email protected] Vladimir Tomov Lawrence Livermore National Laboratory Kathleen Fowler [email protected] Clarkson University Department of Mathematics [email protected] MS279 Co-Design Studies Using Mini-Multifluid-Ppm MS280 Modeling Across the Curriculum: Introduction Abstract not available at time of publication. and Overview

Paul R. Woodward This talk will begin with background information on the Laboratory for Computational Science and Engineering Modeling across the Curriculum, MaC, initiative, an NSF- University of Minnesota sponsored SIAM program aimed at advancing modeling [email protected] and computational applied mathematics throughout the educational spectrum. The main focus will be on the sec- ond MaC workshop held in January 2014 and the resulting MS280 report and recommendations. The subsequent talks will Modeling Across the Undergraduate Curriculum go more deeply into the three primary themes of the work- shops. We report on the findings of the undergraduate group for Peter R. Turner the Modeling Across the Curriculum II Workshop. We dis- Clarkson University cuss the curricular gaps between the status quo in academia School of Arts & Sciences today and what is needed to meet the challenges of a glob- [email protected] ally competitive workforce in the 21st Century. Along the lines of the two NRC reports Mathematical Sciences 2025 report and its companion piece Fueling Discovery and In- MS281 novation, we discuss several recommendations that came Singular Values and Convex Programming for from our group. Power System Synchrophasor Data Management Jeffrey Humpherys This talk centers on the efficient processing of the obser- Brigham Young University vations of phasor measurement units (PMUs) for power 220 CS15 Abstracts

system monitoring. Different from traditional PMU data [email protected] analysis that typically analyzes individual PMU channels separately, we propose a spatial-temporal framework of col- lectively processing measurements of PMUs in electrically MS281 close regions. Leveraging the low-dimensionality of PMU Efficient Algorithms for N-x Contingency Analysis data, various data management issues such as missing data for Power Grids recovery and data substitution detection can be addressed by solving computationally efficient convex programs. N-x contingency analysis on power flow evaluates the sta- bility of a power system by simulating the failures of x Joe Chow,MengWang transmission lines or generators. Currently each N - x con- Renssalaer Polytechnic Institute tingency analysis is performed independently, but since the [email protected], [email protected] number of cases increases exponentially with x, this is com- putationally impractical. We propose new algorithms for MS281 the problem by observing that only a small portion of the system is changed when a component is removed. Policy-switching Schemes for Power System Pro- tection Alex Pothen Current power system protection schemes have proven use- Purdue University ful in order to mitigate several localized contingencies. Department of Computer Science However, there is still ample heterogeneity and uncertainty [email protected] in the design of wide-area Remedial Action Schemes (RAS) for effective restraint of large cascading outages. We pro- Yu-Hong Yeung pose a policy-switching approach to select optimal protec- Purdue University tion schemes during and after a contingency. This talk [email protected] describes the application of the method to a benchmarking test case in order to achieve optimal power system perfor- Mahantesh Halappanavar mance during emergency situations. Pacific Northwest National Laboratory [email protected] Rich Meier, Jesse Hostetler, Eduardo Cotilla-Sanchez, Alan Fern Zhengyu Huang Oregon State University PNNL [email protected], [email protected], [email protected] [email protected], [email protected]

MS282 MS281 Exploring State Estimation Techniques to Accom- A Low-dimensional Approximation to the Stochas- modate non-Gaussian Noises tic Elliptic Interface Problem

Measurement data have always been a key element of power In this presentation, we will discuss a numerical method of grid operation and planning. However, the use of measure- stochastic elliptic interface problem with random interface. ment data is based on a key assumption of Gaussian noises. An efficient finite element scheme is proposed to compute Driven by the investment from the American Recovery and the covariance of the solutions by using a low-dimensional Reinvestment Act of 2009, thousands more sensors are be- approximation of the random input. Error estimate is es- ing put into the power grid. The rate and volume of the tablished and some numerical tests are performed. emerging measurement data are hundred times higher and larger. Power grid operation and planning functions are be- Ju Ming coming more and more dependent on measurement data. Beijing Computational Science Research Center More accurate understanding of the noise properties of the [email protected] data is critical and can make large impact on the outcome of data applications. This talk will examine real phasor measurements and present latest findings in noise proper- MS282 ties as well as potential impact on mathematical algorithms A Finite Element Method for a Stokes Interface for power grid analysis. Problem

Zhenyu Huang We present a higher-order finite element method for solv- Pacific Northwest National Laboratory ing a class of interface problems in two dimensions. The [email protected] methodisbasedoncorrectiontermsaddedtotheright- hand side of the natural method. We prove optimal error Ning Zhou estimates of the method on general quasi-uniform meshes Binghamton University in the maximum norms. In addition, we apply the method [email protected] to a Stokes interface problem obtaining optimal result.

Mihai Anitescu Manuel A. Sanchez-Uribe Argonne National Laboratory Brown University Mathematics and Computer Science Division manuel sanchez [email protected] [email protected]

Shaobu Wang MS282 Pacific Northwest National Laboratory Surfactant Driven Tipstreaming in a Flow Focusing CS15 Abstracts 221

Geometry Department of Electrical and Computer Engineering Carnegie Mellon University We model a surfactant-mediated tipstreaming in a mi- [email protected] crofluidic flow focusing geometry. That microfluidic method for production of submicrometer and potentially nanoscale droplets and particles uses the elongational flow MS283 along with dissolved surfactant in one of the liquid phases to create strong surfaces tension gradient. The concentra- Numerical Eigenvalue Engine towards Extreme- tion of bulk soluble surfactant was found to significantly ef- scale Computing Era fect the mode of formation and size of the emitted droplets. By carefully controlling the surfactant concentration and Towards Exa-scale computing Era, we have been study- other flow quantities, droplets can be created that are an ing next generation eigenvalue library, which must exploit order of magnitude or more smaller than the scale of both high performance, highly parallelism and high portability. the device and droplets produced in the absence of surfac- EigenExa has been developed and released in August 2013 tant. as a prototype of exa-scale library. EigenExa performs on multi-peta scale system such as K computer and a Blue- Jacek Wrobel Gene/Q. We investigate key points to be innovated in the Department of Mathematics, Tulane University heritage stage to 10 to 100 fold-scale complex systems. In Center for Computational Science this mini-symposium, project overview, our goal and key [email protected] technologies in exa-scale library will be discussed. Toshiyuki Imamura Michael Siegel RIKEN Advance Institute for Computational Science New Jersey Institute of Technology [email protected] [email protected] Takeshi Fukaya Michael R. Booty RIKEN, Japan Department of Mathematical Sciences, NJIT Japan [email protected] [email protected]

MS282 Yusuke Hirota Immersed Finite Element Methods with Enhanced RIKEN AICS Stability [email protected]

In this talk, we present new immersed finite element (IFE) Susumu Yamada, Masahiko Machida methods for the second-order elliptic interface problems. Japan Atomic Energy Agency Comparing with classic IFE schemes using Galerkin for- [email protected], mulation, these new IFE methods contain either partial [email protected] stabilization terms on interface edges or full stabilization on all interior edges. Apriorierror estimates show that these new methods converge optimally in corresponding MS283 energy norms. Numerical experiments also indicate that Automatic Tuning for Parallel FFTs on GPU Clus- these stabilized IFE methods outperform classic IFEs at ters vicinity of interfaces.

Xu Zhang In this talk, we propose an implementation of a parallel Purdue University fast Fourier transform (FFT) with automatic performance [email protected] tuning on GPU clusters. Because the parallel FFTs require all-to-all communications, one goal for parallel FFTs on GPU clusters is to minimize the PCI Express transfer time Tao Lin and the MPI communication time. Performance results of Department of Mathematics, Virginia Tech FFTs on a GPU cluster are reported. [email protected] Daisuke Takahashi Faculty of Engineering, Information and Systems MS283 University of Tsukuba Code Generation for Higher Level Spectral Meth- [email protected] ods with Spiral

The FFT is a ubiquitous tool in signal processing and for MS283 solving large-scale PDEs. Many use cases can be built on top of the 1D FFT, which has a very simple math- Statistical Performance Modeling and Autotuning ematical definition. However, extracting maximum per- for Dense QR Factorization in Hybrid CPU-GPU formance on big parallel machines requires rethinking of Systems the FFT as highest-level building block. We will investi- gate Spiral-based code generation for higher-level building We investigate how to adaptively and automatically choose blocks like convolution, interpolation, and Greens Func- the block sizes of a dense QR factorization algorithm to tion approaches and their implication of FFT-based per- maximize the use of CPU and GPU on the same computing formance optimization and show the performance potential node. The decision is based on statistical surrogate models of this approach. of performance and an online monitor, which avoids unex- pected occasional performance drops. Numerical results Franz Franchetti suggest that our approaches are efficient and can lead to 222 CS15 Abstracts

near-optimal block sizes. formance code that solves the coupled thermo-mechanics and unsteady species diffusion equations using the paral- Ray-Bing Chen lel Jacobian-Free Newton-Krylov framework in MOOSE. Department of Statistics BISON can be used to investigate computationally large National Cheng Kung University problems, e.g. a full stack of discrete pellets in a fuel [email protected] rod. We provide a brief overview of the material and be- havioral models and discuss successes with preconditioning Yaohung Tsai and solving the large nonlinear system. Department of Matheamtics National Taiwan University Shane Stafford [email protected] Idaho National Laboratory shane.staff[email protected] Weichung Wang Institute of Applied Mathematical Sciences MS284 National Taiwan University [email protected] Stabilization Methods for High Peclet Number Flows in Heterogeneous Porous Media

MS284 A class of reconstructed Discontinuous Galerkin (rDG) methods are developed for fluid dynamics in heterogeneous Multiphase Sub-Surface Flow Using Moose porous media. Numerical examples demonstrate that the Abstract not available at time of publication. rDG methods are able to maintain stabilization of the so- lution in the case of high Peclet number flows, while ren- Chris Green dering sharp resolution at the vicinity of large gradients University of Melbourne, Australia or discontinuities, indicating a promising methodology for [email protected] liquid convection in computational hydrogeology.

Jonathan Ennis-King Yidong Xia CSIRO Idaho National Laboratory [email protected] [email protected] Hai Huang MS284 Idaho National Laboratory Low Mach and Two-Phase Flow Modeling with Idaho National Laboratory Moose Applications [email protected]

A 7-equation two-phase flow fluid model has been imple- Robert Podgorney mented in the next-generation nuclear reactor safety code Idaho National Laboratory RELAP-7 built upon the MOOSE multiphysics framework. [email protected] The entropy viscosity method, an artificial viscosity tech- nique for hyperbolic conservation laws [Guermond et al., Entropy viscosity method for nonlinear conservation laws, MS285 Journal of Comput. Phys. 230 (2011) 4248–4267], has Reassessing the Missing Point Estimation Model been extended to the low-Mach regimes for single and two- Order Reduction Method phase flows. The entropy viscosity method is a numeri- cal stabilization technique that is spatial-discretization ag- When applied to nonlinear systems, projection-based nostic and satisfies the minimum entropy principle. The model-order reduction requires a second-level approxima- fluid flow governing equations are discretized using stan- tion to achieve its full potential. This talk introduces a dard continuous finite elements and an implicit BDF2 time generalization of one such technique, the so-called Missing discretization. The resulting system of nonlinear equations Point Estimation, which is characterized by its simplicity are solved using the Jacobian-free Newton Krylov solver of and generality. A greedy sampling algorithm based on a MOOSE. Numerical results will be presented. rigorous a priori error bound is proposed. The application to finite element discretizations will be considered. Jean C. Ragusa Department of Nuclear Engineering Julien Cortial Texas A&M University Sandia National Laboratories (Livermore) [email protected] Quantitative Modeling and Analysis [email protected] Marco Delchini Texas A&M University Kevin T. Carlberg [email protected] Sandia National Laboratories [email protected] Ray A. Berry Idaho National Laboratory [email protected] MS285 Reduced Basis Methods for Variational Inequalities

MS284 We consider parabolic variational inequalities with differ- Modeling Nuclear Fuel Behavior with BISON ent trial and test spaces and a possibly non-coercive bi- linear form. Fine discretizations that are needed for such BISON is a modern finite-element based nuclear fuel per- problems resolve in high dimensional problems and in long CS15 Abstracts 223

computing times. To reduce the dimensionality of these presented. problems,we use the Reduced Basis Method. Error es- timators could be obtained by combining Reduced Basis Matthias Bolten Methods with a space-time formulation of the variational University of Wuppertal inequality. We provide numerical results for a heat inequal- Department of Mathematics ity model. [email protected] Silke Glas Michael Minion University of Ulm, Germany Stanford University [email protected] [email protected]

MS285 Robert Speck Juelich Supercomputing Centre Parsimonious Data Acquisition for Data-driven Forschungszentrum Juelich Model Reduction [email protected] Data-driven model reduction methods require input from an external source, such as snapshots for POD. Obtain- Matthew Emmett ing this input can be resource-intensive. This presentation Lawrence Berkeley National Laboratory will discuss methods that limit usage of memory and com- Center for Computational Sciences and Engineering putation time in attempting to meet user-specified error [email protected] tolerances or basis sizes. Daniel Ruprecht Geoffrey M. Oxberry Institute of Computational Science Lawrence Livermore National Laboratory Universita della Svizzera italiana [email protected] [email protected]

MS285 MS286 An Adaptive Parametrized-Background Data- Towards a Multigrid Perspective of MLSDC Weak Approach to State Estimation; Application to Heat Transfer Companion Experiments Spectral deferred corrections (SDC) are a class of itera- We present an adaptive Parametrized-Background Data- tive solvers for the collocation formulation of an ODE sys- Weak (PBDW) formulation for data assimilation prob- tem. The multi-level extension MLSDC, which constitutes lems modeled by parametric PDEs. PBDW combines a the basis for the time-parallel method PFASST, performs prior space, which approximates the solution manifold as- SDC sweeps on a full space-time hierarchy and employs an sociated with the parametric PDE, and M experimen- FAS technique well-known from non-linear multigrid meth- tal observations to provide real-time, in-situ state estima- ods. In this talk we analyze SDC’s smoothing properties tion. The adaptive procedure exploits a novel a posteriori and investigate which concepts of standard multigrid the- observation-based error estimator to refine the prior space ory translate to MLSDC and how these can be exploited using historical data-assimilation solutions. We illustrate further. our method through a synthetic example and a physical thermal patch problem. Dieter Moser,RobertSpeck Juelich Supercomputing Centre Tommaso Taddei Forschungszentrum Juelich MIT [email protected], [email protected] [email protected] Matthias Bolten Masayuki Yano, James Penn University of Wuppertal Massachusetts Institute of Technology Department of Mathematics [email protected], [email protected] [email protected]

Anthony T. Patera Massachusetts Institute of Technology MS286 Department of Mechanical Engineering [email protected] Parallel in Time Multigrid for Nonlinear Equations

The multigrid reduction in time method (MGRIT) creates MS286 a multilevel hierarchy of different temporal discretizations. Interweaving PFASST and Parallel Multigrid For nonlinear equations each iteration of the parallel-in- time method requires expensive, nonlinear, spatial solves. The parallel full approximation scheme in space and time Using a Picard method for the nonlinear solver, we investi- (PFASST) has been introduced by Emmett and Minion gate several methods for reducing the cost of these solves, as an iterative method for the parallelization of ordinary including reducing solver accuracy on coarser temporal lev- differential equations or time-dependent PDEs. On each els and introducing spatial coarsening on coarse temporal (time-)level the systems that arise have to be solved to the levels. same accuracy. The usage of lower accuracy on levels with larger time steps is natural. In this talk different strategies Ben O’Neill for coupling PFASST iterations with multigrid methods are University of Colorado, Boulder 224 CS15 Abstracts

[email protected] Kamer Kaya CERFACS, Toulouse, France [email protected] MS286 An Adaptive Spectral Deferred Time Integrator for Umit V. Catalyurek Vesicle Suspensions The Ohio State University Department of Biomedical Informatics Vesicles are deformable and inextensible capsules, filled [email protected] with and submerged in a viscous fluid. Their dynamics are governed by hydrodynamic and elastic forces which can be formulated as a system of integro-differential-algebraic MS287 equations. I will describe a spectral deferred correction Locality for Sparse Unstructured Communication algorithm that we use to construct high-order vesicle sim- Patterns ulations. Then, I will show how we estimate the error with only one numerical solution and use this to construct an In high performance computing data centers, job alloca- adaptive time stepping scheme. tion and mapping of the parallel tasks to the allocated nodes should comply with the job communication pattern Bryan D. Quaife to reduce the execution time. We discuss the potential of Institute for Computational Engineering and Sciences simultaneous allocation and mapping for jobs with sparse University of Texas at Austin unstructured communication, and propose a graph-based [email protected] algorithm that is based on breadth-first expansion both in node network and in job communication domains. Simu- George Biros lations show that our method outperforms other state-of- University of Texas at Austin the-art approaches. [email protected] Ozan Tuncer Boston University MS287 [email protected] Maximizing Throughput on a Dragonfly Network Vitus Leung In this talk, I will present our analysis of a 100+ Petaflop/s Sandia National Laboratories prototype machine with a dragonfly network, 92,160 high- [email protected] radix routers and 8.8 million cores. We compare network throughput for various routing strategies, job placement Ayse Coskun policies, and application communication patterns. Our Boston University study is based on a novel model that predicts traffic on Electrical and Computer Engineering Department individual links for direct, indirect, and adaptive routing [email protected] strategies. We analyze results for individual communica- tion patterns and some common parallel job workloads. MS288 Abhinav Bhatele Lawrence Livermore National Laboratory Fluctuating Hydrodynamics Methods for Soft Ma- [email protected] terials Many efficient implicit solvent coarse-grained (IS-CG) de- Nikhil Jain scriptions have been developed for equilibrium studies by University of Illinois removing the solvent degrees of freedom and treating their [email protected] contributions implicitly in the free energy of interactions. To study many dynamic responses requires capturing mo- Xiang Ni, Laxmikant V Kale mentum transfer and kinetic effects involving the solvent University of Illinois at Urbana-Champaign degrees of freedom. We present fluctuating hydrodynamic [email protected], [email protected] methods for extending IS-CG models. We present results for dynamic studies of polymeric materials and lipid bilayer membranes. MS287 Topology Aware Mapping using Graph Models for Paul J. Atzberger Exascale Systems University of California-Santa Barbara [email protected] Communication time of parallel applications is limited by various features of the interconnection networks such as latency or bandwidths of the links. Topology aware task MS288 mapping methods that place application tasks on proces- Temporal Integrators for Fluctuating Hydrody- sors by exploiting information about the underlying net- namics work can help to avoid such limitations. In this work, by using the graph models for representing the network We develop temporal integrators for solving Langevin topology and applications communication requirements, stochastic differential equations (SDEs) that arise in fluc- we study topology aware task mapping methods to reduce tuating hydrodynamics (FHD). These methods add fluc- bottlenecks in the applications’ communication time. tuations to standard second-order deterministic solvers in a way that maintains second-order weak accuracy for lin- Mehmet Deveci earized FHD. We also construct integrators for integrating The Ohio State University the overdamped limit of systems of equations with a fast [email protected] and slow variable in the limit of inifinite separation of the CS15 Abstracts 225

fast and slow timescales. We illustrate these integrators on an immersed-boundary Lagrangian representation of rigid applications involving particles suspended in a fluctuating bodies to a finite-volume fluid solver. Our methods (1) fluid, as well as the development of giant nonequilibrium Do not employ time splitting and are thus suitable for the fluctuations in diffusively-mixing fluids. steady Stokes (viscous-dominated or low Reynolds num- ber) regime; (2) Strictly enforce the rigidity constraint; Steven D. Delong and, (3) Ensure fluctuation-dissipation balance in the Courant Institute of Mathematical Sciences Brownian regime in the overdamped limit even in the pres- New York University ence of nontrivial boundary conditions. [email protected] Bakytzhan Kallemov Eric Vanden-Eijnden Courant Institute of Mathematical Sciences Courant Institute NYU New York University [email protected] [email protected] Aleksandar Donev Aleksandar Donev Courant Institute of Mathematical Sciences Courant Institute of Mathematical Sciences New York University New York University [email protected] [email protected] Boyce Griffith University of North Carolina at Chapel Hill MS288 [email protected] A Fluctuating Immersed Boundary Method for Brownian Suspensions of Rigid Particles Amneet Bhalla Courant Institute of Mathematical Sciences I will describe how to model Brownian suspensions of pas- [email protected] sive or active particles and rigid bodies using an immersed boundary (IB) approach. I will first discuss minimally- resolved models in which each suspended spherical parti- MS289 cle is represented by a single IB marker [F. Balboa Us- Gaussian Processes in High-Dimensions abiaga and R. Delgado-Buscalioni and B. E. Griffith and A. Donev, Computer Methods in Applied Mechanics and Gaussian process regression in high-dimensions is challeng- Engineering, 269:139-172, 2014; and S. Delong, F. Balboa ing task. Under special circumstances, active subspace Usabiaga, R. Delgado-Buscalioni, B. E. Griffith and A. methods can effectively deal with high-dimensions. Most Donev, J. Chem. Phys., 140, 134110, 2014]. More complex of the times, the active subspace is defined in an intuitive, rigid bodies suspensed in fluid can be represented with dif- albeit ad hoc manner, using gradient information. Here, ferent degrees of fidelity by enforcing a rigidity constraint we show how traditional machine learning techniques can for each partially- or fully-resolved body [B. Kallemov, A. be used to infer the active subspace with no ad hoc as- Bhalla, A. Donev, and B. Griffith, in preparation]. Ther- sumptions and without gradient information. mal fluctuations and thus Brownian motion can be consis- tently modeled by including a fluctuating (random) stress Ilias Bilionis in the momentum equation, as dictated by fluctuating hy- Purdue University drodynamics. [email protected]

Aleksandar Donev Nicholas Zabaras Courant Institute Cornell University [email protected] [email protected]

Bakytzhan Kallemov Courant Institute of Mathematical Sciences MS289 NYU Numerical Solution for the High-Dimensional Joint [email protected] Response-Excitation Pdf Evolution Equations Evolution equations of the joint response-excitation prob- Boyce Griffith ability density function (REPDF) generalize the existing University of North Carolina at Chapel Hill PDF evolution equations and enable us to compute the [email protected] PDF of the solution of stochastic systems with random ini- tial condition, coefficient, forcing, involving colored noise. Steven D. Delong An efficient algorithm by using adaptive discontinuous Courant Institute of Mathematical Sciences Galerkin method and probabilistic collocation method has New York University been developed for low dimensional systems. In this talk, [email protected] we address the high-dimensionality of the REPDF sys- tem. We focus on two approximations, namely, the Proper Generalized Decomposition (PGD) involving the separated MS288 representation and the ANOVA approximation. Both ap- An Immersed Boundary Method for Rigid Bodies proaches overcome the curse of dimensionality and can compute the PDFs of extremely high-dimensional systems. We develop an immersed-boundary method for fluid- Here, we demonstrate the effectiveness of these methods to structure coupling at small and moderate Reynolds num- the Lorenz-96 model and the advection equation. bers. This is important in problems involving rigid and semi-rigid structures immersed in a fluid. We couple Heyrim Cho 226 CS15 Abstracts

Brown University University of Utah Providence, RI [email protected] heyrim [email protected] Yeonjong Shin Daniele Venturi Scientific Computing and Imaging Institute Division of Applied Mathematics University of Utah Brown University [email protected] daniele [email protected] Dongbin Xiu George E. Karniadakis University of Utah Brown University [email protected] Division of Applied Mathematics george [email protected] MS290

MS289 BDDC Domain Decomposition for Weak Galerkin Methods High-Dimensional Hierarchical Uncertainty Quan- tification for Electronic Systems A Balancing domain decomposition by constraints (BDDC) algorithm is studied for solutions of large sparse We present a hierarchical uncertainty quantification ap- linear algebraic systems arising from weak Galerkin dis- proach for complex electronic systems with several high- cretization of second order elliptic boundary value prob- dimensional subsystems. First, we obtain a sparse surro- lems. The condition number for the preconditioned system gate model for each subsystem, and utilize a tensor-train- is estimated and numerical results are provided to confirm based algorithm to obtain its orthonormal polynomials and the results. Gauss quadrature points. Next, we treat each subsystem as a single parameter and perform the high-level simula- Xuemin Tu tion using stochastic spectral methods. The framework University of Kansas shows 90x speedup over hierarchical Monte Carlo on an xuemin@ku,edu MEMS/IC oscillator circuit with 184 random parameters.

Zheng Zhang MS290 MIT Innovative Weak Galerkin Finite Element Methods z [email protected] with Application in Fluorescence Tomography

Xiu Yang In this talk, I will discuss a new and efficient numerical al- Pacific Northwest National Laboratory gorithm by using weak Galerkin (WG) finite element meth- [email protected] ods for a fourth order elliptic problem arising from Fluores- cence Tomography(FT) model. Fluorescence Tomography George E. Karniadakis is an emerging, in vivo non-invasive 3-D imaging technique Brown University which reconstructs images that characterize the distribu- Division of Applied Mathematics tion of molecules that are tagged by fluorophores. Weak george [email protected] second order elliptic operator and its discrete version are introduced for a class of discontinuous functions defined on a finite element partition of the domain consisting of Ivan Oseledets general polygons or polyhedra. An error estimate of op- Institute of Numerical Mathematics 2 timal order is derived in an H -equivalent norm for the Russian Academy of Sciences, Moscow WG finite element solutions. Error estimates in the usual [email protected] 2 L norm are established, yielding optimal order of con- vergence for all the WG finite element algorithms except Luca Daniel the one corresponding to the lowest order (i.e., piecewise M.I.T. quadratic elements). Some numerical experiments are pre- ResearchLabinElectronics sented to illustrate the efficiency and accuracy of the nu- [email protected] merical scheme.

Chunmei Wang MS289 Georgia Institute of Technology Adaptive Multivariate Interpolation Algorithm on [email protected] Nested Grids and Its Application to Stochastic Col- location MS290 We propose an adaptive method for high dimensional poly- nomial interpolation for efficient stochastic collocation. Weak Galerkin Mixed Finite Element Methods for The method utilizes least orthogonal interpolation on un- Linear Elasticity Problems structured grids. It is based on a greedy algorithm to adap- tively induces nested grids and can be highly flexible for In the talk, I will talk about solving linear elasticity prob- practical stochastic computations. Along with numerical lems by using Weak Galerkin mixed finite element method examples to demonstrate its effectiveness, we also provide (WG-MFEM). It is shown that WG-MFEM provides an convergence proof. accurate approximation for both the stress tensor and the displacement field of linear elasticity problems. The nu- Xueyu Zhu merical experiments will be provided to verify that WG- CS15 Abstracts 227

MFEM is efficient and reliable in computing. [email protected]

Yujie Zhang Oklahoma State University, USA MS291 [email protected] Using Random Butterfly Transformations to Avoid Pivoting in Sparse Direct Methods

MS290 Dynamic pivoting prevents parallel sparse direct solvers from achieving high performance and scalability. In this A Weak Galerkin Finite Element Scheme for Solv- work, we investigate a statistical technique based on Ran- ing the Brinkman Equations dom Butterfly Transformations to avoid pivoting. Previous works showed that this technique is successful in the dense A weak Galerkin (WG) finite element method for solving case; here we investigate the sparse case. We will compare the Brinkman equation in two or three dimensional spaces this method with the static pivoting and the partial pivot- by using polynomials is introduced and analyzed. The WG ing approaches in various performance metrics, including method is designed by using the generalized functions and robustness, sparsity, and runtime in a parallel environment. their weak derivatives which are defined as distributions. The variational form we considered is based on two gra- Francois-Henry Rouet dient operators which is different from the usual gradient- Lawrence Berkeley National Laboratory divergence operators. The WG method is highly flexible [email protected] by allowing the use of discontinuous functions on arbi- trary polygons or polyhedra with certain shape regularity. Xiaoye Sherry Li Optimal-order error estimates are established for the cor- Computational Research Division responding WG finite element solutions in various norms. Lawrence Berkeley National Laboratory Some computational results are presented to demonstrate [email protected] the efficiency of the method. Marc Baboulin Ran Zhang University of Paris-Sud/INRIA Jilin University, China [email protected] [email protected]

MS292 MS291 A Pod Model for Resolving the Angular Dimension of the Boltzmann Transport Equation Preconditioning Stochastic Gradient Algorithms with Randomized Linear Algebra A new method using POD in neutral particle transport problems is described. POD is used to represent the angu- We provide a method for combining SGD (Stochastic Gra- lar direction of particle travel when solving the Boltzmann dient Descent) and RLA (Randomized Linear Algebra) al- equation for time independent problems. It is based on the gorithms. This involves reformulating a deterministic re- method of snapshots which are of the angular flux distri- gression problem as a stochastic optimization problem that butions taken at different instances in space. The method is of the form of an expectation over a nontrivial data- substantially reduces the number of functions required to dependent probability distribution. This permits us to resolve angular direction, this reduces solving times whilst combine stochastic approximation (SA) methods and sam- retaining solution accuracy. ple average approximation (SAA) methods from optimiza- tion theory to develop novel RLA-SGD-hybrid randomized Andrew G. Buchan algorithms for these deterministic regression problems. Department of Earth Science & Engineering Imperial College Michael Mahoney [email protected] Stanford University Applied and Computational Mathematics Atyab Calloo [email protected] Imperial College London [email protected]

MS291 Christopher Pain Randomized Methods for Accelerating Structured Imperial College Matrix Computations [email protected]

Methods based on randomized sampling have over the last Fangxin Fang several years proven to be powerful tools for computing Department of Earth Science and Engineering low-rank approximations to matrices whose singular val- Imperial College London, U.K. ues exhibit appropriate decay. In this talk, we describe [email protected] how such techniques can be extended to certain ”rank- structured” matrices, for which only certain off-diagonal Steven Dargaville blocks (not the matrix itself) admit accurate low-rank ap- Imperial College London proximations. Matrices of this type often arise in the con- [email protected] struction of O(N) direct solvers for elliptic PDEs. Ionel M. Navon Gunnar Martinsson Florida State University Univ. of Colorado at Boulder Department of Scientific Computing 228 CS15 Abstracts

[email protected] University of California, Merced [email protected]

MS292 Toby Isaac Automated Adjoints for Mesh-Independent PDE- ICES Constrained Optimisation The University of Texas at Austin [email protected] We will present a method for automatically deriving ad- joints of finite element models with two major advantages Omar Ghattas over algorithmic differentiation: the adjoints enjoy approx- The University of Texas at Austin imately optimal efficiency (crucial for optimisation and in- [email protected] verse problems), and scale naturally in parallel without dif- ferentiating MPI calls or OpenMP directives. The method is used to derive adjoints of models employing the FEniCS Thomas Hughes framework. We will further discuss how discrete adjoints Institute for Computational Engineering and Sciences can be carefully used to achieve mesh independence in op- The University of Texas at Austin timisation algorithms. [email protected]

Patrick E. Farrell Department of Mathematics MS293 University of Oxford Stability and Convergence of the Co-volume [email protected] Scheme for the Stokes Problem

MS292 The co-volume scheme specifies the mass at cell centers and Challenges in Assimilation of PM2.5 Observations cell vertices, and both of the normal and tangential velocity for Air Pollution Forecast components at cell edges. This scheme is extremely flexi- ble, applicable to unstructured meshes, and avoids the need Air pollution is a big issue in China. A good air qual- to reconstruct the tangential velocity component, as the ity forecast is very useful and important for warning and classical C-grid scheme does. Even though the co-volume management of air pollution. More than 1,000 surface ob- scheme has had some success in simulating geophysical servation stations for PM2.5 monitoring were established flows, there has not been much progress in the theoretical recently. The big data from this observing network has the analysis of the scheme. In this talk, we present stability potential to improve the air quality forecast via advanced and convergence results concerning the scheme applied to data assimilation techniques. Over recent years we have the classical Stokes problem on unstructured meshes. Both being worked on this problem. There are some progresses, the linear and nonlinear cases will be discussed. and some failures too. This talk will focus on some chal- lenges and discuss some possible solutions. Qingshan Chen Clemson University Jiang JZhu [email protected] Institute of Atmospheric Physics Chinese Academy of Sciences [email protected] MS293 Semi-Analytical Time Differencing Methods for MS292 Stiff Problems Inversion of Geothermal Heat Flux in a Thermo- mechanically Coupled Nonlinear Stokes Ice Sheet A semi-analytical method is developed based on conven- Model tional integrating factor (IF) and exponential time differ- encing (ETD) schemes for stiff problems. The latter means To project the contribution of polar ice sheets to future that there exists a thin layer with a large variation in their sea level rise, high-resolution numerical ice sheet models solutions. The occurrence of this stiff layer is due to the are critical. Yet, large uncertainties remain in the bound- multiplication of a very small parameter  with the tran- ary conditions at the base of the ice sheet due to the lack sient term of the equation. Via singular perturbation anal- of direct observations. Here we study mathematical and ysis, an analytic approximation of the stiff layer, which is computational issues in inverse problems for basal bound- called a corrector, is sought for and embedded into the IF ary conditions, in particular, the geothermal heat flux, in and ETD methods. These new schemes are then used to a thermomechanically coupled nonlinear Stokes ice sheet approximate the non-stiff part of the solution. Since the model, using surface velocity observations. stiff part is resolved analytically by the corrector, the new method outperforms the conventional ones in terms of ac- Hongyu Zhu curacy. In this paper, we apply our new method for both Institute for Computational Engineering and Sciences problems of ordinary differential equations and some par- University of Texas at Austin tial differential equations. [email protected] Chang-Yeol Jung Georg Stadler Ulsan National Institute of Science and Technology Courant Institute for Mathematical Sciences South Korea New York University [email protected] [email protected] Thien Binh Nguyen Noemi Petra UNIST CS15 Abstracts 229

[email protected] lation, the numerical discretization, and the parallel imple- mentation. As most simulator writing teams consist of one Ph.D. student, acquiring peak performance can be a daunt- MS293 ing task. We address this challenge with a new open source A New Adaptive Weighted Essentially Non- domain specific language called Equelle. The language di- oscillatory WENO-θ Scheme for Hypberbolic Con- vides the different fields into different software components servation Laws in order to maximize productivity of each researcher. For example, a parallelization expert would mostly contribute A new adaptive WENO-θ scheme is proposed. Depend- to the compiler back-end, and an expert in numerical meth- ing on the smoothness of the large stencil used in the re- ods would contribute with Equelle programs. construction procedure, a parameter θ is set adaptively to switch the scheme between a 5th-order upwind and 6th- Andre R. Brodtkorb order central approximation. A new set of smoothness in- SINTEF ICT, Department of Applied Mathematics dicators for both the sub-stencils and the large one is intro- [email protected] duced. These are constructed symmetrically around xj in Taylor expansions. Numerical results show that WENO-θ substantially improves other comparing WENO schemes. MS294 High Performance High Order Numerical Method Chang-Yeol Jung for Tsunami Wave Propagation Ulsan National Institute of Science and Technology South Korea We present a high order discontinuous Galerkin method for [email protected] the accurate simulation of tsunami wave propagation. We discuss the acceleration of the method on modern many Thien Binh Nguyen core hardware architectures such as GPUs, for the faster UNIST than real time predictions. The developed algorithms use [email protected] a unified multi-threading approach OCCA. A computa- tionalkernelwritteninOCCAcanbeexecutedonsev- eral hardware architectures that support multi-threading MS293 approaches OpenCL, CUDA, OpenMP, Pthreads and Intel The Effective Resolution of Advection Schemes COI.

Typical classification of numerical schemes concerns the Rajesh Gandham convergence order of the scheme and the relative accuracy Rice University in the limit of an infinitesimal grid (in either space or time). Department of Computational and Applied Mathematics We define and analyze the effective resolution of numerical [email protected] schemes designed for the advection equation by calculat- ing the smallest spatial scale that is completely resolved by Timothy Warburton that scheme. This is done via dispersion relation analysis Department of Computational And Applied Mathematics and numerical testing. We also briefly discuss the impact Rice University of these novel approaches to quantify the utility of a nu- [email protected] merical algorithm at accurately representing the influence of waves on mean flow for nonlinear evolution equations in David Medina fluids that incorporate a three-wave interaction. Rice University [email protected] James Kent University of Michigan [email protected] MS294 FEM Integration with Quadrature on the GPU Jared P. Whitehead Brigham Young University Efficient integration of low-order elements on a GPU has [email protected] proven difficult. We have previously shown how to inte- grate a differential form (such as Laplace or elasticity) ef- Christiane Jablonowski ficiently using algebraic simplification and exact integra- University of Michigan tion. This, however, breaks down for multilinear forms Ann Arbor MI 48109-2143 or when using a coefficient. In this work, we show how [email protected] to efficiently integrate an arbitrary form using quadrature. We introduce a technique we call ”thread transposition” Richard Rood which matches the work done during evaluation at quadra- University of Michigan ture points to that done during basis coefficient evaluation. Ann Arbor, MI 48109-2143 We are able to achieve more than 300GF/s for the variable- [email protected] coefficient Laplacian, and provide a performance model to explain these results.

MS294 Matthew Knepley Flooding with Equelle: A Domain Specific Lan- University of Chicago guage for Finite Volume Methods [email protected] Modern hardware is increasingly complex and difficult to Karl Rupp utilize for researchers and scientists. Peak performance is Institute for Analysis and Scientific Computing, TU Wien only acquired through mastering a huge set of fields, includ- Institute for Microelectronics, TU Wien ing the physical problem at hand, the mathematical formu- [email protected] 230 CS15 Abstracts

Andy R. Terrel pled with Maxwells equations to complete the description Institute for Computational Engineering and Sciences for magnetized plasmas. A Godunov-type finite-volume University of Texas at Austin method is proposed for the solution of the multi-fluid model [email protected] by numerical means and results are described for both one- and two-dimensional problems.

MS294 Clinton P. Groth Thermal Comfort Simulations on Massive Parallel University of Toronto Institute for Aerospace Studies Systems Canada [email protected] Many engineering-based problems, which were deemed un- solvable a decade ago, can be simulated today using mod- Ken Miura ern supercomputers such as SuperMUC installed at LRZ, University of Toronto Institute for Aerospace Studies Germany. Computational fluid dynamics play a dominant [email protected] role in simulating urban floods or complex indoor air flow scenarios. We will present our multi-scale CFD approach based on hierarchic, block-structured Cartesian grids for MS295 solving a coupled thermal simulation together with a hu- A High-order Block-adaptive Simulation Frame- man manikin model, running on up to 140,000 cores in work for Ideal and Resistive MHD Equations on parallel. Cubed-sphere Grids Ralf-Peter Mundani Numerical simulations of large-scale space-physics prob- TUM, Faculty of Civil, Geo and Environmental lems typically require the computation of discrete solu- Engineering tions of complex multiphysics phenomena characterized Chair for Computation in Engineering by disparate spatial and temporal scales. Adequate nu- [email protected] merical algorithms capable to resolve the wide range of dynamic scales of such simulations at reduced computa- J´erˆome Frisch tional cost are highly desirable. This talk presents an Chair for Computation in Engineering adaptive, conservative, high-order CENO finite-volume ap- Technische Universit¨at M¨unchen proach for space-plasma phenomena described by the set [email protected] of ideal and resistive MHD equations. Results for sev- eral benchmark problems are presented to illustrate the accuracy and computational performance of the fourth- MS295 order accurate method used in combination with a paral- Scalable Solvers for Extended MHD in the Low-β lel, dynamically-adaptive, simulation framework on cubed- Regime sphere grids.

Extended MHD (XMHD) is a very challenging hyperbolic Lucian Ivan, Hans De Sterck, Andree Susanto PDE system for implicit integration techniques due to the University of Waterloo ill-conditioning introduced by fast dispersive waves. In this Applied Mathematics talk, we will describe our physics-based preconditioning ap- [email protected], [email protected], proach for XMHD in the low-β regime, when a large guide [email protected] field is present. The method exploits the nature of the hyperbolic couplings in XMHD to produce a block diag- Clinton P. Groth onally dominant PDE system, well-conditioned for multi- University of Toronto Institute for Aerospace Studies level techniques. Numerical experiments will demonstrate Canada the scalability of the approach. [email protected] Luis Chacon Los Alamos National Laboratory MS295 [email protected] Block Preconditioners for 3D Incompressible MHD

MS295 The scalable iterative solution of strongly coupled3D Multi-Fluid Magnetohydrodynamic Models for incompressible resistive magnetohydrodynamics (MHD) Partially-Ionized Non-Equilibrium Anisotropic equations is very challenging. This study considers mixed Plasmas FE integration for velocity/pressure (Q2/Q1) and edge- elements for magnetic induction and presents anew approx- A multi-fluid extended magnetohydrodynamic model and imate block factorization (ABF) preconditioner for this numerical solution method are proposed and described system. The ABF preconditioner reduces the system toap- for the treatment of partially-ionized non-equilibrium proximate Schur complement systems that are solved by anisotropic and strongly-magnetized plasmas. The Gaus- nodal and edge-element based AMG methods. sian moment closure is used to describe the non-equilibrium transport of the neutral, ion, and electron components of Eric C. Cyr the plasma in the multi-fluid model. The Gaussian clo- Scalable Algorithms Department sure is a maximum-entropy-based, strictly-hyperbolic clo- Sandia National Laboratotories sure providing approximate solutions to the Boltzmann [email protected] equation which allow for strong pressure/temperature anisotropies. The treatment of reactive collisions is incor- Edward Phillips porated to allow for the effects of ionization-recombination Sandia National Laboratories and charge-exchange. The moment equations are cou- [email protected] CS15 Abstracts 231

John Shadid conservation with careful flux construction at refinement Sandia National Laboratories boundaries, as well as conservative coarse-fine interpola- Albuquerque, NM tion. We show results for simple tests as well as more [email protected] challenging ones that highlight the benefits of refinement.

Hans Johansen MS296 Lawrence Berkeley National Laboratory An HDG Method for Non-Hydrostatic Atmosphere Computational Research Division [email protected] Abstract not available at time of publication.

Tan Bui-Thanh MS296 The University of Texas at Austin Optimization-based Spectral Element Semi- [email protected] Lagrangian Tracer Transport

Transport algorithms are highly important in atmospheric MS296 modeling where hundreds of tracer species must be ef- Towards a Fully 3D Compressible Atmosphere Dy- ficiently transported while maintaining conservation of namical Core with Compatible Finite Elements tracer mass and preservation of physical bounds. We present a new transport algorithm that combines a high- We have recently been developing compatible finite element order spectral element semi-Lagrangian scheme with an methods (i.e., mixed finite element methods using families optimization algorithm to enforce mass conservation and of spaces forming discrete de Rham complexes) as an ex- bounds preservation. We evaluate the new method us- tension of the C-grid staggered finite difference approach. ing several standard two- and three-dimensional trans- These methods lead to higher-order discretisations on ar- port problems on the sphere and compare to existing ap- bitrary meshes with flexibility to adjust the global DOF proaches. ratio between pressure and velocity in order to minimise the impact of spurious mode branches. These methods are Kara Peterson being developed as part of the GungHo dynamical core Sandia Natl. Labs project in the UK, a collaboration between the Met Of- [email protected] fice, STFC and several UK universities. In Phase I of the project, we successfully developed finite element discretisa- Mark A. Taylor tions for the nonlinear rotating shallow-water equations on Sandia National Laboratories, Albuquerque, NM the sphere, which serves as a useful testbed for the horizon- [email protected] tal discretisation in dynamical cores. The compatible finite element structure allows for numerical schemes with sta- ble advection of the implied diagnostic potential vorticity MS297 field, which is important for stable long-time integrations Linear Response Eigenvalue Problem and Excited with minimal numerical dissipation. We are now develop- State Calculations ing these ideas in the context of a full 3D dynamical core, via vertical slice models. This talk will discuss our progress Linear response (LR) eigenvalue problems arise from exci- in addressing the following issues: * What is the finite ele- tation state calculations of collective motion of many par- ment analogue of the Charney-Phillips vertical staggering ticle systems. In this talk, we first present theoretical re- (necessary for good representation of hydrostatic balance sults for the LR eigenvalue problems such as minimization in the vertical)? What is the correct choice of finite ele- principles. Although the LR eigenvalue problems are non- ment space for temperature? * How to obtain stable and symmetric, these results mirror the well-known theoretical accurate advection schemes for temperature in this case? results for symmetric eigenproblems. Then we will discuss * How to extend the velocity advection scheme to three the best approximation of the few smallest positive eigen- dimensions? Can the 3D vorticity equation be incorpo- values via a structure-preserving projection, and describe rated? * How to discretise the nonlinear pressure gradient conjugate gradient-like algorithms for simultaneously com- term in the theta-pi formulation? Proposed solutions to puting these eigenvalues. these questions will be illustrated with numerical exper- iments implemented using Firedrake, a high-performance Zhaojun Bai finite element library targetting geophysical fluid dynam- Departments of Computer Science and Mathematics ics applications. University of California, Davis [email protected] Colin J. Cotter Imperial College London Ren-Cang Li Department of Aeronautics University of Texas - Arlington [email protected] [email protected]

MS296 MS297 A Higher-Order Finite Volume Nonhydrostatic Dy- Accelerating Quantum Transport Calculations namical Core with Space-Time Refinement Through the Feast Algorithm

We present an adaptive non-hydrostatic dynamical core In Quantum Transport the scattering region of a de- based on a higher-order finite volume discretization on the vice is connected to semi-infinite leads, where the energy- cubed sphere. Adaptivity is both in space, using nested dependent reflected modes must be determined by solving horizontal refinement; and in time, using subcycling in re- a polynomial eigenvalue problem. As fast decaying modes fined regions. The algorithm is able to maintain scalar do not significantly contribute, it is sufficient to compute 232 CS15 Abstracts

only those eigenvalues with a small or vanishing imaginary Parameters part. The FEAST algorithm allows for drastically reduc- ing the system size by specifically searching for the desired I demonstrate solving stochastic optimal control problems eigenvalues and for efficiently parallelizing the computa- by adding minimal modifications to their corresponding tional workload. deterministic optimization solvers using Trilinos packages. The process of modifying the deterministic solver to a Sascha Brueck, Mauro Calderara stochastic one can be done systematically and automati- Integrated Systems Laboratory cally given suitable code structure. I illustrate this process ETH Zurich by solving optimal control problems with uncertain model [email protected], [email protected] parameters arising in heat-flux control and oil reservoir op- timization. Hossein Bani-Hashemian, Joost VandeVondele Nanoscale Simulations Xiaodi Deng ETH Zurich Rice University [email protected], [email protected]. [email protected] MS298 Mathieu Luisier Integrated Systems Laboratory On Risk-averse PDE-constrained Optimization us- ETH Zurich ing Convex Risk Measures Inspired by Conditional [email protected] Value-at-risk We consider a class of PDE-constrained optimization prob- MS297 lems in which the underlying PDE-system contains uncer- tain parameters. In order to obtain robust controls that are Parallel Solution of Eigenvalue Problems from both deterministic and risk-averse, we consider the mini- Graphene Modeling with Solvers Based on Inte- mization of the conditional value-at-risk (CVaR) of the re- gration and Approximation duced objective functional. In order to develop efficient nu- merical schemes, regularization approaches are suggested Graphene is a material that recently attracts a lot of in- for the primal and the dual formulation of the minimiza- terest among researchers. Studying its electronic proper- tion problem. The regularized CVaR is shown to be a ties involves solving (typically large scale) sparse eigen- convex risk measure. Sensitivity and consistency results of value problems. In this talk we will present FEAST-like the regularized problems are derived. Finally, we present and polynomial based solvers for the solution of these numerical results for several example problems. eigenvalue problems. We will also discuss approaches to the solution of the arising inner linear systems. We fi- Thomas M. Surowiec nally present numerical examples involving the solution of Department of Mathematics graphene eigenvalue problems. Humboldt University of Berlin [email protected] Bruno Lang, Lukas Kr¨amer University of Wuppertal [email protected], MS298 [email protected] Optimization under Uncertainty: Application to Electrical Circuits Martin Galgon Yniversity of Wuppertal This presentation will demonstrate the application of [email protected] stochastic optimization algorithms to the problem of model calibration and optimal control under uncertainty for sim- ple electrical circuits. Our implementation uses the Rapid MS297 Optimization Library (ROL) from the Trilinos framework Polynomial Techniques and Primme for the Com- to solve optimization under uncertainty problems with al- putation of Large Number of Eigenvalues gebraic and partial differential equation constraints. Our numerical experimentation considers the Shockley ideal A computationally challenging task is the computation of diode equation and drift-diffusion model. a large number, M, of eigenvalues and their eigenvectors. Enforcing orthogonality of a Krylov subspace larger than Timur Takhtaganov M becomes a bottleneck, and computing eigenvectors a Rice University few at a time increases the iteration cost linearly with M. Houston, Tx Polynomial filters have been used to trade orthogonaliza- [email protected] tion for matrix-vector multiplications. We discuss polyno- mial filters both for single and multivectors on top of the PRIMME eigenvalue software. MS298 Maximizing AUC and Buffered AUC in Classifica- Andreas Stathopoulos tion College of William & Mary Department of Computer Science We propose an alternative to the Area Under the Receiver [email protected] Operating Characteristic Curve (AUC) performance met- ric called Buffered AUC (bAUC). We show that bAUC is an intuitive counterpart to AUC. We then show that MS298 bAUC, compared to AUC, can be a more informative mea- Optimal Control Problems With Uncertain Model sure of a classifiers ranking quality. In addition, we show CS15 Abstracts 233

that bAUC is much easier to handle in optimization frame- [email protected] works than AUC, specifically reducing to convex and linear programming. We use these friendly optimization proper- Andrei Ludu ties to introduce the bAUC Efficiency Frontier, a concept Embry-Riddle Aeronautical University that serves to partially resolve the incoherency that arises Mathematics Department when misclassification costs need be considered. We con- [email protected] clude that bAUC avoids many of the numerically trouble- some issues encountered by AUC and integrates much more smoothly into the general framework of model selection and MS299 evaluation. Deep Learning Assessment for Near Real-time, Stan Uryasev Formative Feedback during Complex Problem- University of Florida solving Activities uryasev@ufl.edu A critical factor for progress in cyberlearning involves assessment, especially near real-time, formative feedback MS299 during complex problem-solving activities. Detecting mis- Facilitating Learners Cognitive Presence In A Self- conceptions early is important to help learners gain compe- Directed Online Course tence and build confidence. This presentation will demon- strate one approach to assessing learning in complex do- The study will report our study on students self-directed mains that involves the analysis of student conceptualiza- learning and inquiry in a 15-week graduate-level online tions of the problem space over time and in comparison course. We will investigate learners cognitive presence and with those of experienced persons. These conceptualiza- facilitating behaviors that help create higher-level cogni- tions can be gathered explicitly in the form of annotated tive presence. Online discussion transcripts, semi-structure concept maps or through student models created using interviews, and learning records (i.e. view frequencies, tools such as MATLAB. grades) will be used as the primary data sources. The purpose of this study is to reveal the effective facilitating Michael Spector strategies that trigger or promote learners critical thinking University of North Texas and deep reflection. [email protected] Ye Chen,JingLei Syracuse University MS300 [email protected], [email protected] Weighted Sparsity and Function Interpolation Via Infinite-dimensional Compressed Sensing MS299 Towards Automating Analysis of Midterm We introduce a framework for function interpolation using Semester Feedback Surveys for Improving Course weighted l1 minimization. Two advantages of this frame- Effectiveness work over existing approaches are: (i) in the absence of noise it leads to interpolatory approximations, and (ii) it This talk will report on the use of midterm semester feed- does not require a priori estimates on the expansion tail. back survey for improving teaching and learning effective- We explain the critical role weighted sparsity plays in func- ness in college courses, including data from the Computa- tion interpolation; namely, that of regularizing the problem tional Modeling courses discussed during this session. Ef- and removing aliased solutions. Finally, we present a num- forts to expand and partially automate analysis and feed- ber of near-optimal recovery guarantees. back from these surveys will be explored, with some initial results. Ben Adcock Purdue University Douglas Holton ben [email protected] Embry-Riddle Aeronautical University [email protected] MS300 MS299 Representation Using the Weyl Transform Tri-Located Course in Mathematical Modeling and Complementary Reu Summer Workshop The Weyl transform is introduced as a powerful framework for representing measurement data. Transform coefficients This talk will report the summative evaluation for the are connected to the Walsh-Hadamard transform of multi- project funded by NSF TUES to create a cluster of collab- scale autocorrelations, and different forms of dyadic peri- orating institutions that combine students into common odicity in a signal are shown to appear as different features classes and use cyberlearning technologies to deliver and in its Weyl coefficients. A large group of multiscale trans- manage instruction. We will also share the course-based formations is shown to support very fast pooling since the research experience that was complemented by innovative Weyl coefficients are unique up to permutation and phase undergraduate research summer workshops. We will dis- changes when the original signal is transformed by any ele- cuss ideas how to advance CSE Education through MOOC, ment of this group. The effectiveness of the Weyl transform project-based learning, and deep learning assessment tech- is demonstrated through the example of textured image nology. classification.

Hong Liu Robert Calderbank Department of Mathematics Mathematics Embry-Riddle Aeronautical University Duke University 234 CS15 Abstracts

[email protected] [email protected]

Thomas M. Hagstrom MS300 Southern Methodist University Compressive Parameter Estimation via Approxi- Department of Mathematics mate Message Passing [email protected] The literature on compressive parameter estimation has been mostly focused on the use of sparsity dictionaries MS301 that encode a sampling of the parameter space; these dic- tionaries, however, suffer from coherence issues that must High-Order Upwind Methods for Second-Order be controlled for successful estimation. We propose the Wave Equations on Curvilinear and Overlapping use of statistical parameter estimation methods within the Grids approximate message passing (AMP) algorithm for signal In this talk I will present preliminary results for a promising recovery. Our proposed work leverages the recently high- new technique to PDE discretization. The approach, called lighted connection between statistical denoising methods Galerkin finite differences, blends the attractive features and the thresholding step commonly used during recovery. from finite differences and finite elements to yield schemes As an example, we consider line spectral estimation by with provable energy stability, high-order accuracy, and leveraging the well-known MUSIC algorithm. Numerical well-conditioned discrete systems even for very high order. experiments show significant improvements in estimation Results are presented for the wave equation using both performance. continuous and discontinuous representations. Shermin Hamzehei University of Massachusetts Jeffrey W. Banks [email protected] Lawrence Livermore National Laboratory [email protected] Marco F. Duarte University of Massachusetts Amherst MS301 [email protected] A Discontinuous Galerkin Method for the Spher- ically Reduced Einstein Field Equations with MS300 Second-Order Operators Fast and Robust Dictionary Learning, with Invari- ances and Multiresolution A discontinuous Galerkin (dG) method for evolving a spherically reduced formulation of the Einstein field equa- We introduce a novel dictionary learning procedure for tions of general relativity is proposed. The system is dis- learning sparsifying representations for images. Sparse cretized in its natural first-order in time second-order in representations have been used successfully for a variety space form. I will discuss in some detail our scheme as of imaging tasks, from denoting to imprinting to super- well as our treatment of the second-order spatial operators resolution. Key features of our construction are (1) the which appear in this particular system. By approximating ability of seamlessly construct a dictionary for patches of the second-order spatial derivatives of the system, we avoid images at different scales, rather than on patches of a fixed the need to introduce extra fields and equations which can size; (2) the ability to produce representations that are lead to new challenges. We demonstrate stable, long-time invariant under a known, given desired invariances (e.g. evolutions achieved by our scheme, which also constitutes translations, rotations); (3) having fast algorithms for both the first use of dG methods in computational general rel- the construction of the dictionary, and for computing the ativity. I will conclude with a brief overview of current sparse representation of a signal onto the dictionary; (4) status of dG methods within the computational relativity theoretical finite sample guarantees on the learning algo- community. rithm. Scott Field Mauro Maggioni,SamuelGerber Department of Astronomy Department of Mathematics Cornell University Duke University sfi[email protected] [email protected], [email protected] Jan Hesthaven EPFL MS301 jan.hesthaven@epfl.ch Upwind DG for Acoustic and Elastic Wave Equa- tions Stephen Lau Mathematics We develop and analyze a new strategy for the spatial dis- The University of New Mexico continuous Galerkin discretization of wave equations in sec- [email protected] ond order form. The method features a direct, parameter- free approach to defining interelement fluxes. Both energy- Abdul Mroue conserving and upwind discretizations can be devised. We Canadian Institute for Theoretical Astrophysics derive a priori error estimates in the energy norm for cer- [email protected] tain fluxes and present numerical experiments showing that optimal convergence in L2 is obtained.

Daniel Appelo MS301 University of New Mexico Uncertainty Quantification for High Frequency CS15 Abstracts 235

Waves Software and Services Group Intel Corporation, Hillsboro, OR, USA We consider the wave equation with highly oscillatory ini- [email protected] tial data, where there is uncertainty in the wave speed, ini- tial phase and/or initial amplitude. To estimate quantities Anand Deshpande of interest related to the solution, and their uncertainty, Parallel Computing Laboratory we combine a high frequency method based on Gaussian Intel Corporation, Bangalore, India beams with stochastic collocation. We show that this is [email protected] an efficient approach for quadratic quantities of interest, since they vary smoothly with respect to the random vari- ables, with derivatives bounded independently of the wave Alexander Heinecke frequency. Parallel Computing Laboratory Intel Corporation, Santa Clara, CA, USA Olof Runborg [email protected] KTH, Stockholm, Sweden [email protected] Dheevatsa Mudigere Parallel Computing Laboratory Intel Corporation, Bangalore, India MS302 [email protected] A Consistent and Robust Discrete Adjoint Solver for the SU2 Framework Mikhail Smelyanskiy Intel Corporation In this talk we discuss the development of a discrete adjoint [email protected] solver, which enables the computation of consistent gradi- ents in a robust way based on the exploitation of the fixed- point structure of the flow solver. All occurring derivatives MS302 in this formulation can be calculated using advanced tech- Large Scale Design Using Su2 and a Continuous niques of Algorithmic Differentiation so that the extension Adjoint Rans Approach to arbitrary complex flow models can be performed along with the development of the primal code. Abstract not available at time of publication. Tim Albring TU Kaiserslautern Francisco Palacios [email protected] Stanford University [email protected] Nicolas R. Gauger RWTH Aachen University MS302 [email protected] A Discrete Adjoint Framework for Lift- Constrained Noise Minimization Using SU2 MS302 This talk presents an discrete adjoint-based framework High-Performance Optimizations of the Unstruc- for aeroacoustic shape optimization. The unsteady ad- tured Open-Source SU2 Suite joint solver is developed by applying algorithmic differen- Strategies and lessons learned from applying high- tiation (AD) to the open source SU2 code. A practical lift- performance optimizations to an open-source computa- constrained noise minimization formulation is presented in tional fluid dynamics suite, SU2, are presented. We fo- which the acoustic signal is minimized at a far-field obser- cus on performance optimizations of solver execution with vation point while a lift constraint is imposed to ensure emphasis on parallelization and on finding well-suited algo- adequate aerodynamic performance in low speed operating rithms. The resulting code modifications are geared toward conditions. achieving high scalability with edge-based CFD solvers such as SU2, making efficient use of memory, and choosing Beckett Zhou appropriate algorithms for maximizing parallelism, espe- TU Kaiserslautern cially for solving linear systems arising from implicit time [email protected] discretizations. Nicolas R. Gauger Thomas Economon RWTH Aachen University Department of Aeronautics and Astronautics [email protected] Stanford University [email protected] Thomas Economon Department of Aeronautics and Astronautics Francisco Palacios Stanford University Stanford University [email protected] [email protected] Francisco Palacios Juan J. Alonso Stanford University Department of Aeronautics and Astronautics [email protected] Stanford University [email protected] Juan J. Alonso Department of Aeronautics and Astronautics Gaurav Bansal Stanford University 236 CS15 Abstracts

[email protected] has been observed in numerical experiments with splines than for Lagrange basis functions with equal support.

MS303 Elwin Van ’t Wout Time-Domain Simulation of Two Dimensional Elas- University College London tic Scattering Centre for Medical Image Computing [email protected] We show how a combination of a simple Nystrom discretization in the Laplace domain and Convolution Quadrature can be used for simulation of transient elas- MS303 tic waves around a finite number of obstacles and cracks in Recent Advances in the Convolution Quadrature two dimensions. The implementation of most of the inte- and Temporal Galerkin Approaches to Transient gral operators is based on naive quadrature formulas and Electromagnetics well chosen mixing parameters. Only the hypersingular integral operator requires the careful use of a regulariza- Time domain integral equation based methods for the so- tion formula that is known in the literature. The Calder´on lution of electromagnetics and scattering problems have Calculus thus defined can be used for exterior scattering been increasing in popularity in recent years. Two meth- problems, transmission problems in locally homogeneous ods, convolution quadrature and temporal Galerkin, have materials, and even in problems in wave-structure interac- become popular for the discretization of these equations, tion. and have spawned many variants. This talk will compare and contrast these methods, especially in their most recent Victor Dominguez incarnations in electromagnetics, with respect to stability, Universidad Publica de Navarra accuracy, and efficiency. Spain [email protected] Daniel Weile University of Delaware [email protected] Tonatiuh Sanchez-Vizuet University of Delaware [email protected] Balasubramaniam Shanker Department of Electrical and Computer Engineering Michigan State University Francisco J. J. Sayas [email protected] Department of Mathematical Sciences University of Delaware [email protected] MS304 Development of a Contact MiniApplication Using MS303 Kokkos Variable Order Fast Multipole Method for an Elas- We present a new approach at the contact global search al- todynamic BEM gorithm, targeted at providing high performance on many- core computer architectures. Sandias ACME contact li- A fast time domain BEM based on the CQM is under brary was chosen to serve as the reference implementa- study. Chebyschev polynomials are used as kernel expan- tion. A new global search algorithm was implemented, us- sion within the Fast Multipole Method. Furthermore, a di- ing the Kokkos performance portable programming model, rectional clustering schema is applied to establish the hier- that is based on a Morton-code linearized Bounding Vol- archical cluster tree. A variable order FMM is implemented ume Hierarchy (BVH) developed by Nvidia for execution to obtain optimal complexity while ensuring convergence. on GPU co-processors. We conclude with results that com- Some examples show the suitability of the proposed ap- pare the reference ACME search approach using MPI with proach. the new Morton algorithm using MPI and multicore pro- cessing within each MPI rank. Thomas Traub Graz Univeristy of Technology Glen Hansen,PatrickXavier,SamMish Institute of Applied Mechanics Sandia National Laboratories [email protected] [email protected], [email protected], [email protected] Martin Schanz Technical University of Graz [email protected] MS304 Co-Designing Hierarchical Algorithms: Applica- tion to Vlasov-Maxwell Particle-in-Cell Methods MS303 Accuracy of the Marching-on-in-Time Scheme for Often, multiscale mathematical descriptions admit a multi- Td-Bie Methods layered (hierarchical) description based on a systematic coarse-graining procedure. Recently, such hierarchical de- The marching-on-in-time (MOT) scheme is a popular dis- scriptions have been demonstrated to provide significant al- cretization technique for Time Domain Integral Equation gorithmic acceleration in a number of challenging applica- methods. The choice of temporal basis function has a pro- tions. Moreover, the layered nature of these algorithms has found impact on the computational characteristics. We opened novel opportunities for co-design, which can be ex- will present an analysis of the accuracy in time of the MOT ploited to maximize FLOPs and minimize communication. scheme based on the interpolation accuracy of the tempo- In this presentation, we will discuss our co-design strat- ral basis functions. Surprisingly, a higher order of accuracy egy for hierarchical algorithms, exemplified with a particle- CS15 Abstracts 237

based implementation of the Vlasov-Maxwell system. King Saud University [email protected] Joshua Payne, Luis Chacon, Guangye Chen, Chris Newman, Dana Knoll, Allen McPherson Los Alamos National Laboratory PP1 [email protected], [email protected], [email protected], cnew- Numerical Study of Thin Viscoelastic Films on [email protected], [email protected], [email protected] Substrates

We numerically study the interfacial dynamics and insta- MS304 bility of a thin viscoelastic film on a substrate. We use the Uintah/Wasatch: Addressing Multiphsyics Com- long wave approximation to describe the non-linear evo- plexity in a High-Performance Computing Envi- lution of the interface. We consider different regimes of ronment slippage, and in each regime, we investigate the role of the liquid viscoelasticity and of the contact angle on the thin To address the coding and software challenges of modern film break-up. Numerical solutions of the full non-linear hybrid architectures, we propose a modern approach to equations are compared with the results of the linear sta- multiphysics code development. The approach is based on bility analysis. using a Domain Specific Language in tandem with runtime algorithm generation. When coupled with a large-scale Valeria Barra parallel framework, the result is an architecture-proof code New Jersey Institute of Technology capable of executing on hybrid platforms. We share our [email protected] experience developing such a code - an effort that spans an interdisciplinary team of engineers and computer scientists. Shahriar Afkhami Tony Saad Department of Mathematical Sciences The Institute for Clean and Secure Energy New Jersey Institute of Technology Department of Chemical Engineering, University of Utah [email protected] [email protected] PP1 Christopher Earl A Novel Modeling Approach for Multiscale, Mul- University of Utah tiphysics Flow [email protected] Turbulent combustion simulation remains a challenging Abhishek Bagusetty problem due to the wide range of time and length scales Chemical Engineering associated with the governing physics. We propose a novel University of Utah methodology, termed Lattice-Based Multiscale Simulation [email protected] (LBMS) that creates a 3D network of widely spaced lines with fully resolved 1D physics along each line. Local tur- Matthew Might bulence along a line is modeled stochastically while lattice- The University of Utah scale advection is captured directly. LBMS is ideal for sit- [email protected] uations where multiscale coupling is key like wall-bounded flows, reacting flows, etc. James C. Sutherland Department of Chemical Engineering Derek A. Cline The University of Utah University of Utah [email protected] Chemical Engineering Department [email protected]

PP1 PP1 Lid Driven Cavity Simulations in 2d and 3d Using High Accurate Methods Flusepa - a Navier-Stokes Solver for Unsteady Problems with Bodies in Relative Motion : Toward in this poster, numerical simulations of two-dimensional a Task-Based Parallel Version over a Runtime Sys- and three-dimensional partial differential equations are tem for Large Simulations presented by solving the steady navier-stokes equations in a lid driven cavity at high Reynolds numbers where FLUSEPA code is designed to handle unsteady prob- it becomes difficult. in two dimensions, we use the lems with bodies in relative motion (stage separation) and streamfunction-vorticity formulation to solve the problem strong shocks. A finite volume formulation is used to solve in a square domain. a numerical computational method is the RANS equations. Time integration consists on an ex- employed to discretize the problem in the x and y directions plicit temporal adaptive solver. We present a task based with a spectral collocation method. the problem is coded parallel version of the aerodynamic solver designed from in the matlab programming environment. solutions at high the previous MPI/OpenMP one and using a modern run- reynolds numbers are obtained up to re=20000 on a fine time system to schedule the tasks. An Ariane 5 booster grid. Also in this poster, the numerical computational sim- separation computation will be presented. ulation for the three-dimensional lid-driven cavity problem are obtained by solving the velocity-vorticity formulation Jean Marie Couteyen Carpaye of the navier-stokes equations (which is the first time that Airbus Defence and Space this has been simulated with special boundary conditions) Inria for various Reynolds numbers. [email protected] Badr Alkahtani Jean Roman 238 CS15 Abstracts

INRIA [email protected] [email protected] Kai Schneider Pierre Brenner Universite de Provence, Aix-Marseille Airbus Defence and Space Centre de Mathematiques et Informatique [email protected] [email protected]

Rupert Klein PP1 Freie Universit¨at Berlin Efficiency of an Adjoint Industrial CFD Code [email protected]

We apply Algorithmic Differentiation on the commercial flow solver CFD-ACE+ to derive a discrete adjoint code. PP1 The objective is to assess its performance and to improve A Numerical Study of Shock-Induced Cavity Col- its efficiency in terms of memory consumption and runtime. lapse in a Solid Explosive To achieve that, we combine the flexibility of an operator overloading tool with the efficiency of an adjoint code gen- The shock-induced collapse of a gas-filled cavity in a solid erated by source transformation. In addition, we speed up explosive is examined. The system is modeled as a multi- the adjoint computation by exploiting the mathematical material compressible fluid with a mixture equation of aspect of the involved fixed-point iteration. state and an ignition-pressure reaction rate. The govern- Zahrasadat Dastouri ing equations are solved numerically using a Godunov-type STCE,RWTH Aachen University scheme designed to accommodate the large impedance mis- [email protected] match at the fluid-solid interface. Results are described for ellipsoidal cavities of various shapes to determine whether the collapse initiates a detonation in the reactive material. Johannes Lotz STCE, RWTH Aachen University Germany James R. Gambino [email protected] RPI [email protected] Uwe Naumann RWTH Aachen University Ashwani K. Kapila Software and Tools for Computational Engineering Rensselaer Polytechnic Inst. [email protected] [email protected]

PP1 Donald W. Schwendeman Rensselaer Polytechnic Institute Production of Dissipative Vortices by Solid Bodies Department of Mathematical Sciences in the Inviscid Limit of Incompressible Fluid Flows: [email protected] Comparison Between Prandtl, Navier-Stokes and Euler Solutions William Henshaw We revisit the problem posed by Euler in 1748 that lead Rensselaer Polytechnic Institute d’Alembert to formulate his paradox and we address the [email protected] following question: does energy dissipate when boundary layer detaches from a solid body in the vanishing viscosity limit? To trigger detachment we consider a vortex dipole PP1 impinging onto a wall and we compare the numerical solu- Scalable Advection Algorithms for Multi-Tracers in tions of Euler, Prandtl, and Navier-Stokes equations. We Climate Codes observe the formation of two opposite-sign boundary layers whose thickness scales as predicted by Prandtl’s 1904 the- One of the important goals of ACES4BGC project (Apply- ory. But after a certain time Prandtl’s solution becomes ing Computationally Efficient Schemes for BioGeochemical singular, while the Navier-Stokes solution collapses down Cycles) is to implement and optimize new computationally to much finer thickness for the boundary layers, in accor- efficient advection algorithms for large number of tracer dance with Kato’s 1984 theorem. Then the boundary layers species. This work demonstrates a framework that uses in- roll up and form vortices which detach from the wall and tersection algorithms developed in MOAB (Mesh Oriented dissipate a finite amount of energy, even in the vanishing datABase), linked with a HOMME dynamical core driver. viscosity limit.

Marie Farge Iulian Grindeanu LMD-CNRS Argonne National Laboratory Ecole Normale Superieure [email protected] [email protected] Kara Peterson Romain Nguyen van yen Sandia Natl. Labs Freie University, Berlin, Germany [email protected] [email protected] Vijay Mahadevan, Navamita Ray, Rajeev Jain Matthias Waidmann Argonne National Laboratory Freie University, Berlin (Germany [email protected], [email protected], CS15 Abstracts 239

[email protected] [email protected]

Ricardo Cortez PP1 Tulane University Fast Ship Hydrodynamics Via Novel Methods Mathematics Department [email protected] An existing high-order finite difference, potential flow solver for large-scale ocean wave modeling is extended to include interaction with floating bodies via a new PP1 immersed-boundary technique based on weighted least Computational Hydrodynamics: How Portable squares. High-order WENO schemes are used for the free- and Scalable Are Heterogeneous Programming surface boundary conditions to obtain stable solutions for Paradigms? the linear seakeeping response of a ship at forward speed. The code is implemented on massively parallel GPU archi- Many-core era applications at the interface of mathemat- tectures using the CUDA API. ics and computer science adopt modern parallel program- ming paradigms and expose parallelism through proper al- Stavros Kontos gorithms. We present results for a novel massively parallel DTU - Technical University of Denmark free surface wave model suitable for advanced experiments [email protected] in Numerical Wave Tanks. Our application exhibits ex- cellent performance portability and scalability using hy- Ole Lindberg brid MPI-OpenCL/CUDA and running on arbitrary sys- FORCE Technology tem sizes including desktops, superclusters and cloud uti- [email protected] lizing heterogeneous devices like multi-core CPUs, GPUs, andXeonPhicoprocessors. Allan Engsig-Karup The Technical University of Denmark Wojciech Pawlak [email protected] DTU Compute, Technical University of Denmark Allan P. Engsig-Karup Associate Professor, Ph.D. [email protected] Harry Bingham Technical University of Denmark DTU MECHANICAL ENGINEERING Allan Engsig-Karup [email protected] The Technical University of Denmark [email protected]

PP1 Stefan Glimberg A Conservative, Positivity Preserving Scheme for Lloyd‘s Register Consulting Reactive Solute Transport Problems in Moving Do- [email protected] mains

We study the mathematical models and numerical schemes PP1 for reactive transport of a soluble substance in deformable A Fully Discrete Derivation of a Direct Ale Conser- media. The problem is modeled by a convection-diffusion vative Scheme for Compressible Hydrodynamics adsorption-desorption equation in moving domains. We present a conservative, positivity preserving, high resolu- Lagrange plus remap schemes have been used for years in tion ALE-FCT scheme for this problem in the presence industrial applications. However, this kind of scheme can of dominant transport processes and wall reactions on the lead to some difficulties with conservativity and computa- moving wall. A Patankar type time discretization is pre- tional cost. In this work, a direct ALE scheme is provided sented, which provides conservative treatment of nonlinear using a least action principle to a discretized action inte- reactive terms. Consequences of this result are significant gral in both space and time. The internal energy equation in the area of, e.g., nano-particle cancer drug delivery. Our follows from the conservation of the total energy. This result shows that periodic excitation of the cancerous tissue mimetic procedure guarantees the physical compatibility using, e.g., ultrasound, may enhance adsorption of cancer between the thermodynamical variables. drugs carried by nano-particles via the human vasculature. Thibaud Vazquez-Gonzalez CEA Bruyeres le Chatel Sibusiso Mabuza [email protected] University of Houston [email protected] Antoine Llor, Christophe Fochesato CEA [email protected], [email protected] PP1 Singly-Periodic Stokes Flow with a Wall PP2 A closed formula for the 2D singly-periodic laminar veloc- A Non Standard Scheme for Nagumo Type Differ- ity field near a solid straight boundary is derived using the ential Equations method of images. The flow is induced by regularized peri- odic forces. This result provides a model, for instance, for In this work, we design explicit difference schemes for the the modeling of cilia. Nagumo reaction-diffusion and the Allen-Cahn equations. The Nonstandard exact schemes that we design for the Forest O. Mannan space-independent sub-equations help to reduce the com- Tulane University putational cost common with difference schemes approx- 240 CS15 Abstracts

imation of singularly perturbed equations like the Allen- Alexander Kurganov Cahn. A careful assemblage of these schemes with the en- Tulane University ergy preserving scheme of the steady state equation yields Department of Mathematics a uniformly convergent difference scheme for the equations. [email protected]

Zhuolin Qu Adebayo A. Aderogba Tulane University University of Pretoria [email protected] South Africa aderogba [email protected] Tao Tang Hong Kong Baptist University Michael Chapwanya, Pius Chin [email protected] Department of Mathematics and Appl Math. University of Pretoria [email protected], [email protected] PP2 Method of Lines Transpose Schemes for Parabolic PP2 Problems Reduced Basis Methods for Calibration and Option Pricing We present a novel numerical scheme suitable for solv- ing parabolic differential equation model using the Method We present reduced basis approximations for parametrized of Lines Transpose (MOLT ) combined with the successive time-dependent variational (in-)equalities with the special convolution operators. The primary advantage is that the focus on applications from finance. In particular, we con- operators can be computed quickly in O(N) work, to high sider the case of calibrating European and American op- precision; and a multi dimensional solution is formed by tions with the Heston model. With the use of an offline- dimensional sweeps. We demonstrate our solver on the online computational procedure, we significantly reduce Allen-Cahn and Cahn-Hilliard equation. the computational cost of the calibration phase. Numerical tests illustrate the approximation quality and convergence Hana Cho of the reduced basis methods and it’s advantage in appli- Michigan State University cation to the calibration algorithms. [email protected] Olena Burkovska Technical University of Munich Andrew J. Christlieb [email protected] Michigan State Univerity Department of Mathematics [email protected] Kathrin Glau Technical University Munich [email protected] Matt Causley Kattering University [email protected] Mirco Mahlstedt Technical University of Munich Chair of Mathematical Finance David Seal [email protected] Michigan State University [email protected] Barbara Wohlmuth Technical University of Munich [email protected] PP2 Comparison of Nonlinear and Linear Stabilization PP2 Schemes for Advection-Diffusion Equations A Fast and Stable Explicit Operator Splitting Standard finite element discretizations of advection- Method for Phase-Field Models diffusion equations introduce unphysical oscillations around steep gradients. Therefore, stabilization must be We propose a combined finite difference and pseudo- added to the discrete formulation to obtain correct solu- spectral method for one- and two-dimensional nonlinear tions. The SUPG, dCG91, and Entropy Viscosity schemes diffusion equations for thin film epitaxy with slope selection are compared using stationary and non-stationary test and Cahn-Hilliard equation. Equations are split into non- equations. Differences in maximum overshoot and under- linear part, solved using the method of lines approach to- shoot, smear, and convergence orders are compared using gether with an efficient large stability domain ODE solver; code written using deal.ii and linear part, solved by a pseudo-spectral method, which is based on the exact solution and thus has no stability re- striction on the size of time step. Finally, an adaptive Ryan R. Grove time-stepping strategy is introduced for long time simula- SIAM Webmaster at Clemson University tion. [email protected]

Yuanzhen Cheng Timo Heister Tulane University Clemson University [email protected] Mathematical Sciences CS15 Abstracts 241

[email protected] of the BSQI scheme.

Rakesh Kumar PP2 IIT Bombay A Task-Parallel Approach for Solving PDEs on a [email protected] Lattice Sambandam Baskar We solve PDE’s on a lattice. This creates a unique set of Indian Institute of Technology Bombay communication patterns, at the intersections of the lines [email protected] on the lattice, creating a coarse mesh, and between parallel lines, creatine overlapping fine meshes. We use a directed a-cyclical graph to order the execution and communication PP2 in parallel across the lattice, via sender-poller; allowing, in NIST AMR Benchmarks parallel, different pieces of the problem to be solved con- currently while communication is happening. Adaptive mesh refinement (AMR) techniques for the nu- merical solution of PDEs have been under development for John T. Hutchins many years. Most research papers conclude with numeri- Boise State University‘ cal results to demonstrate the effectiveness of a proposed [email protected] method. Although there are some commonly used prob- lems, like the L-domain problem, many disparate test prob- Derek A. Cline lems have been used. NIST has mined the AMR literature University of Utah to create a collection of standard test/benchmark problems Chemical Engineering Department for AMR. The resulting web resource will be demonstrated. [email protected] William F. Mitchell James C. Sutherland NIST, Gaithersburg, MD Department of Chemical Engineering [email protected] The University of Utah [email protected] PP2 PP2 Finite Element Methods for the Evolution Problem in General Relativity Finite Element Analysis of Free Material Optimiza- tion Problems Gravitational waves can be understood as small ripples in the fabric of the Universe, caused by moving masses. To In Free Material Optimization, the design variable is the detect such weak waves, several new gravitational wave full material tensor of an elastic body. Written in matrix observatories are being built. Computer simulations are notation one obtains a control-in-the-coefficients problem essential for determining expected signals and interpreting for the material tensor. With this poster we present re- the data. This project consists of the design and implemen- cent results in the finite element analysis in Free Material tation of a new mixed finite element method for the prop- Optimization. We employ the variational discretization ap- agation of gravitational waves, by adapting the recently proach, where the control (i.e., material tensor) is only im- developed Finite Element Exterior Calculus framework. plicitly discretized. Numerical examples supplement our analytical findings. Vincent Quenneville-Belair School of Mathematics Tobias Jordan University of Minnesota University of Hamburg [email protected] Department of Mathematics [email protected] PP2 Michael Hinze Massively Parallel Radiation Transport Sweeps on Universit¨at Hamburg Unstructured Grids Department Mathematik [email protected] The massively parallel radiation transport code PDT has recently scaled to 432,000 processes with an efficiency greater than 70%. The discretization techniques employ PP2 a Discontinuous FEM method in space and a discrete- Higher Order Numerical Schemes for Convec- ordinate collocation in angle. The algorithm is based on tion Diffusion Equation Based on B-Spline Quasi- a transport sweep, whereby the solution for a given an- Interpolation gle is done one cell at a time. The parallel transport sweep algorithm is provably optimal for logically Cartesian In the present work, we propose B-Spline Quasi- meshes. However, complex geometries cannot be efficiently Interpolation (BSQI) based higher order numerical scheme meshed with regular grids, even with point motion. In this for convection-diffusion equation in one and two space di- work, we present an unstructured mesh generation capa- mensions. The linear stability of BSQI scheme is establish bility that satisfies most of the requirements for optimal using the von-Neumann analysis. We find the CFL con- sweeps. Notably, the subdomain partitions remain convex dition under which BSQI scheme is stable. Numerical ex- and pipe-filling within a subdomain is preserved; however, periments are performed for the non-linear problems like a load imbalance in terms of spatial unknowns may ex- Burgers’ equation, Buckley-Leverett, and the incompress- ist between subdomains due to local geometrical features. ible flow to measure the accuracy and rate of convergence Numerical results are presented and strategies to mitigate 242 CS15 Abstracts

spatial load imbalance are discussed. [email protected]

Jean C. Ragusa, Tarek Ghaddar Department of Nuclear Engineering PP2 Texas A&M University A Second-Order Maximum Principle Preserving [email protected], [email protected] Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations Michael Adams Texas A&M University Based on one of our accepted paper (J.-L. Guermond et [email protected] al.), this poster will show an explicit, (at least) second- order and maximum principle satisfying lagrange finite el- ement method for solving nonlinear scalar conservation PP2 equations. The algorithm works for arbitrary meshes in any space dimension and for all Lipschitz fluxes. The for- The Discrete Maximum Principle in the Family of mal second-order accuracy and the convergence properties Mimetic Finite Difference Methods are tested on a series of linear and nonlinear benchmark problems. The Maximum Principle is the important property of PDEs. To mimic this property in simulations is very de- Jean-Luc Guermond sirable in wide range of applications. The mimetic finite Department of Mathematics difference method produces a family of schemes with equiv- Texas A&M, USA alent properties such as the stencil, stability region, and [email protected] convergence order. Each member is defined by parameters which can be chosen locally for every cell. We present a new adaptation methodology that identifies members Murtazo Nazarov which satisfies the discrete maximum principle. TAMU [email protected] Daniil Svyatskiy Los Alamos National Laboratory Bojan Popov [email protected] Department of Mathematics Texas A&M University Gianmarco Manzini [email protected] LANL [email protected] Yong Yang Texas A&M University Konstantin Lipnikov [email protected] Los Alamos National Laboratory [email protected] PP3 A New Test for Exclusion Algorithm to Find the n PP2 Optimum Value of Function in R A Locally Adaptive RBF-FD Method The problem of finding the global minimum of a vector function is very common in science, economics and engi- Conventional Radial Basis Function (RBF) methods for neering. One of the most notable approaches to find the numerically solving partial differential equations use global global minimum of a function is that based on interval approximations resulting in dense matrices that grow in analysis. In this area, the exclusion algorithms (EAs) are size if the algorithm refines. The Radial Basis Function – a well-known tool for finding the global minimum of a func- Finite Difference (RBF-FD) approach is a local approxima- tion over a compact domain. There are several choices for tion method that utilizes nearest neighbor nodes and yields the minimization condition. In this paper, we introduce a a sparse implementation. Unfortunately RBF-FD matrices new exclusion test and analyze the efficiency and compu- have fixed stencils and the approximations can lose accu- tational complexity of exclusion algorithms based on this racy. In this paper we propose using local approximations approach. We consider Lipschitz functions and give a new with locally adaptive stencils that take advantage of both minimization condition for the exclusion algorithm. Then global and local approximations. In this approach the sten- we study the convergence and complexity of the method. cil sizes stay fixed where the solution is smooth but grow in size only where refinement is needed. The advantage of Ibraheem Alolyan this method is that it is computationally efficient and sta- King Saud University ble offering comparable accuracy to global approximations [email protected] with significantly lower computational cost.

Wade Meyers PP3 University of Wisconsin - Stout Approximation and Error Estimation in High Di- [email protected] mensional Space for Stochastic Collocation Meth- ods on Arbitrary Sparse Samples Talin Masihimirzakhanian Cal Poly Pomona We have develop a fast method that can capture piece- [email protected] wise smooth functions in high dimensions with high order and low computational cost. This method can be used for Keith Wojciechowski both approximation and error estimation of stochastic sim- University of Wisconsin - Stout ulations where the computations can either be guided or CS15 Abstracts 243

come from a legacy database. We demonstrate how this Nie Jiawang method compares to Gaussian processes. Department of Mathematics, University of California San Diego Richard Archibald [email protected] Computational Mathematics Group Oak Ridge National Labratory [email protected] PP3 A Python Toolbox for Shape Optimization in Imag- ing and Data Analysis PP3 Rational Least Squares Fitting using Krylov Spaces Many data analysis and image processing problems are nat- urally expressed as shape optimization problems, e.g. im- For given square matrices A, F and a vector v,weconsider min age segmentation, surface reconstruction. The shape opti- the problem of finding a rational function Rm of type mization approach is a great fit for such problems because (m, m) such that of its intuitiveness and the ?exibility to easily incorporate data ?delity, geometric regularization and statistical prior 2 F v − Rm(A)v2 → min, terms. However, carrying out the actual minimization in an ef?cient and reliable manner requires overcoming many and propose an iterative algorithm for its solution. In the technical challenges. In this work, we introduce a Python special case when A =diag(λj )andF =diag(ψj )are toolbox that implements a diverse collection of shape ener- diagonal we have a weighted rational least squares fitting gies for image processing, and state-of-the-art optimization N 2 2 problem j=1 |vj | ·|ψj − Rm(λj )| → min, and compare methods to compute their solutions. our method to the popular vector fitting algorithm. Gunay Dogan Mario Berljafa Theiss Research, NIST School of Mathematics [email protected] The University of Manchester [email protected] PP3 Stefan Guettel Discovering Block Structure in Graphs with Ap- The University of Manchester proximate Eigenvectors [email protected] Graphs and Networks are important in modeling structure across disciplines. We demonstrate that graph partition- PP3 ing in a minimum cut sense can be improved with an en- A Hybrid Openmp/mpi Cg Iterative Eigensolver semble of low-fidelity eigenvectors which can outperform for First-Principles Plane Wave Materials Science a single high-fidelity eigenvector. These ensembles can be Codes computed faster and be more helpful than one high-fidelity eigenvector. Since the individual ensemble members are in- First-principles materials science codes based on density dependent they can be computed in parallel. functional theory (DFT) and using plane waves (PW) have become the largest user (by method) of computer cycles at James Fairbanks scientific computer centers around the world. We present Georgia Institute of Technology a hybrid OpenMP/MPI Conjugate Gradient based itera- [email protected] tive eigensolver that allows this approach to scale to tens of thousands of cores on modern many core parallel com- Geoffrey D. Sanders puters. Performance results will be presented for the Cray Center for Applied Scientific Computing XE6 and XC30 architectures. Lawrence Livermore National Lab [email protected] Andrew M. Canning Lawrence Berkeley National Laboratory [email protected] PP3 Efficient Multigrid Methods for Distributed Opti- mal Control Problems Constrained by Parabolic PP3 Equations All Real Eigenvalues of Symmetric Tensors In this work we present numerical computations in sup- This poster displays how to compute all real eigenvalues port of our theoretical results regarding convergence prop- of a symmetric tensor. As is well known, the largest or erties of multigrid preconditioners for linear systems aris- smallest eigenvalue can be found by solving a polynomial ing in the solution process of space-time distributed opti- optimization problem, while the other middle eigenvalues mal control problems constrained by linear and semi-linear can not. We propose a new approach for computing all real parabolic equations. As for elliptic-constrained problems, eigenvalues sequentially, from the largest to the smallest. the number of preconditioned linear iterations per opti- We show that each eigenvalue can be computed by solving mization iteration is shows to decrease with increasing res- a finite hierarchy of semidefinite relaxations. Numerical olution, but the rate of decrease is suboptimal by half an experiments are presented. order.

Cui Chunfeng, Dai Yu-Hong Mona Hajghassem Academy of Mathematics and Systems Science, Department of Mathematics and Statistics Chinese Academy of Sciences University of Maryland, Baltimore County [email protected], [email protected] [email protected] 244 CS15 Abstracts

Andrei Draganescu University of Wisconsin-Milwaukee Department of Mathematics and Statistics, UMBC [email protected] University of Maryland, Baltimore County [email protected] PP4 Computed Tear Film and Solute Dynamics on An PP3 Eye-Shaped Domain Computing the Heat Kernel of a Graph for a Local Clustering Algorithm The concentration of ions (osmolarity) in the tear film is a key variable to understanding its dynamics. We derive We present an efficient local clustering algorithm that finds a system of nonlinear partial differential equations (PDEs) cuts in large graphs by performing a sweep over a heat that couples solutes and fluid dynamics on a 2D eye-shaped kernel pagerank vector. We show that for a subset S of domain. We solve these PDEs using the Overture computa- Cheeger ratio φ,manyverticesinS may serve as seeds tional framework with a hybrid BDF/RKC time-stepping for a heat kernel√ random walk which will find a cut of scheme. Our results agree with existing 1D models and conductance O( φ). Further, the random walk process is provide new insight into the osmolarity distribution and performed in time sublinear in the size of the graph. fluorescence imaging for in vivo experiments.

Olivia Simpson Richard Braun University of California, San Diego University of Delaware [email protected] Department of Mathematical Sciences [email protected]

PP4 Longfei Li Reduced Order Modelling for Optimal Cancer Department of Mathematical Sciences Treatment University of Delaware [email protected] We study reduced order modelling for optimal radiother- apy treatment plan. Boltzmann equation is used to model the interaction between radiative particles with tissue. At Tobin Driscoll first, we solve optimization problems: minimizing the de- University of Delaware viation from desired dose distribution. Then we consider a Mathematical Sciences parameterized geometry. In offline stage we solve a prob- [email protected] lem for sampled parameter values. The online phase then consists of solving the reduced problem for the actual set William Henshaw, Jeffrey Banks of parameters. Numerical results are presented. Rensselaer Polytechnic Institute [email protected], [email protected] Bahodir Ahmedov Aachen Institute for Advanced Study in P. Ewen King-Smith Computational Engineering Science (AICES) Ohio State University [email protected] [email protected]

Michael Herty, Martin Grepl RWTH Aachen University PP4 [email protected], [email protected] The Transcriptomic Clock of Human Cerebral Cor- tex Development

PP4 Singular value decomposition and clustering analysis of A Mesh Free Method for Numerical Simulation of stem cell RNA transcription data reveals the genes associ- Calcium Dynamics In Ventricular Myocytes ated with the stages of human embryonic cerebral cortex development. The method discovered a previously uniden- We consider a coupled system of non-linear reaction- tified stage between pluripotency and neural differentia- diffusion equations that model the spatio-temporal vari- tion containing distinct transcriptional patterns for over ation of intracellular calcium concentration in ventricular two thousand differentially expressed genes. Enrichment myocytes. We introduce a modified mesh free method and analyses of genes associated with neurological diseases with utilize exponential time differencing to significantly reduce respect to the resulting corticogenesis clock reveal distinct the simulation time. At the end we present numerical re- stages of development associated with root causes of the sults demonstrating the stability of the method when used disease. on uneven distribution of nodes. Elisabeth M. Brown Emmanuel O. Asante-Asamani Rensselaer Polytechnic Institute Department of Mathematical Sciences [email protected] University of Wisconsin-Milwaukee [email protected] Kristin Bennett Mathematical Sciences Bruce Wade Rensselaer Polytechnic Institute Department of Mathematical Sciences, UW-Milwaukee [email protected] Milwaukee, Wisconsin 53201-0413 [email protected] Hannah De Los Santos, Joey Lea Rensselaer Polytechnic Institute Zeyun Yu [email protected], [email protected] CS15 Abstracts 245

Nathan Boles, Thomas Kiehl, Sally Temple, Christopher Use of Gpu Computing Fasano Neural Stem Cell Institute Graphics Processing Units (GPUs) have been successfully [email protected], [email protected], sal- employed to accelerate scientific computing applications [email protected], [email protected] in several disciplines, including medical image process- ing. We demonstrate a novel computation- and memory- efficient diffeomorphic multi-level B-Spline transform com- PP4 posite method on GPUs for improving performance of non- Computational Methods to Study the Coordina- rigid registration of two CT lung images. The GPU method tion of Mechanical Forces Involved in Amoeboid is compared against its CPU counterpart, with GPU per- Cell Migration formance 112 times faster than the single-threaded CPU version occurring at highest resolutions while preserving We present a computational model to study the interplay accuracy. of cellular mechanics, substrate mechanics and cell-matrix interaction and the resulting migration. Our mathemat- Nathan Ellingwood, Youbing Yin ical framework considers a porous viscoelastic cytoplasm, University of Iowa adhesion dynamics, and substrate mechanics. Our model [email protected], [email protected] introduces a novel way of simulating a viscoelastic deform- ing network. Using our methodology we present insight Matthew Smith into the 3D cell-substrate forces for cells migrating on flat National Cheng Kung University substrates. The development and maintenance of multi- [email protected] cellular organisms relies on cell migration. During these processes, cells encounter a wide range of extracellular en- Ching-Long Lin vironments and adapt their migration strategy in response University of Iowa to mechanical properties of their environment. One of the [email protected] current challenges in cellular biology is to understand how the extracellular environment modulates the deployment of the cells’ molecular machinery to produce different mi- PP4 gratory behaviors. Reaction of a Solid Tumor According to the Injec- tion of Medical Supplies into Heart and Liver Calina A. Copos University of California Davis A mathematical model is developed to describe the varia- [email protected] tion of a solid tumor cells density in response to medical supplies. Two factors, random motility and chemotaxis in Robert D. Guy response to TAF gradients are considered for the equation Mathematics Department of tumor cells motion. The flow rate of medicines exerts University of California Davis influence on tumor cells density and tumor cells react sen- [email protected] sitively to the medical supplies at the first second, and the density decreases to around 20% of the initial amount.

PP4 Jaegwi Go Segmentation and Processing of Brain Images of Changwon National University Multiple Modalities in 2 and 3 Dimensions [email protected] Medical imaging of various modalities continues to ad- vance, providing higher resolution and higher signal to PP4 noise ratios than ever before. Software must keep up by Shear Wave Filtering in Bouligand Structures not only accounting for better quality images, but also with larger and larger datasets. We present work on segment- We propose that the presence of Bouligand-like structure ing and processing Magnetic resonance (MRI) and Elec- in the dactyl club of the Stomatopod lead to wave filter- tron microscopy (EM) images using advanced algorithms ing. The (nearly) periodicity of the microstructure suggest designed to scale in both 2 and 3 dimensions. an interaction between the microstructure and propagat- ing stress waves. The propose model use a combination of John Edwards, Brian Summa propagator matrix approach and the Floquet-Bloch theo- Scientific Computing and Imaging Institute rem. From these combined analyses we compute the trans- University of Utah mitted energy for different microstructural configurations. [email protected], [email protected]

Valerio Pascucci Nicolas Guarin Zapata SCI Institute - University of Utah Purdue University [email protected] [email protected]

Christopher Johnson Juan Gomez University of Utah Universidad EAFIT Department of Computer Science jgomezc1@eafit.edu.co [email protected] Nick Yaraghi, David Kisailus University of California PP4 [email protected], [email protected] Improving Performance of Multi-Level Nonrigid Registration of Two Ct-Based Lung Images With Pablo Zavattieri 246 CS15 Abstracts

Purdue University [email protected] [email protected]

PP5 PP4 Probability Measures on Numerical Solutions of Newtonian and Non-Newtonian Fluid Dynamics in Odes for Uncertainty Quantification and Inference Abdominal Aortic Aneurysms Deterministic ODE solvers are widely used, but charac- Biomedical research has recently indicated that some spe- terizing the error in numerical solutions within a coher- cific dynamic characteristics, such as the blood wall shear ent statistical framework is challenging. We successfully stress and oscillatory shear index, of the blood flow inside address this problem by constructing a probability mea- arteries with aneurysms are risk factors for both the en- sure over functions consistent with the ODE solution that largement and rupture of the associated aneurysm. The provably contracts to a Dirac measure on the unique so- primary objective of the project is to determine the influ- lution at rates determined by an underlying deterministic ence that the geometry of an abdominal aortic aneurysm solver. The measure straightforwardly derives from im- and the fluid constitutive model have on these specific char- portant classes of numerical solvers and is illustrated on acteristics. uncertainty quantification and inverse problems.

Danielle D. Masse, Jason Howell Patrick R. Conrad College of Charleston Massachusetts Institute of Technology [email protected], [email protected] [email protected]

Mark Girolami PP5 University College London [email protected] Adaptive Spectral Tensor-Train Decomposition for the Construction of Surrogate Models Simo Sarkka Aalto University We present a novel method for approximating high- simo.sarkka@aalto.fi dimensional functions, the cost of which scales linearly with the input parameter dimensionality. It hinges on the combination of the low-rank approximation of Andrew Stuart functions through the functional form of the tensor- Mathematics Institute, train decomposition and on the theory of polynomial University of Warwick approximation [D. Bigoni, Y. M. Marzouk, and A. [email protected] P. Engsig-Karup, Spectral tensor-train decomposition, arXiv preprint arXiv:1405.5713], using anisotropic adap- Konstantinos Zygalakis tive strategies to meet the desired accuracy. The method University of Southampton is relevant for high-dimensional Uncertainty Quantification [email protected] and inference. Synthetic and real applications will be pre- sented. PP5 Daniele Bigoni, Allan Engsig-Karup Adaptive Bayesian Selection, Calibration, and Vali- The Technical University of Denmark dation of Coarse-Grained Models of Atomistic Sys- [email protected], [email protected] tems Youssef M. Marzouk Massachusetts Institute of Technology The predictive power of coarse-grained (CG) approxima- [email protected] tions of atomistic systems is explored. Bayesian methods for statistical calibration, validation, and model selection using model plausibilities are used to develop basic princi- ples for developing CG and, eventually, macro-scale mod- PP5 els. An adaptive algorithm for Bayesian calibration and A Posteriori Error Estimation for a Cut Cell Finite selection of CG models is described and examples of appli- Volume Method in the Presence of Uncertainty cation to polymer chains is presented.

We consider a posteriori error estimates for interface prob- Kathryn Farrell lems. These are differential equations whose data is defined Institute for Computational Engineering and Sciences piecewise across a curve, or interface, partitioning the do- University of Texas at Austin main into two sections. Often, this interface is determined [email protected] from a small number of measurements, each of which has uncertainty associated with it, giving a stochastic interface J. Tinsley Oden problem. We develop a method of computing the error for The University of Texas at Austin each sample interface that is independent of the number of ICES samples. [email protected]

James B. Collins,SimonTavener,DonEstep Danial Faghihi Colorado State University Institute for Computational Engineering and Sciences [email protected], [email protected], es- University of Texas at Austin CS15 Abstracts 247

[email protected] Streamline Method

We give an analytical expression for the one-point distribu- PP5 tion functions of the water saturation for the 1D stochas- tic Buckley-Leverett problem with uncertainty in porosity Emgr - Empirical Gramian Framework and in the total Darcy flux. These distribution functions particularly lead to any one-point statistics of the water Gramian-based model reduction is a well established saturation. Comparisons with both MC simulations and a method for linear state-space systems. Beyond linear sys- low order approximation approach are provided. Finally, tems, empirical gramians expand the scope of gramian- based on the streamline concept, a generalization to mul- based methods to nonlinear systems. Furthermore, empir- tiple spatial dimensions is outlined. ical gramians can also be used for parametric model order reduction, parameter identification and parameter reduc- Fayadhoi Ibrahima tion. The empirical gramian framework is a Matlab soft- Stanford University ware toolbox enabling the computation of seven types of fi[email protected] empirical gramians, which have applications in model re- duction, system identification and uncertainty quantifica- Daniel W. Meyer tion. Institute of Fluid Dynamics [email protected] Christian Himpe Institute for Computational und Applied Mathematics Hamdi Tchelepi Universtiy of Muenster Stanford University [email protected] Energy Resources Engineering Department [email protected] Mario Ohlberger Universit¨at M¨unster Institut f¨ur Numerische und Angewandte Mathematik PP5 [email protected] Hybridized Reduced Basis Method and General- ized Polynomial Chaos for Solving Partial Differ- ential Equations PP5 Kernel Density Estimation for Implicit Monte The generalized Polynomial Chaos(gPC) method is a popu- Carlo Radiation Transport lar method for solving partial differential equations (PDEs) with random parameters. However, when the probabil- We use kernel density estimation in the Fleck-and- ity space has high dimensionality, the solution ensemble Cummings implicit Monte Carlo method to obtain smooth size required for an accurate gPC approximation can be solution estimates in thermal radiative transfer problems. large.We show that this process can be made more ef- The kernel density estimators obtain conservative esti- ficient by closely hybridizing gPC with Reduced Basis mates when using reflective boundary corrections and re- Method(RBM). solve steep gradients with locally adaptive bandwidths. We Jiahua Jiang show that solutions obtained using kernel density estima- University of Massachusetts, Dartmouth tors are smoother and exhibit substantially less statistical [email protected] noise than traditional histogram tallies.

Aaron M. Holgado PP5 Texas A&M University Kriging and Spatial Design Accelerated by Orders [email protected] of Magnitude: Combining Low-Rank Covariance Approximations with FFT-Techniques Robert Holladay Virginia Polytechnic Institute and State University Computational power poses heavy limitations to the [email protected] achievable problem size for Kriging. In separate research lines, Kriging algorithms based on FFT and low-rank rep- Allan Wollaber resentations of covariance functions have been developed, LANL both leading to drastic speedup factors. The current study [email protected] combines these ideas, reducing the computational complex- ∗ ∗ ity of Kriging to O(kq mdL log L ), where kq is the rank of approximation, m the number of measurements, d di- Mathew Cleveland, Todd Urbatsch ∗ Los Alamos National Laboratory mension, L the number of lattice points along the longest [email protected], [email protected] edge of the regular d-dimensional lattice. These benefits can be fully exploited when leaving the final result in low- rank format, or when further low-rank operations follow. Ryan McClarren The current study assumes second-order stationarity and Texas A&M University simple Kriging on a regular, equispaced lattice. USA [email protected] Alexander Litvinenko SRI-UQ Center, King Abdullah University of Science and Techn PP5 [email protected] Distribution Functions of Water Saturation for the Stochastic Buckley-Leverett Problem Via the Wolfgang Nowak 248 CS15 Abstracts

Institute for Modelling Hydraulic and Environmental [email protected], [email protected] Systems University of Stuttgart [email protected] PP5 Time Series Estimation of a Stochastic Processes Coupled to Pdes for Multiscale Modeling PP5 A Nonlinear Non-Gaussian Smoother for Continu- The well-studied molecular mechanics of atomic irradia- ous Stochastic Dynamical Systems tion damage have long-standing simulation codes model- ing binary collision cascades. Long range spatial correla- We present a novel non-Gaussian smoothing methodol- tions between damages are generally modeled using phase- ogy for high-dimensional stochastic fields governed by gen- field models. However, we propose a simulation scheme eral nonlinear dynamics. The history of the system is to model the meso-scale void accumulation damages us- quantitatively estimated using its stochastic dynamics and ing a stochastic cellular automata. This model allows us information gathered from noisy observations. Uncer- to bridge the gap between the micro and macro scales by tainty is quantified using the reduced-order Dynamically- modeling the stochastic cellular automata process using a Orthogonal equations, and smoothing is performed by ef- time series. This time series can then be run at a much ficiently carrying out Bayesian-inference in an evolving less computationally intensive simulation until reaching a low-dimensional dominant subspace. Various examples steady state. The statistical properties of the steady state from computational-fluid-dynamics are provided, illustrat- can then be coupled to the macro scale pde, ie continuum ing the superior performance of the smoother compared to models, in a form that it can better understand. its Gaussian/Monte-Carlo counterparts. Charlie Vollmer,DonEstep Colorado State University Tapovan Lolla, Pierre Lermusiaux [email protected], [email protected] MIT [email protected], [email protected] Anter A. El-Azab Purdue University PP5 [email protected] Uncertainty Quantification in Incompressible Flow Using Sparse Grids PP5 Fast Stochastic Simulation of Non-Gaussian Corre- This work based on a bachelor thesis introduces a sparse lated Process Variations grid stochastic collocation method for uncertainty quantifi- cation. We adapted the C++ sparse grid library SGpp for The recently developed stochastic spectral methods can es- benchmark scenarios in Matlab. The method was tested timate more efficiently the process variations effects com- on a simple ODE example as well as on an incompress- pared with Monte-Carlo. However, existing publications ible flow scenario in 1-D and 3-D random parameter space. mostly assume variation-parameters to be independent and The sparse grid collocation solutions show promising re- Gaussian. In this paper, we develop an efficient simu- sults with respect to accuracy and runtime compared to lation technique based on stochastic collocation for non- Monte Carlo methods. Gaussian and correlated random parameters. The tech- nique is applied to silicon photonic process variations and Friedrich Menhorn shows 124-times speedup compared with Monte-Carlo. Department of Informatics, Technische Universit¨at M¨unchen Tsui-Wei Weng [email protected] MIT Research Lab of Electronics Tobias Neckel [email protected] Technische Universit¨at M¨unchen [email protected] Zheng Zhang MIT z [email protected] PP5 Matrix Splitting Techniques for Sampling a High- Luca Daniel Dimensional Gaussian M.I.T. ResearchLabinElectronics Langevin and Hamiltonian proposals in the Metropolis- [email protected] Hastings algorithm applied to Gaussian target distribu- tions correspond to matrix splittings, similar to station- ary iterative methods for solving systems of linear equa- PP5 tions such as Gauss-Seidel and SSOR. We prove a result for Uncertainty Quantification for Integrated Circuits how the efficiency of the Metropolis-Hastings algorithm de- and MEMS pends on a general matrix splitting in high dimensions, re- vealing new efficient proposals for the Metropolis-Hastings We present a simulator to quantify the uncertainties of algorithm. nano-scale integrated circuits and microelectromechanical systems (MEMS). We show the stochastic spectral methods Richard A. Norton, Colin Fox for stochastic static, transient and periodic steady-state University of Otago (i.e., limit cycle) analysis, as well as some techniques to Department of Physics handle high parameter dimensionality and design hierar- CS15 Abstracts 249

chy. locality of the method compared to traditional FFT-based methods. Multigrid methods efficiently solve the resulting Zheng Zhang sparse matrix problem. MIT z [email protected] Natalie N. Beams University of Illinois at Urbana-Champaign Ibrahim Elfadel [email protected] Microsystem Engineering Masdar Institute of Science and Engineering Luke Olson [email protected] Department of Computer Science University of Illinois at Urbana-Champaign Luca Daniel [email protected] M.I.T. ResearchLabinElectronics Jonathan B. Freund [email protected] University of Illinois at Urbana-Champaign [email protected]

PP6 Reproducible Numerical Computing with PP6 HashDist Boltzmann Collision Operator for Cylindrically Symmetric Velocity Distributions in Plasmas HashDist provides a critical component of the devel- opment workflow, enabling highly customizable, source- We develop a model for collision processes in industrially driven, and reproducible builds for scientific software relevant plasmas. To reduce the computational cost of solv- stacks. HashDist features intelligent caching of sources ing the Maxwell-Boltzmann equations, we assume that the and builds, parametrized build specifications, and the velocity distribution function is cylindrically symmetric in ability to interoperate with system compilers and pack- velocity space and only axially dependent in physical space. ages. HashDist enables the easy specification of ”software We show that if the external force is only axially dependent, stacks”, which allow both the novice user to install a de- then the Boltzmann collision operator is also cylindrically fault environment and the advanced user to configure every symmetric, which reduces the Maxwell-Boltzmann system aspect of their build in a modular fashion. All HashDist to two velocity and one spatial dimensions. builds are reproducible, with a unique build hash identify- ing exactly how each component of the software stack was Yanping Chen, Yannan Shen, John Zweck, Matthew installed. Goeckner University of Texas at Dallas Aron Ahmadia [email protected], [email protected], US Army Engineer Research and Development Center [email protected], [email protected] [email protected] PP6 Ondrej Certik Department of Mathematics and Statistics Analysis of a Heterogeneous Multiscale Method for University of Nevada, Reno Poroelasticity [email protected] In this paper, we develop a highly parallelizable numeri- cal method to solve the heterogeneous linear poroelastic- Christopher Kees ity equations in multiple dimensions via operator splitting US Army Engineer Research and Development Center and a finite-volume based heterogeneous multiscale method [email protected] for the linear elasticity and reaction diffusion equations. We demonstrate convergence both analytically and numer- Dag Sverre Seljebotn ically, and analyze its computational complexity on high University of Oslo performance computers. [email protected] Paul M. Delgado Andy R. Terrel UTEP Institute for Computational Engineering and Sciences [email protected] University of Texas at Austin [email protected] Vinod Kumar, Son Young Yi University of Texas at El Paso [email protected], [email protected] PP6 A Scalable Fast Method for N-Body Problems Based on Exact Finite Element Basis Screen Func- PP6 tions Cell List Algorithms for Nonequilibrium Molecular Dynamics We introduce a fast method for computing N-body inter- actions based on the particle-particle–particle-mesh (P3M) A common approach in the molecular simulation of ho- approach in which the calculation is split into rapidly de- mogeneous linear background flow is the use of boundary caying short-range interactions and mesh-resolvable long- conditions that deform with the flow. Recent developments range interactions. Our method employs screening func- have been made in finding long-term compatible boundary tions designed to yield a long-range component that is conditions for a general class of three-dimensional flows. found exactly by a finite element method, increasing the We present two modifications of the standard cell list algo- 250 CS15 Abstracts

rithm for nonequilibrium molecular dynamics. The modi- high accuracy and only requires to solve tridiagonal linear fied algorithms handle the dynamic, deforming simulation systems of equations (to compute the spatial derivatives). geometry and reduce the computational complexity of force The instabilities that arise in high contrast media are al- computations from O(N 2)toO(N) in the number of par- leviated when using these schemes. We show examples for ticles N. different media configurations.

Matthew Dobson Ursula Iturraran-Viveros, Reymundo Itza University of Massachusetts Amherst Facultad de Ciencias [email protected] Universidad Nacional Autonoma de Mexico [email protected], [email protected] PP6 Convex-Hull Classification of Molecular Data on a PP6 Cluster Graph-Based Analysis of Three-Dimensional, There has been considerable interest in understanding vari- Large Scale Phase-Field Simulations ations in molecular signatures between normal and disease states using novel classification approaches. The proposed In large scale phase-field simulations of ternary eutectic study will elucidate the choice of convex-hull ensemble clas- solidification, multiple patterns emerge and evolve while sification for discerning distinct disease groups. The al- growing. To study the transformation of patterns depend- gorithms were implemented in R and parallelized across a ing on thermodynamical properties or processing condi- high-performance computing cluster using readily available tions and to analyze the respective microstructure charac- wrappers. teristics, algorithms exploiting large datasets are discussed. Basic features of the arrangement of the three solid phases Sally R. Ellingson, Radha Nagarajan are derived from the voxel data via graph representations. University of Kentucky The targeted reduction of the data allows to visualize single [email protected], [email protected] three-dimensional structures and evaluate the correlations of different patterns effectively. Thereby it is possible to augment current 2D statistics and analyze projections of PP6 the data. Spectral Noise Filtering for Fourier Transform Pro- filometry Marcus Jainta Karlsruhe Institute of Technology (KIT) In Fourier transform profilometry, an optical system Institute of Applied Materials (IAM-ZBS) projects light with a sinusoidally-varying pattern on a 3-D [email protected] surface and records the resulting image. The spectrum of the depth-modulated sinusoid is overlapped by other com- Daniel Stubenvoll, Johannes H¨otzer ponents of the spectrum, limiting accurate reconstruction Karlsruhe University of Applied Sciences (HSKA) of the surface. We present a new noise removal method to Institute of Materials and Processes (IMP) estimate the obscuring spectral components and filter them [email protected], out. Surfaces reconstructed using this de-noising method [email protected] feature increased precision and suffer from fewer aberra- tions. Phillip Steinmetz, Britta Nestler Thomas H¨oft Karlsruhe Institute of Technology (KIT) University of St. Thomas Institute of Applied Materials (IAM-ZBS) Department of Mathematics [email protected], [email protected] [email protected] PP6 PP6 Uncertainty Quantification for the Estimation of Direct Evaluation of Unified Extended Splines the Diffusion Coefficient from Md Simulations

In this poster we demonstrate a method for direct eval- The diffusion coefficient D of a tracer particle suspended uation of unified extended spline basis functions, which in a fluid is estimated either from the time integral of the were first introduced by Wang and Fang in 2008. We also velocity autocorrelation (VACF) or from the slope of the demonstrate the advantages of B´ezier extraction of unified mean-squared displacement (MSD). We derive relations be- extended splines in Isogeometric analysis. tween the statistical errors present in VACF or MSD and in D and show that the statistical errors in D estimated by Ian D. Henriksen both methods have the same variance if VACF and MSD Brigham Young University are calculated from the same MD trajectories. [email protected] Changho Kim, George E. Karniadakis PP6 Brown University Division of Applied Mathematics Numerical Modeling of Wave Propagation in changho [email protected], george [email protected] Poroelastic Media Using Optimal Staggered Im- plicit Finite Differences

We apply a recently proposed optimal staggered implicit fi- PP6 nite difference scheme to model wave propagation in poroe- Adaptive Model Order Reduction in Forward and lastic media. The advantage of this method is that it has Inverse Multi-Frequency Problem for Maxwell’s CS15 Abstracts 251

Equations Andrew Wissink United States Army Aeroflightdynamics Directorate A model order reduction method is developed for solution NASA Ames Research Center of a forward and inverse multi-frequency problem for mag- [email protected] netotellurics. The Helmholtz decomposition allows to ex- tend the MOR method to the case of a on-trivial operator’s null space. We use Pade approximation of the forward re- PP6 sponse and the jacobian, which are analytic functions of Matched Asymptotic Analysis to Solve the Narrow frequency. An adaptive choice of interpolating frequencies, Escape Problem in a Domain with a Long Neck based on minmax optimization of several error estimates, uses a fast calculation of the residual across a frequency In this study, we mainly consider the narrow escape prob- range. lem in a two-dimensional domain Ω with a long neck, which is the two-dimensional analogue of a dendritic spine geom- Michal A. Kordy etry. The narrow escape problem requires the computa- Department of Mathematics, University of Utah tion of the mean escape time of a Brownian particle start- Energy & Geoscience Institute, University of Utah ing from the head until it exits from the end of the neck, [email protected] where the particle is absorbed. We divide the domain into the neck part Ωn and the head part Ωh, with the common Elena Cherkaev boundary Γε.TheescapetimeinΩh canbeconsideredto University of Utah be the time from the head to the end of the neck, while the Department of Mathematics escape time in Ωn canbeconsideredtobethetimefromthe [email protected] neck to the end of the neck. We compute the two exit times separately and match them by considering some boundary Phil Wannamaker value problem with an impedance boundary condition on University of Utah Γε, which we refer to as the Neumann-Robin boundary [email protected] model. Xiaofei Li PP6 Department of Mathematics, Inha University [email protected] Sparse Spectral Tau-Method for Binary Neutron Stars Hyundae Lee Inha University We describe ongoing work toward construction of initial Department of Mathematics data for binary neutron stars via a multidomain modal [email protected] tau-method. Sparse systems are achieved through the use of “integration preconditioning”. We focus on (i) realiza- tion of the low-regularity interface between the stellar sur- PP6 face and exterior through tau conditions and (ii) necessary further preconditioning beyond the “integration precondi- Computational Homogenization for the Modeling tioning”. of Soft Matter Materials This contribution outlines the development of mathemat- Stephen Lau ically rigorous and computationally efficient homogeniza- Mathematics tion frameworks for soft matter with intrinsic network mi- The University of New Mexico crostructures. Those are commonly encountered in mate- [email protected] rials such as elastomers, hydrogels, soft biological tissues, non-woven fabrics, cellular foams, and muscles and are all PP6 microscopically composed of elongated 1D fibers. When these soft materials are subject to a macroscopic strain, Time-Parallel Approaches for Complex Rotorcraft the underlying microstructure undergoes a peculiar defor- Calculations mation and highly affect the macroscopic stress response of the material. Unsteady rotorcraft CFD calculations may require hun- dreds of thousands of timesteps to resolve the flow of spin- Christian Linder ning rotors. Spatial decomposition alone limits the num- Stanford University ber of processors that can be effectively utilized; exploiting [email protected] parallelism in the temporal dimension could significantly increase the degree of scalability. We demonstrate sev- eral approaches to achieve temporal parallelism, including PP6 the Time-Spectral method for periodic and quasi-periodic Precice – Flexible Parallel Multi-Physics Coupling cases and a Parallel in Time (PIT) approach for the general case of fully unsteady flow. Flexible and extensible partitioned multi-physics simula- tion environments require efficient and modular tools with Joshua I. Leffell a broad coupling functionality. preCICE is a library for United States Army Aeroflightdynamics Directorate flexible numerical coupling of single-physics solvers. It NASA Ames Research Center uses a partitioned black-box coupling scheme, thus requir- joshua.i.leff[email protected] ing only minimal modifications to existing solvers. Codes currently coupled with preCICE comprise both commer- Jay Sitaraman cial and academic solvers, with a particular focus on fluid- University of Wyoming structure interaction. preCICE features a clean and mod- [email protected] ern software design with extensive unit and integration 252 CS15 Abstracts

testing while maintaining minimal external dependencies. body of unknown interior geometry. We investigate which Inter-solver parallelism, parallel communication and data boundary fields will cause failure in the material, either mapping techniques will help to max out future exa-scale fracture or plastic yielding for brittle and ductile materials computers. respectively. Using knowledge of volume fractions and ma- terial properties, bounds are obtained on the fields which Florian Lindner, Miriam Mehl the material can safely support. From this we are able to Universit¨at Stuttgart determine which boundary fields may be sustained by the fl[email protected], body. [email protected] Nathan C. Briggs, Graeme Milton, Zoe Last Koch, Benjamin Uekermann Andrew Boyles, Jonathan Boyle, Michael Primrose, TU Munich Michael Zhao [email protected] University of Utah [email protected], [email protected], [email protected], eldrewomagnifi[email protected], PP6 [email protected], [email protected], A Sparse Interpolation Algorithm for Dynamical [email protected] Simulations in Computational Chemistry

We present an implementation of Smolyak’s sparse grid PP7 interpolation algorithm designed for simulating reaction Charge Transfer Processes at Semiconductor- paths of photo-induced molecular transformations. Cur- Electrolyte Interfaces in Solar Cell Modeling rent reaction path methods are computationally burden- some, but Smolyak’s algorithm yields a cheap surrogate This project discusses results from the numerical ap- model. Furthermore, our implementation of Smolyak’s al- proximation and simulation of reactive semiconductor- gorithm facilitates the computation of several thousand re- electrolyte interfaces in solar cells using a drift-diffusion- actions paths simultaneously. We describe our new imple- Poisson model. A mixed finite element method is employed mentation of Smolyak’s algorithm and compare its perfor- to approximate the potential and the electric field, while a mance to MATLAB’s Sparse Grid Interpolation Toolbox. local discontinuous Galerkin method is employed to com- We also present simulation results for 2-butene. pute the densities and currents. The non-linear reactive interface conditions are treated using a Schwarz domain James Nance decomposition method applied to the semiconductor and North Carolina State Univ electrolyte regions. [email protected] MichaelD.Harmon ELENA Jakubikova Institute for Computational and Engineering Sciences North Carolina State University [email protected] [email protected]

C.T. Kelley PP7 North Carolina State Univ Student Chapter Develops Future Professionals Department of Mathematics tim [email protected] SIAM at Embry-Riddle Aeronautical University has fos- tered an unrelenting passion for professional development of its student body. From K-12 outreach to robotics re- PP6 search, members of our organization have gained skills that P2NFFT - A Versatile Framework for Computing translate to industry-level capabilities. The talk describes NFFT-based Fast Ewald Summation the components of the organization that creates an envi- ronment for growth and enriches each student and industry The Particle-Particle–NFFT (P2NFFT) is a framework for partner connection. computing the long range Coulomb interactions of the clas- sical N-body problem with O(N log N) arithmetic opera- Stacey Joseph-Ellison tions on massively parallel architectures. Recently, it has Embry-Riddle Aeronautical University been generalized to 2d- and 1d-periodic boundary condi- [email protected] tions by a combination of P3M and fast summation tech- niques based on nonequispaced fast Fourier transforms (NFFT). We review these new algorithms and present per- PP7 formance results of our publicly available implementation. Optimal Control of Miscible Displacement Equa- tions Using Discontinuous Galerkin Methods Michael Pippig, Franziska Nestler Chemnitz University of Technology In the energy industry, reservoir simulators enable oil com- Department of Mathematics panies to optimize oil and gas production. I analyze the ac- [email protected], curacy of the discontinuous Galerkin method when solving [email protected] an optimal control problem for the miscible displacement equations, which model a tertiary oil recovery process. The control variables are the flow rates at the injection wells PP7 and the state variables are the fluid mixture pressure and Fields That Cause Elastic Breakdown in Inhomo- velocity, as well as the concentration of the injected fluid. geneous Media Brianna Lynn We study the inverse problem of an elastic two phase Rice University CS15 Abstracts 253

[email protected] last, we will propose an iterative approximation-projection algorithm with boundary adjustment for signals to live in a inite-dimensional reproducing kernel subspaces. PP7 Elastic Deformation Due to Dislocations in a Trans- Cheng Cheng versely Isotropic Viscoelastic Halfspace UNIVERSITY OF CENTRAL FLORIDA [email protected] Many materials in nature have transversely isotropic (TI) viscoelastic behavior and this time-dependent phenomenon can be addressed by advanced continuum mechanics and PP8 computational analysis. A model is developed to repre- AWM Workshop: A Lattice of Poincare Duality sent the viscoelastic behavior of a TI media due to polyg- Algebras with Acyclic Annihilators and Finite Di- onal dislocation loops. Applying the Laplace transform to mension Associated to a Manifold the constitutive equations and adopting the algorithm pro- posed by Honig and Hirdes for the inverse transform, the One is motivated by the algebraic theory of surgery to deformation fields in the physical domain will be obtained. study finite dimensional differential commutative algebras with an invariant nondegenerate pairing. Using Hodge de- Amirhossein Molavi Tabrizi, Ernian Pan, Ali Sangghaleh compositions, we show there is a lattice of such algebras, University of Akron which share many familiar algebraic properties of differen- [email protected], [email protected], tial forms on manifolds. We hope to use these ideas to solve [email protected] differential equations on manifolds, which use d, *, and , and to give a straightforward combinatorial description of what it means to be a manifold. PP7 Identifying and Tracking Multiple Underwater Cameron Crowe Acoustic Sources Using Characteristic Signatures Stony Brook University [email protected] When using passive sonar to locate sound sources, the gen- eral practice is to implement a particle filter to track the source using its previous locations. Our goal is to improve PP8 this method by including discrete characteristics to the fil- AWM Workshop: Residual Based Aposteriori Er- ter and calculating the likelihood that the source falls un- ror Estimation in a Fully Automatic Hp –fem for der one or a set of these characteristics. This will improve the Stokes Equations our estimates of source location by narrowing down move- ment patterns, will help us distinguish between multiple Aposteriori error estimator as a computable quantity in sources, and can give us valuable information such as what terms of known quantities gives a tool to assess the approx- thesourcetypeis. imation quality in order to improve the solution adaptively. In This work we present a fully automatic hp-adaptive re- Zoi-Heleni Michalopoulou, Jacob Moorman, Jake Brusca, finement strategy using a residual based aposteriori error Shan Fung estimation which is based on the solution of local boundary Department of Mathematical Sciences value problems. The reliability and efficiency for estima- New Jersey Institute of Technology tor has been proved. Implementation for Stokes problem [email protected], [email protected], [email protected], shows the convergence of our algorithm. [email protected] Arezou Ghesmati Texas A&M University PP7 [email protected] Simulation and Modeling of Unmanned Systems for Humanitarian Applications in Industry Markus Buerg Texas A&M University Unmanned systems are a burgeoning technology in the Visiting Professor robotics and autonomy space. Utilized for decades in the [email protected] military and defense complex, unmanned systems are now poised to play a key role in solving some of the most press- ing international capacitance issues. With notable appli- Wolfgang Bangerth cations across the agricultural space, we will demonstrate Texas A&M University the importance and utility of simulation and modeling of [email protected] complex systems to solve real-world problems.

Courtney E. Thurston PP8 Commonwealth Connections Academy AWM Workshop: Residual-Based A Posteriori Er- [email protected] ror Estimate for Interface Problems: Nonconform- ing Linear Elements

PP8 The residual-based a posteriori error estimation for the AWM Workshop: Sampling and Reconstruction in non-conforming linear finite element approximation to the Inite-Dimensional Reproducing Kernel Subspace interface problem is studied. We introduce a new and di- rect approach, without using the Helmholtz decomposition, We will introduce quasi-optimal signal reconstruction of to analyze the reliability of the estimator. It is proved that admissible sampling schemes in Banach space setting. We a slightly modified estimator is reliable with the constant will investigate the admissibility of sampling schemes for independent of the jump of the interfaces, with- out the as- inite-dimensional reproducing kernel subspaces of Lp. At sumption that the diffusion coefficient is quasi-monotone. 254 CS15 Abstracts

Numerical results are also presented. Texas A&M University [email protected] Cuiyu He Purdue University [email protected] PP8 AWM Workshop: Propagation Failure in Discrete Zhiqiang Cai Inhomogeneous Media Using a Caricature of the Purdue University Cubic Department of Mathematics [email protected] We consider a bistable differential-difference equation with inhomogeneous diffusion across an interval lattice. Previ- Shun Zhang ous research uses a discontinuous nonlinearity to construct City University of Hong Kong exact solutions. We employ a continuous piecewise lin- [email protected] ear nonlinearity, a caricature of the cubic, to derive exact steady-state front solutions. Diffusion coefficients are var- ied on a finite interval, representing the inhomogeneous me- PP8 dia. The interval of propagation failure, dependent upon AWM Workshop: Enhancements for Reduced Ba- the diffusion coefficients and wave speed, determines when sis Methods: Reducing Offline Computational and where stationary front solutions occur. Costs Elizabeth Lydon The reduced basis method (RBM) is a new technique for University Central Florida finding approximate solutions to parametric partial differ- [email protected] ential equations. It tries to reduce the total cost of com- putation, by approximating the solution space by a linear PP8 combination of pre-- computed solutions. However, the current algorithm (greedy algorithm) is still costly. So we AWM Workshop: Nontrivial Structure in Top Ho- are designing a more efficient greedy algorithm. The im- mology of a Space plementation of our new approach also opens the power of parallel computing into the world of RBM. The top homology of a reasonable compact topological space X is naturally sitting inside a vector space V with Jiahua Jiang a canonical coordinate system. The position of this sub- University of Massachusetts, Dartmouth space relative to the axes is a non-trivial invariant of the [email protected] homeomorphism type of X. The canonical coordinate axes of V are given by oriented components of the set of top dimensional manifold points. PP8 Chandrika Sadanand AWM Workshop: Combinatorial Navier-Stokes Stony Brook University Equation [email protected] Form the cubical grid of three space. Replace differen- tial forms, exterior d and wedge product by cochains, the PP9 coboundary operator and cup product. Replace the hodge star by the Poincare dual cell operation followed by trans- A Synchronized Co-Volume Scheme for the Large- lation. Now one can form the combinatorial analog of the Scale Shallow Water Equations continuum Navier-Stokes equation. The co-volume scheme specifies the mass at cell centers and Aradhana Kumari cell vertices, and both of the normal and tangential veloc- City University Of New York ity components at cell edges. This scheme is extremely [email protected] flexible, applicable to unstructured meshes, and avoids the need to reconstruct the tangential velocity component, as the classical C-grid scheme does. But the co-volume has PP8 been shown to be a generalization of the Z-grid scheme, AWM Workshop: An Adaptive Gmsfem for High- and therefore inherits all the known defects of the latter. Contrast Flow Problems From another point view, a recent study shows that, for the co-volume scheme on the f-plane, the mass-vorticity- In this paper, we derive an a-posteriori error indicator for divergence fields on the primary are completely decoupled the Generalized Multiscale Finite Element Method (GMs- from the mass-vorticity-divergence fields on the dual mesh. FEM) framework. This error indicator is further used to We propose to periodically synchronize the fields on the develop an adaptive enrichment algorithm for the linear primary mesh and the fields on the dual mesh. In this pre- elliptic equation with multiscale high-contrast coefficients. sentation, we explore approaches for the synchronization, We consider two kinds of error indicators where one is and the effects of them. based on the L2-norm of the local residual and the other is based on the weighted H-1-norm of the local residual where Qingshan Chen the weight is related to the coefficient of the elliptic equa- Clemson University tion. We show that the use of weighted H-1-norm residual [email protected] gives a more robust error indicator which works well for cases with high contrast media. The convergence analysis of the method is given. PP9 Physics-Based Preconditioning and Dual Guanglian Li Timestepping for Stiff Combustion Problems CS15 Abstracts 255

with Detailed Chemical Mechanisms Ravi Samtaney KAUST Time-accurate simulation of low-Mach combustion is chal- [email protected] lenging due in part to the wide range of tightly-coupled physical time scales. Traditional integration techniques are severely constrained when strongly nonlinear and stiff PP9 chemistry is introduced to the Navier-Stokes equations at Adaptive Wavelet Simulation for Weakly Com- low Mach number. Kinetic stiffness is exceptionally de- pressible Flow Bounded by Solid Walls of Arbitrary manding when detailed, fine-grained reaction mechanisms Shape are utilized. We are developing local physics-based precon- ditioning techniques for detailed chemical mechanisms and We develop an adaptive simulation method for comput- extending dual timestepping for high-fidelity combustion ing compressible flow bounded by solid walls of arbitrary simulation on next-generation platforms. shape. A finite volume approach is coupled with wavelet analysis for local grid refinement. A volume penalization Michael A. Hansen method is employed to compute the flow in Cartesian coor- University of Utah dinates. We assess the quality and efficiency of the method Sandia National Laboratories for a flow in a channel with an expanded section. The re- [email protected] sults are compared with a reference flow computed on a uniform grid.

PP9 Naoya Okamoto Rods with Bend and Twist in a Brinkman Fluid Nagoya University [email protected] We develop a Lagrangian algorithm to model an elastic rod in a porous medium. The three dimensional fluid is Margarete Domingues governed by the incompressible Brinkman equation and Instituto Nacional de Pesquisas Espaciais the Kirchhoff rod model captures bend and twist of the [email protected] rod. Regularized solutions are derived and we compare numerical results to asymptotics for swimming speeds in Katsunori Yoshimatsu a Brinkman fluid. Numerical results showing bending Nagoya University and twisting energies in fluids of different porosity will be [email protected] shown.

Nguyenho Ho Kai Schneider Mathematical Sciences Department Universite de Provence, Aix-Marseille Worcester Polytechnic Institute Centre de Mathematiques et Informatique [email protected] [email protected]

Sarah D. Olson PP9 Worcester Polytechnic Institute [email protected] Multiple Solutions in Curved-Pipe Flow The project deals with fluid flows in uniformly curved pipes PP9 driven by a steady axial pressure gradient, with focus on blood flow in arteries. The problem is known to have Discrete Exterior Calculus Solution of Incompress- multiple solutions and the primary solution involving the ible Flows formation of two-vortices(Dean vortices) was found and Navier-Stokes equations are discretized using discrete ex- validated. Bifurcation was found for curved pipes with terior calculus (DEC) on simplicial meshes. The govern- a square cross-section. In addition, wall shear stresses, ing equations are first rewritten, using the smooth exterior stream function and vorticity were computed for different calculus notation, in terms of velocity and pressure forms. curvature ratios and Dean numbers. The smooth forms and operators are then substituted with Harsh Ranjan their corresponding discrete definitions based on the DEC Indian Institute of Technology Guwahati framework. Several numerical test cases are presented to [email protected] demonstrate numerical convergence, stability, and conser- vation properties of the developed numerical scheme. PP9 Mamdouh S. Mohamed Physical Sciences and Engineering Division Cooperation and Efficiency in Sperm Motility Pat- KAUST terns [email protected] To fertilize the egg, sperm of certain species engage in co- operative swimming behaviors. These cooperative motil- Sudantha Balage ity patterns result in differences in velocity and efficiency. Physical Sciences and Engineering Division We employ a preferred curvature flagellum model and the KAUST, Jeddah, KSA method of regularized Stokeslets to simulate the viscous [email protected] fluid environment sperm encounter. Using these methods, we compare a single flagellum with two flagella systems to Anil Hirani understand the empirical effects of cooperative swimming. Department of Mathematics University of Illinois at Urbana-Champaign, IL, USA Owen Richfield [email protected] Tulane University 256 CS15 Abstracts

Center for Computational Science [email protected] orichfi[email protected]

Paul Cripe PP9 Tulane University Discrete Adjoint Openfoam and Applications [email protected] A discrete adjoint version of OpenFOAM obtained using Algorithmic Differentiation[1] by operator overloading is Julie Simons appliedtoobtainderivativesbasedonexternalaerodynam- Tulane University ics of a Volkswagen Polo Car. The results are validated Department of Mathematics qualitatively against a ’frozen turbulence’ continuous ad- [email protected] joint implementation[2]. We demonstrate the robustness and flexibility of differentiating a turbulence model dis- cretely to obtain exact derivatives. Strategies to tackle PP9 spatial and temporal complexities characteristic to discrete adjoint methods are also discussed. References: [1] Nau- Efficient Simulation of Fluid-Structure Interactions mann, U., The Art of Differentiating Computer Programs, Modeled by Regularized Stokes Formulation Using SIAM, 2012. [2] Othmer, C., A continuous adjoint for- Kernel-Independent Fast Multipole Method mulation for the computation of topological and surface sensitivities of ducted flows,Int. J. Num. Meth. Fluids, Regularized Stokes formulation has been shown to be very 2006 effective at modeling fluid-structure interactions when the fluid is highly viscous. However, its computational cost Arindam Sen grows quadratically with the number of particles immersed Software and Tools for Computational Engineering, STCE in the fluid. We demonstrate how kernel-independent fast RWTH Aachen University multipole method can be applied to significantly improve [email protected] the efficiency of this method, and present numerical results for simulating the dynamics of a large number of elastic Markus Towara rods immersed in 3D Stokes flows. STCE, RWTH Aachen University [email protected] Minghao W. Rostami, Sarah D. Olson Worcester Polytechnic Institute Uwe Naumann [email protected], [email protected] RWTH Aachen University Software and Tools for Computational Engineering [email protected] PP9 Scalable Parallel Solvers for Highly Heterogeneous PP9 Nonlinear Stokes Flow Discretized with Adaptive Strategy for Efficiently Simulating Reactive Flows High-Order Finite Element with Large Detailed Chemical Kinetics

We present scalable parallel solvers for convection-driven A highly efficient numerical approach for simulating reac- flow in Earth’s mantle with associated plate motions, tive flows with large detailed chemical kinetics is proposed. which is governed by nonlinear Stokes equations. Crucial The present approach consists of a robust and fast explicit solver components are parallel geometric multigrid meth- time integration method for chemical reaction equations ods for preconditioning the linearized Stokes systems that and a species building technique for diffusion coefficient arise upon discretization with high-order finite elements calculations. The computational results with a realistic on adaptive meshes (resolution below 1km) and improved combustion problem verify the high efficiency of the present BFBT/LSC preconditioners for the Schur complement. We approach. show robustness with respect to extreme viscosity varia- tions and carry out global mantle flow simulations with Hiroshi Terashima real Earth data as we progress towards solving realistic The University of Tokyo global mantle flow inverse problems. [email protected]

Johann Rudi, Toby Isaac Youhi Morii ICES Japan Aerospace Exploration Agency The University of Texas at Austin [email protected] [email protected], [email protected] Mitsuo Koshi Georg Stadler Yokohama National University Courant Institute for Mathematical Sciences [email protected] New York University [email protected] PP9 An Exact and Consistent Adjoint Method for High- Michael Gurnis Fidelity Unsteady Compressible Flow Simulations Caltech [email protected] We consider high-resolution discretizations commonly used for compressible turbulent flows. A corresponding discrete- Omar Ghattas adjoint can produce gradients that include spurious numer- The University of Texas at Austin ical modes, restricting its utility. A continuous-adjoint ap- CS15 Abstracts 257

proach does not, but provides an inaccurate gradient. We the wave propagation has to be considered. Combining introduce a dual-consistent finite-difference discretization fluid dynamics with structural analysis traditionally poses based on common workhorse methods for compressible tur- a formidable challenge for even the most advanced numer- bulent flows, which enjoy the benefits of both approaches. ical techniques due to the disconnected, domain-specific Demonstrations with an unsteady mixing layer show that nature of analysis tools. We present the state-of-the-art in the gradient is both exact up to roundoff and consistent. computational methods and techniques for wave propaga- tion with FSI effect that go beyond the fundamentals of Ramanathan Vishnampet computational fluid and solid mechanics. Also this project Department of Mechanical Science and Engineering aims to develop efficient numerical methods for wave prop- University of Illinois at Urbana-Champaign agation phenomena in composite material with FSI effect, [email protected] which combine modern techniques from PDE-constrained optimization, adaptive and multigrid simulation methods. Daniel J. Bodony University of Illinois at Urbana-Champaign Department of Aerospace Engineering Bhuiyan Shameem M. Ebna Hai [email protected] Numerical Methods for Computational Science and Engineering, Jonathan B. Freund Mechanical Engineering Department, Helmut Schmidt University of Illinois at Urbana-Champaign University [email protected] [email protected]

Markus Bause PP9 Helmut-Schmidt-University Periodic Stokes Flow in 2 Dimensional Space University of the Federal Armed Forces Hamburg [email protected] We present a new boundary integral method to solve in- compressible Stokes flow with low Reynolds number in a periodic background with high accuracy and efficiency. PP10 Reducing the Impact of the Cfl Condition for Dis- Lin Zhao persive Wave Propagation Problems Dartmouth College [email protected] To solve dispersive wave propagation problems in complex geometries efficiently and accurately, it is attractive to use Alex H. Barnett explicit time-integration and high-order unstructured spec- Department of Mathematics tral element discretization in space. This combination may Dartmouth College have a severe global conditional CFL time-step restriction. [email protected] For specific models, we describe conditions placed on dis- persive terms for making the CFL condition independent of discretisation method and meshsizes. In this sense the PP10 CFL condition impose a minimal constraint on the effi- Etd Spectral Deferred Correction Methods ciency without compromising accuracy.

We introduce a new class of arbitrary-order exponential Allan P. Engsig-Karup time differencing (ETD) methods based on spectral de- Technical University of Denmark ferred correction. We study the stability and accuracy Department of Informatics and Mathematical Modeling properties of these methods and conduct numerical experi- [email protected] ments against existing ETD and implicit-explicit schemes. We find that our new high-order ETD spectral deferred Claes Eskilsson correction schemes outperform state-of-the-art time inte- Chalmars University of Technology grators for computations requiring high accuracy, making Gothenburg, Sweden. them well-suited to work in conjunction with spatial spec- [email protected] tral methods.

Tommaso Buvoli PP10 Department of Applied Mathematics, University of Explicit Strong Strong Stability Preserving Multi Washington Step Runge-Kutta Methods Seattle, WA 98195 USA [email protected] High-order spatial discretizations of hyperbolic PDEs are often designed to have strong stability properties, such as monotonicity. We study explicit multistep RungeKutta PP10 strong stability preserving (SSP) time integration methods Adaptive Multigrid Methods for An Integrated for use with such discretizations. We prove an upper bound Structural Health Monitoring (SHM) Systems for on the SSP coefficient of explicit multistep RungeKutta Composite Material with Fluid-Structure Interac- methods of order two and above.Numerical optimization tion (FSI) Effect is used to find optimized explicit methods of up to five steps, eight stages, and tenth order. These methods are To design a SHM system, it is important to understand tested on the advection and Buckley-Leverett equations, phenomenologically and quantitatively the wave propaga- and the results for the observed total variation diminish- tion in composite material and the influence of the geo- ing and positivity preserving time-step are presented. material and mechanical properties of the structures. To accelerate the design of SHM systems, the FSI effect on Zachary J. Grant 258 CS15 Abstracts

University of Massachusetts at Dartmouth [email protected] [email protected]

PP10 PP10 Numerical Investigation of Influence of Node Robust Residual-Based A Posteriori Error Esti- Alignment on Stable Calculation for Meshless Time mate for Interface Problems: Nonconforming Lin- Domain Method ear Elements The meshless time domain method (MTDM) is one of A robust residual-based a posteriori error estimation for meshless methods. The shape function derived from the the non-conforming linear finite element approximation to radial point interpolation method (RPIM) is adopted for the interface problem is studied. We introduce a new and discretization process instead of meshes in MTDM. In addi- direct approach, without using the Helmholtz decomposi- tion, the radial basis function (RBF) is employed in RPIM, tion, to analyze the reliability of the estimator. It is proved and the multi quadratic function is adopted for the present that our estimator is reliable with the constant indepen- study. The purpose of the present study is to investigate dent of the jump of the interfaces, without the assumption influence of node alignment and RBF on stable calculation. that the diffusion coefficient is quasi-monotone. Numerical results are also presented. Yoshiharu Ohi Cuiyu He RIKEN Advanced Institute for Computational Science Purdue University [email protected] [email protected] Yoshihisa Fujita Zhiqiang Cai Nagoya University Purdue University [email protected] Department of Mathematics [email protected] Taku Itoh, Soichiro Ikuno Tokyo University of Technology Shun Zhang [email protected], [email protected] City University of Hong Kong [email protected] PP10 Asymptotics of High-Frequency Scattering Prob- PP10 lems Monolithic Multi-Time-Step Coupling Methods for First and Second-Order Transient Systems Various strategies for simulating wave scattering problems through the Helmholtz equation typically become compu- New frameworks for coupling different integration meth- tationally expensive for high frequencies. The solution of ods (either temporal or spatial) for first- and second-order its integral representation exhibits asymptotic behaviour ikφ(y) ∞ −j transient systems will be introduced. These methods al- q(y) ∼ ke j=0 aj (y)k as the wave number k tends low different numerical time-integrators, time-steps, and to ∞, which can reduce costs. Oscillatory integrals aris- numerical formulations in different regions of the compu- ing when solving for q(y) on the boundary, can be ap- tational domain. Unique features of the proposed methods proximated asymptotically using the (numerical) method will be demonstrated through several numerical examples. of steepest descents. We explain this method, the case of multiple reflections and the extension to 3D. Saeid Karimi University of Houston Peter Opsomer [email protected] KU Leuven [email protected] Kalyana Nakshatrala University Of Houston - Main Campus Daan Huybrechs [email protected] Department of Computer Science K.U. Leuven [email protected] PP10 Total Order Function Space Spectral Collocation Methods Using the Padua Points PP10 Accurate Derivative Computation for Finite Ele- Multivariate Chebyshev spectral collocation methods typ- ment Codes ically are implemented using Lagrange interpolating poly- nomials corresponding to tensor products of Chebyshev It is common in physics to solve a PDE for some poten- nodes. The Padua points are an analogue of the Cheby- tial, while the physically relevant quantities are actually shev nodes that interpolate the smaller bivariate total order derivatives of said potential. Classical finite element meth- 2 function space Pn. These points can be used to implement ods, however, lose an order of accuracy for every derivative a spectral collocation scheme, however careful treatment of taken. We present an integral equation-based technique boundary conditions is required. This issue is explored for that, in the case of 2-D semilinear Poisson equations, en- Poisson and Helmholtz problems with arbitrary, variable ables the computation of arbitrary derivatives to the same coefficient, Robin boundary conditions. order as a given FEM solution. We present particular ap- plications to the Grad-Shafranov equation. Scott Moe University of Washington Lee F. Ricketson CS15 Abstracts 259

UCLA simulations. [email protected] Qiang Du, Xiaochuan Tian Antoine Cerfon Columbia University NYU Department of Applied Physics and Applied Mathematics [email protected] [email protected], [email protected]

Manas Rachh PP11 Courant Institute The Sparse Grid Combination Technique for Solv- NYU ing Eigenvalue Problems [email protected] Identifying microinstabilities in hot fusion plasmas can be done by solving the gyrokinetic eigenvalue problem which is PP10 a computationally demanding task. Our approach for solv- Comparison of Weak Galerkin Finite Element ing this problem is the combination technique. It combines Method with Dgfem and Mfem several solutions of the eigenvalue problem from different grid-sizes. That can diminish the curse of dimensionality, This poster presents a comparative study on the since it creates a sparse grid approximation. It also in- newly introduced weak Galerkin finite element meth- creases the scalability by introducing an additional layer ods (WGFEMs) with the widely accepted discontinu- of parallelism which is reusing the current parallelism. ous Galerkin finite element methods (DGFEMs) and the classical mixed finite element methods (MFEMs) for Christoph Kowitz solving second-order elliptic boundary value problems. TU Munich We examine the differences, similarities, and connection [email protected] among these methods in scheme formulations, implemen- tation strategies, accuracy, and computational cost. The Markus Hegland comparison and numerical experiments demonstrate that Australian National Unversity WGFEMs are viable alternatives to MFEMs and hold some [email protected] advantages over DGFEMs, due to their properties of local conservation, normal flux continuity, no need for penalty factor, and definiteness of discrete linear systems. Hans-Joachim Bungartz Technische Universit¨at M¨unchen, Department of Farrah Sadre-Marandi Informatics Colorado State University Chair of Scientific Computing in Computer Science [email protected] [email protected]

PP10 PP11 A Weighted Sequential Splitting Method for the A Tangential Interpolation Framework for MIMO 3D Maxwell’s Equations Eigensystem Realization Algorithm

We present a Weighted Sequential Splitting (WSS) method The Eigensystem Realization Algorithm (ERA) is a com- for Maxwell’s equations in 3D. The solution obtained by monly used data- driven method for system identification the WSS scheme in a given time step is a weighted aver- and model reduction of dynamical systems. The main com- age of solutions of several 1D Maxwell systems, discretized putational difficulty in ERA arises when the system under using a Crank Nicolson method. We prove convergence of consideration has large number of inputs and outputs, thus the scheme for all weights 0 ≤ θ ≤ 1, and show that it is requiring to compute a full SVD of a large-scale dense Han- unconditionally stable of first order in time when θ =0 .5, kel matrix. In this work, we present an algorithm that aims and second order when θ =0.5. to resolve this computational bottleneck via tangential in- terpolation. A numerical example is presented. Puttha Sakkaplangkul Oregon State University Boris Kramer [email protected] Virginia Tech [email protected]

PP10 Serkan Gugercin Asymptotically Compatible Schemes for Robust Virginia Tech. Discretization of Nonlocal Models Department of Mathematics [email protected] Nonlocality is ubiquitous in nature. While partial differ- ential equations (PDE) have been used as effective mod- els of many physical processes, nonlocal models and non- PP11 local balanced laws have become possible alternatives to Multi-Set Data Analysis and Simultaneous Matrix treat anomalous process and singular behavior. In this Block Diagonalization: Models and Algorithms talk, we use a recently developed nonlocal vector calcu- lus and nonlocal calculus of variations to study a class of We present joint independent subspace analysis (JISA) of constrained value problems associated with nonlocal op- stationary sources as a statistical signal processing ap- erators. In addition, we present asymptotically compati- proach to multi-set data analysis. From an algebraic per- ble discretizations that provide convergent approximations spective, JISA may be viewed as a set of coupled block di- to both nonlocal models and their local limit. Such dis- agonalization (CBD) problems. We evoke some new results cretizations are useful for model validation and multiscale for JISA-CBD, and linkage to recent results on ISA of non- 260 CS15 Abstracts

stationary sources based on joint block diagonalization of ful Mediators covariance matrices. We focus on algorithms, performance, identifiability and the associated matrix factorizations. The classical approach to have selfish agents route opti- mally in network congestion games is to impose edge tolls Dana Lahat, Christian Jutten that depend on agents’ demands. However, this fails when GIPSA-Lab demands are unknown to the mechanism designer. We de- [email protected], sign a weak mediator that can impose tolls such that it [email protected] is an asymptotic ex-post Nash equilibrium for agents to truthfully report their demands to the mediator and faith- fully follow its suggested route, which results in an approx- PP11 imately optimal flow. Overcoming the Gibbs Phenomenon : Fast Fourier Extension Ryan M. Rogers University of Pennsylvania Fourier series of smooth functions on an interval [−1, 1] are [email protected] known to exhibit the Gibbs phenomenon, and have overall slow convergence. The Fourier extension technique over- Aaron Roth comes these problems by constructing a Fourier approxima- University of Pennsylvania, USA tion on an extended interval [−T,T], through least-squares [email protected] optimization. We present FE algorithms for approxima- tions from equidistant points that match the O(N log N) Jonathan Ullman complexity of the discrete Fourier transform, and comment Columbia University on the associated difficulties. [email protected]

Roel Matthysen Steven Wu KULeuven University of Pennsylvania [email protected] [email protected]

PP11 PP11 Big Graph Analytics of Human Connectome Net- Security in Data Mining Through Cloud Comput- works ing Using Expert System

Analyzing the very dense human connectome network with This study presents an expert system to optimize the secu- billions of links has become a central and challenging topic rity of data mining in cloud computing.These systems still in computational neuroscience. Yet, it offers neuroscien- suffer from privacy and security concerns. The main se- tists great opportunities to understand the complex struc- curity issues in cloud computing are identifying identity, ture and functionality of the human brains. In this project access control, confidentiality, integrity, availability and we demonstrate how to use big data technology and tools, non-repudiation. The main goal of this investigation is such as Spark GraphX and SAP HANA, to approximate designing an expert system to increase the security of data various graph measurements from the brain connectivity mining in cloud computing systems. To do this, the effi- graphs released by the Human Connectome Project. ciency of these techniques is examined for the same data set .Subsequently, an inference engine has been developed J¨urgen Ommen, Chih Lai, Yulin Yang and this engine automatically selects the model which has University of St. Thomas best efficiency by using artificial intelligence techniques. Graduate Programs in Software [email protected], [email protected], Ana Sadeghitohidi, Azadeh Roozbehi [email protected] Azad Tehran University [email protected], [email protected] PP11 Componentwise Sensitivity of Matrix Functions PP11 and Applications Big Data Analytics Application in Genomics Data Processing Matrix functions, such as the exponential, are used in a va- riety of applications. Previous sensitivity analyses involve Genomics datasets are large. In this project we are process- mainly normwise condition numbers. Componentwise con- ing genomics data on a HPC cluster using Hadoop. Our dition numbers and perturbation bounds are more appro- goal is to identify from the genome data any disease pat- priate when sensitivity with respect to particular compo- tern. Eventually we plan to have access to clinical data for nents is of interest. We develop such analysis and ap- minorities that will help identify risk factors when com- ply it to a parameterized ODE problem arising in physics bined with genomics data. Our processing at this time where the matrix components are flux coefficients describ- is experimental and as such no patient privacy issues are ing chemical interaction. involved because the clinical data will be anonymized.

Samuel Relton SSrinivasan University of Manchester, UK Texas Southern University [email protected] JHJ School of Business [email protected]

PP11 Hector Miranda Inducing Approximately Optimal Flow Via Truth- Texas Southern University CS15 Abstracts 261

[email protected] [email protected]

Daniel Vrinceanu Texas SOuthern PP11 [email protected] Parallel Bayesian Global Optimization, With Ap- plication To Metrics Optimization at Yelp Terence Vaughn Texas Southern University We consider parallel global optimization of expensive-to- [email protected] evaluate functions, and propose an efficient method based on stochastic approximation for implementing a conceptual Bayesian optimization algorithm proposed by Ginsbourger PP11 et al. (2010). We also introduce an open-source software implementation of this algorithm, called Metrics Optimiza- Generalized Low Rank Models tion Engine, developed in collaboration with engineers at Yelp Inc. and used internally at Yelp to optimize predic- Principal components analysis (PCA) is a well-known tech- tion models and performance metrics. nique for approximating a data set represented by a matrix by a low rank matrix. Here, we extend the idea of PCA to Jialei Wang, Peter I. Frazier handle arbitrary data sets consisting of numerical, Boolean, Cornell University categorical, ordinal, and other data types. This framework [email protected], [email protected] encompasses many well known techniques in data analysis, such as nonnegative matrix factorization, matrix comple- Scott Clark, Eric Liu tion, sparse and robust PCA, k-means, k-SVD, and max- Yelp Inc imum margin matrix factorization. The method handles [email protected], [email protected] heterogeneous data sets, and leads to coherent schemes for compressing, denoising, and imputing missing entries across all data types simultaneously. It also admits a num- PP12 ber of interesting interpretations of the low rank factors, The Modified Bidomain Model with Periodic Dif- which allow clustering of examples or of features. We pro- fusive Inclusions pose several parallel algorithms for fitting generalized low rank models, and describe implementations and numerical Bidomain equations are the standard way to model the results. electric potential in cardiac tissue. We propose the modifi- cation of this model for the case of the diseased heart, e.g. Madeleine R. Udell fibrosis of the heart tissue. On microscale, we assume to Stanford University have periodic diffusive inclusions embedded in the healthy Stanford University tissue modelled by the bidomain equations. We derive [email protected] the macroscale model using the homogenisation technique. We recover a bidomain model with modified conductivi- Corinne Horn, Reza Zadeh ties, that depend on the volume fraction of the diffusive Stanford University inclusions but also on their geometries. [email protected], [email protected] Andjela Davidovic Stephen Boyd INRIA Bordeaux Sud-Ouest, Bordeaux, France Stanford University University Bordeaux, Bordeaux, France Department of Electrical Engineering [email protected] [email protected] Yves Coudiere Universit´e Bordeaux 1 PP11 Inria & IMB (UMR 5251) [email protected] A Structured Cholesky Factorization for Fock Ma- trix Construction Clair Poignard INRIA Bordeaux Sud-Ouest The bottleneck of Fock matrix construction is computa- University Bordeaux tion and storage of Electron Repulsion Integrals (ERIs). [email protected] We present new high performance software implemented in GTFock which pre-computes a structured lazy evaluation pivoted Cholesky factorization of the matrix unfolding of PP12 the fourth-order ERI tensor. In addition to reducing ERI Simulation-Based Solute Transport in Kidney Cells computation and storage by an order of magnitude, this new approach utilizes symmetry and sparsity structure. Based on solute and water conservation and electroneu- trality constraints, we developed mathematical models Joseph Vokt of kidney cells. With the models, we computed intra- Cornell University cellular Na+ concentration and membrane hyperpolariza- [email protected] tion/depolarization behavior as a function of extracellular NaCl. Mathematical models like these can be adapted to Edmond Chow formulate hypotheses of a system response after a pertur- School of Computational Science and Engineering bation. Furthermore, they can help in the development Georgia Institute of Technology of new drugs prior to in vivo testing, thereby minimizing 262 CS15 Abstracts

research costs, and time. yses of Biomolecular Simulations

Monica Nadal-Quiros Allosteric interaction network is an intrinsic complex prob- University of Puerto Rico, Rio Piedras Campus lem in computational bio-molecular researches and very Department of Biology scarce analysis tools are available. Here I present a python [email protected] package named “Allostery” for calculation of biomolecu- lar interaction networks using Lange-Grubmuller general- Aniel Nieves-Gonzalez ized correlation coefficient, based on Kraskov-Stogbauer- University of Puerto Rico Grassberger Mutual Information estimator. It features: Institute of Statistics and Information Systems distance and k-d tree based implementation, memory ef- [email protected] ficient serial and cluster level parallel execution and user- friendly tools for data IO and visualization. Leon Moore Yuhang Wang SUNY HSC University of Illinois, Urbana-Champaign Department of Physiology and Biophysics [email protected] [email protected] Emad Tajkhorshid Mariano Marcano University of Illinois, Urbana-Chamnpaign University of Puerto Rico [email protected] [email protected]

PP12 PP12 Numerical Methods for Protein Adsorption in An Adaptive Markov Chain Monte Carlo Method Porous Membranes Applied to Simulation of a Tumor Growth Model Protein therapeutics are used as treatments for various ill- The inference of mechanistic descriptions of oncogenesis is nesses (diabetes, cancer, hemophilia, infectious diseases). often a challenge due to limited experimental data. Markov Most of the cost of protein production is associated with Chain Monte Carlo (MCMC) methods have been developed the downstream separation/purification. Developing more and widely used in Bayesian analysis. This project applies efficient purification methods would decrease the cost of an adaptive MCMC technique based on the Metropolis- protein therapeutics. In this presentation, we will dis- Hastings algorithm to calibrate the parameters of a tumor cuss protein separation using multi-modal membranes de- growth model to experimental data. The study is sup- veloped in Clemson University’s chemical engineering de- ported by the NIGMS of NIH grant as part of the West partment. We will present numerical simulations of the Virginia INBRE (P20GM103434). advection-diffusion-reaction equation, comparing and con- trasting solution methods and adsorption models. Qing Wang,ZhijunWang Dept. of Computer Science, Math and Engineering Anastasia B. Wilson Shepherd University, Shepherdstown, WV Clemson University [email protected], [email protected] Department of Mathematical Sciences [email protected] David Klinke Dept. of Chemical Engineering West Virginia University, Morgantown, WV PP12 [email protected] Modeling Core Body Temperature during Exercise

Dynamics of core body temperature of rats running on PP12 treadmills with varied speeds at different ambient temper- Numerical Simulation of a Tumor Cell Population atures were modeled. The model was used to estimate heat Growth Dynamics Model Using Genetic Algorithm generated in the body for thermoregulation and additional heat produced by the muscles during exercise. We found Tumor cell growth models involve high-dimensional param- that the latter grows with exercise intensity in ambient eter spaces that require computationally tractable methods temperature independent way. In contrast, the thermoreg- to solve. Genetic algorithm is applied to search for parame- ulatory component reduces at room temperature, while re- ter values that fit experimental data from mice cancel cells. maining unchanged at high temperature implying existence Dynamically variable crossover and mutation methods are of compensatory mechanisms. used to produce new generations. Fitness functions, which measure the difference between calculated results and ex- Yeonjoo Yoo perimental data, are minimized. This study is supported Indiana University-Purdue University Indianapolis by the NIGMS of NIH grant as part of the WV INBRE IUPUI (P20GM103434). [email protected]

Zhijun Wang,QingWang Dept. of Computer Science, Math and Engineering PP12 Shepherd University, Shepherdstown, WV Ensemble Kalman Filters for Dynamic Dipole Es- [email protected], [email protected] timation from Magnetoencephalography

We discuss the dynamic imaging of electromagnetic cere- PP12 bral activity based on magnetoencephalography (MEG) ”Allostery”: A Python Package for Network Anal- data. In this presentation, we develop two time evolution CS15 Abstracts 263

models combined with the ensemble Kalman filter to local- the asymptotic error convergence order depends on the ize the electric source currents and capture the rapid neural sequences used in estimation integration. In this paper, activity in the brain. The utilization of the Bayesian frame- we investigate a family of related quasi-random sequences, work allows sequential updating of the preceding estimates known low-discrepancy sequences, and study their effects of the activations. The effectiveness of the algorithms is to convergence of error estimation. Our experimental re- demonstrated with simulated data. sults show that some low-discrepancy sequences signifi- cantly improve the performance of error estimation. Lijun Yu Case Western Reserve University Hongmei Chi [email protected] Computer Science Florida A&M University Daniela Calvetti [email protected] Case Western Reserve Univ Department of Mathematics [email protected] PP13 Optimal Source Encoding in Medium Parameter Erkki Somersalo Reconstruction Problems Case Western Reserve University The computational cost of medium parameter reconstruc- [email protected] tion scales linearly with the number of sources used. To alleviate that bottleneck, several authors proposed to solve PP13 instead for a few linear combinations of the sources. In order to preserve consistency with the original problem, Decomposition-Based Uncertainty Quantification those combinations must be chosen randomly. Instead we with Application to Environmental Impacts of Avi- propose to select the combinations that provide the most ation confidence in the reconstructed parameters, in the Bayesian We present a decomposition-based uncertainty quantifica- sense. This leads us to minimize the nuclear norm of the tion approach for feed-forward multicomponent systems. variance of the posterior distribution evaluated at the MAP The aim is to decompose the uncertainty quantification point. task among the various components comprising a system, Benjamin Crestel then synthesize these results to quantify uncertainty at the University of Texas at Austin system level. We introduce concepts that extend our ap- Institute for Computational Engineering and Science proach to systems containing a large number of component- [email protected] to-component interface variables. We apply the proposed method to quantify how uncertainty in aviation technology affects uncertainty in environmental impacts. Omar Ghattas The University of Texas at Austin Sergio Amaral [email protected] Department of Aeronautics & Astronautics Massachusetts Institute of Technology Georg Stadler [email protected] Courant Institute for Mathematical Sciences New York University [email protected] PP13 The Combined Block by Block - Monte Carlo Methods for Numerical Treatment of the Mixed PP13 Nonlinear Stochastic Integral Equation Randomized Likelihood Method: A Scalable Ap- proach to Big Data in Large-Scale Pde-Constrained In this paper, we study the random effects, W(s), on Bayesian Inverse Problems a mixed nonlinear integral equation of the second kind with time dependent. Two contributions are made: the In this poster we present a scalable approach to tackle the first contribution discuses the existence and uniqueness of big-data challenge in large-scale PDE-constrained Bayesian the solution of this equation and the second contribution inverse problems. In particular, we propose a MAP ap- presents an algorithm in which we combine both Block- proximation algorithm whose convergence is independent by-Block method and Monte-Carlo method, to accurately of the data dimension The idea is to randomize the likeli- and efficiently solve a mixed nonlinear stochastic integral hood to extract active/important/independent data which equation. Numerical examples are given to illustrate the is in general much less compared to the original big data. presented numerical method. The active data is then used to obtain approximate MAP point. We rigorously analyze the convergence of the pro- Abdallah A. Badr posed randomized likelihood method for a large class of Alexandria University inverse problems under mild conditions. One of the key Department of Mathematics results is that approximate MAPs converge to the big-data [email protected] MAP in probability, independent of the amount of data. Several numerical results for large-scale PDE-constrained Bayesian inverse problems are presented to show the effec- PP13 tiveness of the proposed method and to verify the theoret- Computational Investigation of Quasi-Random Se- ical results. quences for Error Estimation Aaron Myers Quasi-Monte Carlo methods has become a major vehi- UT Austin, ICES cle for estimating high-dimensional integrations. However, [email protected] 264 CS15 Abstracts

Tan Bui-Thanh The University of Texas at Austin [email protected] Catherine Powell School of Mathematics Ellen Le University of Manchester University of Texas at Austin - ICES [email protected] [email protected] Alex Bespalov University of Birmingham, United Kingdom PP13 [email protected] MUQ (MIT Uncertainty Quantification): Flexible Software for Connecting Algorithms and Applica- David Silvester tions School of Mathematics University of Manchester It is difficult to interface uncertainty quantification [email protected] algorithms—e.g., Bayesian inference, robust optimization, surrogate building, sensitivity analysis—with computa- tional models in a way that exposes model structure to the PP13 algorithms while accommodating easy development of new Inference of Constitutive Parameters in a Nonlin- models and new algorithms. The MIT Uncertainty Quan- ear Stokes Mantle Flow Model tification (MUQ) library addresses these issues with a flex- ible software framework for constructing complex multi- component models and for developing new algorithms. We Motivated by inverse problems in mantle flow models discuss our design goals and demonstrate MUQ by both with plate tectonics, we estimate constitutive parame- implementing a new MCMC algorithm and constructing a ters in a nonlinear Stokes system using a Bayesian in- coupled PDE model. ference approach. We compute the maximum a posteri- ori (MAP) point of the posterior parameter distribution, Matthew Parno, Patrick R. Conrad which amounts to the solution of a PDE-constrained op- Massachusetts Institute of Technology timization problem. To quantify the uncertainty in the [email protected], [email protected] parameters, we compare a local Gaussian approximation of the posterior distribution at the MAP point with results obtained using MCMC sampling. Andrew Davis MIT [email protected] Vishagan Ratnaswamy California Institute of Technology Seismological Laboratory Youssef M. Marzouk [email protected] Massachusetts Institute of Technology [email protected] Georg Stadler Courant Institute for Mathematical Sciences PP13 New York University [email protected] A Stochastic Dynamic Programming Method for Controlling a Combined Hydro/Wind Power Pro- Michael Gurnis ducer California Institute of Technology [email protected] We develop a computationally efficient nonlinear stochas- tic dynamic programming model to determine the optimal control of a combined hydro and wind power producer. The Omar Ghattas algorithm efficiency is improved through use of a radial ba- The University of Texas at Austin sis function approximation within a corridor. [email protected]

Kyle Perline Cornell University PP13 [email protected] Uncertainty Quantification for Thermally Driven Flow

PP13 The uncertainty in a scalar quantity of interest is quanti- Efficient Error Estimation for Elliptic PDEs with fied for a natural convective flow in a cavity with random Random Data boundary data. The performance of sparse grid stochastic collocation is compared to quasi Monte Carlo, depending When PDE models have uncertain inputs, efficient numer- on the variance of the random perturbation. The methods ical methods for the forward problem are needed for un- are accelerated by making use of simulation results from certainty quantification. Stochastic Galerkin finite element previously visited sampling points. In particular, improved methods have attractive approximation properties but are starting conditions for the iterative non-linear solver and too expensive to implement on standard computers when POD-Galerkin reduced-order modeling are considered. the dimension of the random input space is high. To im- prove efficiency, we look to adaptive Galerkin schemes. We Sebastian Ullmann,LangJens introduce a cheap a posteriori error estimator for elliptic TU Darmstadt problems that can be implemented in a non-intrusive way. [email protected], [email protected] CS15 Abstracts 265

darmstadt.de Gideon Simpson Department of Mathematics Drexel University PP13 [email protected] Computational and Statistical Tradeoffs: a Frame- work PP13 The recent explosion in the quantity and dimension of data has brought up many new computational and statistical Utilizing Adjoint-Based Techniques to Effectively challenges that must be addressed simultaneously such that Perform Uq on Discontinuous Responses inference is both tractable and meaningful. We propose a framework that provides an explicit opportunity for the Uncertainty is ubiquitous in predictive modeling and sim- practitioner to specify how much statistical risk they are ulation due to unknown model parameters, initial condi- willing to accept for a given computational cost. We illus- tions, etc. A number of recently developed methods for un- trate this with an example of estimation from a stream of certainty quantification have focused on constructing sur- iid normal variables. rogates of high-fidelity models using only a limited number of model evaluations. Unfortunately, many of these tech- Alexander Volfovsky niques perform poorly when the response surface is discon- Statistics Department, Harvard University tinuous. In this poster, we show how adjoint-based tech- Harvard University niques can be used to efficiently construct discontinuous [email protected] surrogate approximations.

Edoardo Airoldi, Daniel Sussman Tim Wildey Harvard University Optimization and Uncertainty Quantification Dept. [email protected], [email protected] Sandia National Laboratories [email protected]

PP13 Eric C. Cyr Efficiency of the Girsanov Transformation Ap- Scalable Algorithms Department proach for Parametric Sensitivity Analysis of Sandia National Laboratotories Stochastic Chemical Kinetics [email protected]

Monte Carlo methods for sensitivity analysis of stochastic John Shadid reaction networks can be classified into three categories, Sandia National Laboratories the pathwise derivative (PD) method, the finite differ- Albuquerque, NM ence (FD) method and the Girsanov transformation (GT) [email protected] method. It has been numerically observed that when ap- plicable, the PD method and FD method tend to be more efficient than the GT method. We provide a theoretical justification for this observation in terms of system size PP13 asymptotic analysis. Optimization of Modeled Land Surface Fluxes by Bayesian Parameter Calibration Ting Wang Department of Mathematics and Statistics University of Maryland Baltimore County The integration of observations and advanced modeling [email protected] tools is critical for resolving issues of uncertainty in cli- mate models. We present results from an isotopically- enabled land surface model, including experiments parti- Muruhan Rathinam tioning evapotranspiration into contributions from plant University of Maryland, Baltimore County transpiration and surface evaporation. We demonstrate a [email protected] model calibration approach in a Bayesian estimation frame- work, requiring Markov chain Monte Carlo sampling of the posterior distribution, which is shown to constrain uncer- PP13 tain parameters and inform relevant values for operational Convergence of the Robbins-Monro Algorithm in use. Infinite Dimensional Hilbert Spaces Tony E. Wong Good proposal distributions can significantly improve the University of Colorado at Boulder performance of random walk Metropolis algorithms. Re- Department of Applied Mathematics cent work has suggested that finding the best Gaussian, [email protected] fit with respect to the relative entropy metric against the target distribution, can provide such speedup. Minimizing relative entropy may be non-trivial, particularly in the case David Noone of distributions on infinite dimensional spaces. We demon- University of Colorado at Boulder strate that the Robbins-Monro algorithm can be used to Cooperative Institute for Research in Environmental find the optimal Gaussian proposal distribution in infinite Sciences dimensional Hilbert spaces. [email protected]

Daniel Watkins William Kleiber Drexel University University of Colorado at Boulder [email protected] Department of Applied Mathematics 266 CS15 Abstracts

[email protected] We apply the methodology to particle tracking velocimetry experiments and demonstrate reconstruction of smooth, physically-correct fields from limited data. PP13 Efficient Monte Carlo Scheme for the Simulation of Iliass Azijli, Richard Dwight, Jan Schneiders the Association of Lattice-model Proteins Delft University of Technology [email protected], [email protected], A lattic Monte Carlo model with implicit membrane and [email protected] water is used to model certain types of protein aggregation in biological membranes. We describe a sampling scheme Hester Bijl that attempts to combine the merits of parallel temper- Faculty Aerospace Engineering ing and multicanonical sampling. The key to this scheme Delft University of Technology, NL is deriving best estimates for the log density of states [email protected] from the MBAR estimator [Shirts, Michael R., and John D. Chodera. ”Statistically optimal analysis of samples from multiple equilibrium states.” The Journal of chem- PP14 ical physics 129.12 (2008): 124105.] Parallel-in-Time Integration with Pfasst++ Yuanwei Xu, Mark Rodger Iterative parallel-in-time integration methods like the re- University of Warwick cently developed “parallel full approximation scheme in [email protected], [email protected] space and time’ (PFASST) provide parallelism along the temporal axis by integrating multiple time-steps simul- taneously. We present PFASST++, a new performance- PP14 oriented library enabling time-parallelization for existing Visualising Protein Sequence Alignment codes. PFASST++ provides flexibility and ease of use while maintaining portability across many HPC architec- In bioinformatics, protein sequence alignment used strings tures. We present preliminary results using a high-order of contiguous letters of amino acids, arranged in vertical Boris integrator for charged particle dynamics in external register in order to highlight regions of similarity and dif- magnetic fields. ference. When sequences have different lengths, gap char- acters are inserted to denote insertions or deletions; how- Torb j¨orn Klatt ever, gaps have no meaning in 3D structures. This project Juelich Supercomputing Centre aims to revisit the protein sequence alignment problem by [email protected] exploring possible ways to visualise the relationships be- tween sequences in 3D space wile eliminating gap charac- Robert Speck ters. In our work, an N -body Hamiltonian system in con- Juelich Supercomputing Centre tact with a heat bath is built and it’s configuration in 3D Forschungszentrum Juelich space forms the basis of our visualisation. The novel 3D vi- [email protected] sualisation method opens the possibility of analysing much larger alignments that wouldn’t be possible with conven- Mathias Winkel, Daniel Ruprecht tional visualisations produced by current alignment tools Institute of Computational Science and editors. Universita della Svizzera italiana [email protected], [email protected] Shaimaa M. Aljuhani PhD student The University of Manchester Matthew Emmett [email protected] Lawrence Berkeley National Laboratory Center for Computational Sciences and Engineering [email protected] Prof. Teresa Attwood The University of Manchester Faculty of Life Sciences PP14 [email protected] An Optimization-Based Approach Toward Elasto- plasticity: Introducing a Projected Newton Algo- Dr. Tony Shardlow rithm University of Bath Department of Mathematical Sciences In this study, we explore an alternative treatment of clas- [email protected] sical plasticity by casting the theory into a mathemati- cal program. We propose a precise development and im- plicit implementation of a projected Newton algorithm to PP14 directly solve the dual optimization problem of incremental Reconstructing Physically Realistic Flow Fields state update in nonlinear models. In particular, implemen- from Sparse Experimental Data tation of multi-surface plasticity models turns out to be no different from that of single surface models. Flow measurements from wind-tunnel experiments suffer from noise and low spatio-temporal resolution. To recon- Zahra S. Lotfian, Mettupalayam Sivaselvan struct complete flow fields we use physics-based interpola- SUNY at Buffalo tion, enforcing a vorticity formulation of momentum con- zahrasad@buffalo.edu, mvs@buffalo.edu servation using a vortex-based solver. Its mesh-free nature and desirable stability characteristics enable a flexible and efficient framework. We formulate the data-assimilation PP14 procedure as an adjoint-based optimization for efficiency. Redesigning Laser-Plasma Simulations to Optimize CS15 Abstracts 267

the Use of Limited Memory Bandwidth [email protected]

Memory bandwidth limitations are a growing problem af- fecting pf3D, a large-scale multi-physics code simulating PP14 laser-plasma interactions. Implementing lossy hardware Simple Yet Fast Integration Method Using Qss for compression between DRAM and cache could improve Stiff Chemical Kinetic Odes available bandwidth use in the future. pf3D is resilient to errors from lossy compression at each time step. We pre- A simple yet robust and fast time integration method is dict pf3Ds hardware compression requirements, describe proposed for efficiently solving stiff chemical kinetic ordi- strategies to optimize data movement to utilize hardware nary differential equations. The proposed method is based compression for a variety of physics kernels, and present on a general formula which preserves the conservation laws software experiments on several existing architectures. for any integration operators constructed using the La- grange multiplier method. And a quasi-steady-state ap- proximation is used as the integrator. The time step size is Eileen R. Martin automatically controlled by keeping a Lagrange multiplier Stanford University small. The proposed method, named ERENA, provides [email protected] the good performances.

Steve Langer Youhi Morii Lawrence Livermore National Laboratory Japan Aerospace Exploration Agency [email protected] [email protected]

Hiroshi Terashima PP14 The University of Tokyo [email protected] Parallel Numerics for Partitioned Multiphysics Coupling Mitsuo Koshi Yokohama National University Massively parallel multi-physics simulations require effi- [email protected] cient parallel coupling schemes. This holds in particular for partitioned simulations where singlephysics components Taro Shimizu, Eiji Shima are combined in a flexible and extensible way. Parallelism Japan Aerospace Exploration Agency and more than two coupled fields pose new to a coupling [email protected], [email protected] scheme. Not all established coupling schemes can cope with these challenges. We propose a set of new implicit coupling schemes that meet all requirements by replacing PP14 the usual fixed-point equation by a different one. To acho- eve fast convergence, the resulting fixed-point equation is PtychoLib: Parallel Ptychographic Reconstruction combined with efficient quasi-Newton methods suitable for Ptychography is a phase retrieval technique for recon- black-box solvers. structing a specimen’s image from its diffraction patterns in light, X-ray, and electron microscopes. Despite the poten- Miriam Mehl tial for ptychography there is a lack of tools for data online Universit¨at Stuttgart analysis while it is being acquired. PtychoLib is a library [email protected] for real-time ptychographic phase retrieval. It uses a hy- brid parallel strategy to divide the computation between Benjamin Uekermann multiple graphics processing units then merge partial re- TU Munich constructions into one coherent phase contrast image. [email protected] Youssef Nashed Florian Lindner Argonne National Laboratory Universit¨at Stuttgart [email protected] fl[email protected] David Vine Advanced Photon Source Argonne National Laboratory PP14 [email protected] Applied Math and CS R&D on Doe Leadership Computing Facilities Tom Peterka Mathematics and Computer Science Division The DOE Leadership Computing Facilities at Argonne and Argonne National Laboratory Oak Ridge national laboratories welcome applied mathe- [email protected] maticians and computer scientists to carry out their re- search on our largest supercomputers. These systems, Junjing Deng among the most powerful in the world, provide a unique en- Applied Physics vironment to explore algorithm scalability and implemen- Northwestern University tation at full scale. Examples of current projects and ways [email protected] to gain access to our systems will be described. Rob Ross Paul C. Messina Argonne National Laboratory Argonne National Laboratory [email protected] 268 CS15 Abstracts

Chris Jacobsen [email protected] Advanced Photon Source Argonne National Laboratory [email protected] PP14 Bridging Multiple Structural Scales with a Gener- alized Finite Element Method PP14 Efficient Numerical Algorithm for Virtual Design In thermo-mechanical problems subjected to intense heat- in Nanoplasmonics ing effects, locally high solution fidelity is required near material-scale interfaces to capture strong gradients which Nanomaterials have given rise to many devices, from high- might not be resolved using, for example, traditional ho- density data storage to optical bio-sensors capable of de- mogenization approaches. Effective numerical methods tecting specific biochemicals. The design of new nanode- must also bridge important localized, nonlinear behavior to vices relies increasingly on numerical simulations, driving a the structural scale. This poster introduces a generalized need for efficient numerical methods. In this work, integral finite element method (GFEM) involving the solution of in- equations are used to efficiently solve the electromagnetic terdependent coarse- and fine-scale problems for resolving transmission problem at the interface of a dielectric and a localized material interfaces on the structural scale. periodic metal nanostructure. Moreover, the same integral equations are used as the basis for an optimization method. Julia A. Plews Department of Civil and Environmental Engineering Alexandra Ortan University of Illinois at Urbana-Champaign University of Minnesota [email protected] [email protected] C. Armando Duarte PP14 University of Illinois at Urbana-Champaign [email protected] Model-Reduction for Closed-Loop Control of Un- steady Flows Using Plasma Actuators

Flow instabilities in aircraft aerodynamics increase noise PP14 emissions and drag. Active closed-loop flow control using A Parallelization Strategy for Large-Scale Vibronic plasma actuators is a promising way to reduce these effects. Coupling Calculations However, a rigorous model is required for the feedback control design. The spatially discretized actuator/flow dy- The vibronic coupling model of K¨oppel, Domcke, and namics is high-dimensional, nonlinear and, thus, computa- Cederbaum is a powerful means to understand, predict, tionally intractable for real-time applications. Therefore, a and analyze electronic spectra of molecules. We describe suitable control-oriented reduced-order model, which cap- a new distributed-memory parallel algorithm for carrying tures the essential physics dominating the system dynamic out such calculations, based on a stencil representation of response, while accounting for the closed-loop dynamics, is the required computational steps. Our algorithm utilizes required. coarse-grained parallelism to achieve near-linear scaling. The algorithm is demonstrated by simulating the low en- Laura Pasquale, Paul Houston, Pericle Zanchetta ergy portion of the VUV spectrum of trans-1,3-butadiene. University of Nottingham [email protected], Scott Rabidoux [email protected], Institute for Computational Engineering and Sciences [email protected] The University of Texas at Austin [email protected] PP14 Victor Eijkhout Moving Pictures: Animating Still Images The University of Texas at Austin Texas Advanced Computing Center We present a means of developing digital image transfor- [email protected] mations that allow a still image to be turned into a short and visually pleasing animation. Rather than manually al- John Stanton tering successive frames to create the illusion of motion, Department of Chemistry the method presented here requires only the input of a The University of Texas at Austin few parameters for each transformation. We developed a [email protected] mathematical framework wherein we defined animations as sequences of still images, and ’transformations’ as compos- able functions on such sequences. PP14 To implement this work, we have built a Matlab library of composable functions that streamline the process of turn- Some Numerical Methods for Modified Bessel ing still images into novel animations. Examples include Functions manipulation of contrast, intensity, and colors of pixels, as well as warps of contours, positions, and size of select The high-quality numerical methods for the computation regions. The transformations allow for easy animation of of modified Bessel functions of the second kind with imag- regions of interest, giving some semblance of life to still inary, complex order and real argument are elaborated. A images by turning them into animated GIFs. Tau method computational scheme is applied for the con- structive approximation of hypergeometric type differential Michael Pilosov equations and their systems. The numerical solution of University of Colorado: Denver some mixed boundary value problems for the Helmholtz CS15 Abstracts 269

equation in wedge domains is developed. Robert Harrison Brookhaven National Laboratory and Stony Brook Juri M. Rappoport University Russian Academy of Sciences [email protected] [email protected] Scott Thornton Institute for Advanced Computational Science PP14 [email protected] Oof: An Object-Oriented Finite-Element Solver for Materials Science PP14 Materials scientists frequently have a requirement to build finite-element models of microstructural systems in order Analysis of Anderson Acceleration for Coupled to explore structure-property relationships. The OOF soft- Neutronic and Thermal Hydraulic Calculations in ware provides researchers with a modeling tool which starts aLightWaterReactor from familiar image data formats, speaks the language of materials science, and provides push-button access to so- In a coupling between Insilico (neutronics) and AMP (fuel phisticated tools for image manipulation and mesh con- performance, subchannel flow), Picard iteration shows in- struction. The recently-released 3D version allows for more stability due to oscillatory error modes arising at high complex and realistic virtual experiments to be performed. enough power. We consider Anderson acceleration as an alternative solution method to Picard. We develop a sim- Andrew Reid plified model which captures the relevant physics from the Center for Theoretical and Computational Materials high fidelity simulation, and perform parametric studies Science which suggest that Anderson should be more robust and National Institute of Standards and Technology faster converging than Picard for the Insilico/AMP cou- [email protected] pling.

Stephen Langer Alexander R. Toth Information Technology Laboratory North Carolina State University National Institute of Standards and Technology [email protected] [email protected] C.T. Kelley North Carolina State Univ PP14 Department of Mathematics Analyzing and Classifying ”Two-Cycles” of tim [email protected] Trigonometric Functions in Newton’s Method Stuart Slattery For this research we are analyzing trigonometric functions, Computer Science and Mathematics Division specifically f(x)=sin(x), in order to find initial values Oak Ridge National Laboratory that when iterated upon, using Newton’s Method, will give [email protected] usanewvalue,whichwheniterateduponwillgiveusthe initial value again, This process then repeats. So far we Steven Hamilton have found reliable characterizing equations which give us ORNL the exact roots that correspond to these special initial val- [email protected] ues. Kevin Clarno Morgan Rupard, Jennifer Switkes Oak Ridge National Laboratory Cal Poly Pomona [email protected] [email protected], [email protected] Roger Pawlowski Multiphysics Simulation Technologies Dept. PP14 Sandia National Laboratories Orbital Localization in Madness [email protected] The Multiresolution ADaptive Numerical Environment for Scientific Simulation (MADNESS) library provides a high- PP14 level environment for the solution of integral and dif- ferential equations in many dimensions using adaptive, The Rapid Optimization Library (rol) in Trilinos fast methods with guaranteed precision based on multi- resolution analysis and novel separated representations. The Rapid Optimization Library (ROL) in Trilinos These features provide a backdrop in which linear scaling provides an object-oriented framework for large-scale, electronic structure algorithms may be realized. Towards derivative-based optimization. The library is matrix-free this goal, we will explore avenues such as fourth order and linear-algebra agnostic permitting easy interface with molecular orbital localization to advance scalability with application code. ROL implements a suite of unconstrained system size while maintaining accuracy and parallelism. and constrained optimization algorithms including: gradi- ent descent, quasi-Newton, and inexact-Newton with line- Bryan E. Sundahl search and trust-region globalization. A stochastic opti- Institute for Advanced Computational Science mization subpackage (SOL) supplies default implementa- Stony Brook University tions of numerous risk measures and adaptive sampling [email protected] capabilities. Examples demonstrate solutions of large op- 270 CS15 Abstracts

timization problems with model uncertainties. acterizing cracks smaller than the imaging resolution.

Bart G. Van Bloemen Waanders Andrew Loeb, Christopher Earls Sandia National Laboratories Cornell University [email protected] [email protected], [email protected]

Drew P. Kouri Optimization and Uncertainty Quantification PP15 Sandia National Laboratories Numerical Simulation of Ni Grain Growth in a [email protected] Thermal Gradient The Potts model is well developed to simulate normal, Denis Ridzal curvature-driven grain growth and has been used exten- Sandia National Laboratories sively to study various aspects of grain growth. In this [email protected] work, we use this model, implemented into the SPPARKS code to simulate grain growth of Ni turbine blades that are PP14 heat treated with temperature gradient intentionally intro- duced to vary the grain size for varied mechanical proper- Integrating Software Tools to Parallel Adaptive ties across the extent of the blade. We will present the Simulations of Fusion Plasma in Tokamaks model, demonstrate its application and estimate mechani- cal properties as a function of position. Mesh-based methods are extensively applied in macro- scopic studies of fusion plasmas in the tokamak. Software John A. Mitchell tools that include the parallel unstructured mesh man- Sandia National Laboratory agement infrastructure (PUMI), the mesh adaption pro- [email protected] cedure (meshAdapt), Simmetrix meshing tool and PETSc equation solver are integrated to the physics simulation Veena Tikare codes under development at Princeton Plasma Physics Lab Sandia National Laboratories (PPPL) such as M3D-C1. [email protected] Fan Zhang Rensselaer Polytechnic Institute PP15 [email protected] Supply Chain Disruptions

Mark S. Shephard, E. Seegyoung Seol Forecasting supply chain disruptions provides buyers with Rensselaer Polytechnic Institute a tool to mitigate risk, avoid liability and increase revenue. Scientific Computation Research Center A diffusion type algorithm is presented that can be used by [email protected], [email protected] a wholesale buyer to predict supply chain disruptions from multiple distributors. A client use case is presented with a discussion of the success of this algorithm via comparison PP15 to a logistic regression model designed for the same use Using Radar Imagery Data to Invert for Maritime case and comparison to chance. Environments Thomas Morrisey Predicting in situ maritime conditions is of great impor- Infosys tance to radar detection in marine atmospheric bound- thomas [email protected] ary layers. To predict the maritime conditions, the radar wave propagation can be modeled using radar imagery data Ravi Prasad through proper orthogonal modes indexed on a specific en- Infosys Limited vironment. These modes live on the compact Stiefel mani- ravi [email protected] fold, and by exploiting the Riemannian structure of it, in- terpolation between the modes is possible and can be used to invert for the maritime environment. PP15 Computational and Experimental Analysis of Den- Vasileios Fountoulakis, Christopher J. Earls tal Implants under Different Loading Conditions Cornell University and Locations [email protected], [email protected] The use of dental implants to solve different problems in dentistry has been growing rapidly. The success rates of PP15 dental implants are also very important for patients. This Thermal Imaging of Sub-Pixel Cracks Through study investigates the stability of dental implants under Metal Plates different loading locations and conditions with the use of Finite Element Analysis. The CAD model is obtained from Active thermography has been studied as a non-destructive CT images. Designed dental implants were fabricated and evaluation technique for structural components, using the experimentally tested (ISO 14801) to compare with com- well-understood theory of heat conduction to infer the pres- putational(FEA) results. ence, location, and characteristics of flaws in a solid. We here use both theory and simulation to determine optimal Emre Ozyilmaz ranges of several operational parameters to be used in ther- Hitit University Engineering Faculty, Dep. of Mechanical mographic evaluation of thin metal plates, such as aircraft Eng skins. We also implement a stochastic approach for char- [email protected] CS15 Abstracts 271

Eda Ozyilmaz, Halil Aykul domain size for statistical reliable results. Hitit University Engineering Faculty, Dept. of Mechanical Eng. Philipp Steinmetz, Johannes H¨otzer, Marcus Jainta, [email protected], [email protected] Britta Nestler Karlsruhe Institute of Technology (KIT) Mehmet Dalkiz Institute of Applied Materials (IAM-ZBS) Mustafa Kemal University Dentistry Faculty [email protected], [email protected], [email protected] [email protected], [email protected]

Ahmet Cini Yuksel Yabansu, Surya Kalidindi Hitit University Engineering Faculty, Georgia Institute of Technology Dept. of Mechanical Eng. Materials Informatics for Engineering Design [email protected] [email protected], [email protected]

PP15 PP15 Math Projects with Tracker Video Analysis Multidisciplinary Development of An Autonomous Underwater Vehicle: Cooperative Fleet for Surveil- Using Tracker freeware, students analyze own-recorded lance Mission video clips and construct mathematical models in explor- ing real-world mathematical applications of concepts from A fleet of cooperative autonomous underwater vehicles algebra through calculus and differential equations. (AUV) called Eco-Dolphin was designed to collect coastal science data under saltwater condition. One AUV Euguenia Peterson equipped both long-range wireless and Wireless sonar com- Richard J. Daley College munication and the others equipped short-range acoustic [email protected] and wireless sonar communication. The fleet position can be tracked via GPS and Wi-Fi and individual positions can be calculated. Successful achieved wireless sonar commu- PP15 nication on prototype one this summer.

Investigation of Numerical Models for New High Ci Wen, Stacey Joseph-Ellison, Junzhen Shao, Qi Zhou, Temperature Superconductors Jonathan Jaworski, Zakaria Daud Embry-Riddle Aeronautical University Chad Sockwell, Florida State University [email protected], [email protected], [email protected], [email protected], ja- Dr. Janet Peterson and Dr. Max Gunzburger, Florida [email protected], [email protected] State University

Recent discoveries of new high temperature super- PP15 conductors initiated investigations to harness these new material’s properties. Unfortunately, many new high Towards Real-Time Blob-Filaments Detection in temperature superconductors come with odd properties Fusion Plasma such as multiband interactions and anisotropic behav- ior, as is the case for Magnesium Diboride. In this Magnetic fusion is a viable energy source for the future. research Ginzburg Landau model variants are modified The success of magnetically confined fusion reactors de- and simulated to try and simulate these materials more mand steady-state plasma confinement which is challenged realistically. This extends to three dimensional domains, by the edge turbulence such as the blob-filaments. We anisotropy, and microscopic corrections such as the present a real-time outlier detection algorithm to effi- Extended Ginzburg Landau model. ciently find blob-filaments in fusion simulations and ex- periments. We have implemented this algorithm with hy- Chad Sockwell brid MPI/OpenMP and demonstrated the accuracy and Florida State University efficiency with a set of data from the XGC1 fusion simula- Department of Scientific Computing tions. [email protected] Lingfei Wu Department of Computer Science PP15 College of William & Mary [email protected] Characterization of Ternary Eutectic Solidification Patterns from Phase-Field Simulations and Exper- imental Micrographs Kesheng Wu NERSC, Lawrence Berkeley National Lab Large scale three-dimensional phase-field simulations based [email protected] on the grand potential are used to model the microstruc- ture evolution from directional solidification of ternary eu- Alex Sim tectics. To compare the computational cross-sections and Lawrence Berkeley National Lab experimental micrographs, principal component analysis is [email protected] applied. With this, the influence of single parameters from the different reported data sets on the evolving patterns Andreas Stathopoulos can be quantified. This allows to determine both, the con- College of William & Mary vergence of microstructure simulations and the necessary Department of Computer Science 272 CS15 Abstracts

[email protected] demands of different models with different resolutions

Nishant Panda PP101 Colorado State University [email protected] Bet: Algorithmic and Error Analyses

We review the basic theory behind the non-intrusive PP102 measure-theoretic algorithm for solving stochastic inverse problems for deterministic models. We define sigma- Tsunami Modeling In North Africa Using Geo- algebra constraints on sampling methods to achieve cer- claw Software: a Tool for the Tsunami Scenario tain approximation properties of events. We provide con- Database in the West Mediterranean vergence results and a priori and a posteriori error anal- yses producing fully computable a posteriori error esti- North Africa exhibits an active plate boundary with Eu- mates. The fully computable a posteriori error estimates rope, highlighted by a moderate seismicity.The triggering provide lower and upper bounds for computed probabili- of regional tsunamis is due to (1) earthquakes generated in ties of events. We demonstrate the use of this analysis on North Algeria and (2) landslides. Modeling carried out us- numerical results utilizing a posteriori error estimates to ing tsunami sources located along the Algerian coast is pre- improve the accuracy of computed probability measures. sented hereby. Computing scenarios using the Riemanns algorithm implemented within the GEOCLAW software to Troy Butler solve the non linear shallow water equations provides ac- University of Colorado Denver curate results in comparison with other tsunami software. [email protected] Lubna Amir PP101 USTHB University [email protected] BET: Applications for an Open Source Inverse Problems Package Walter Dudley University of Hawaii at Hilo We present example applications of the BET Python Pack- 200 W. Kawili Street, Hilo, Hawaii, USA age to solve the stochastic inverse problem within a mea- [email protected] sure theoretic framework. We demonstrate various features of the BET package for approximating inverse probability measures including goal-oriented adaptive sampling algo- Jean Roger rithms, parallel capabilities, differing approximation op- G-Mer Etudes Marines tions, and visualization capabilities. BET can interface Av. de l’Europe - Saint Francois Guadeloupe, France with a variety of physics-based computational models. [email protected]

Lindley C. Graham University of Austin at Texas PP102 Institute for Computational Engineering and Sciences ForestClaw : Parallel, Adaptive, Multiblock Simu- (ICES) lations for Clawpack [email protected] We describe our recent progress in developing ForestClaw, Steven Mattis an adaptive mesh refinement code based on the dynamic University of Texas at Austin octree library p4est (C. Burstedde, Univ. of Bonn) and [email protected] finite volume solvers, including ClawPack (R. J. LeVeque). One particular feature of ForestClaw is the ease with which it can handle multi-block domains such as the cubed- Troy Butler sphere, or other geometries not easily described by a sin- University of Colorado Denver gle logically rectangular domain. ForestClaw preserves all [email protected] of the scalability and performance of the underlying grid management library p4est. Clint Dawson Institute for Computational Engineering and Sciences Donna Calhoun University of Texas at Austin Boise State University [email protected] [email protected]

PP101 PP102 Bet: Modifications and Analysis for Model Dis- Adjoint Methods for Guiding Adaptive Mesh Re- crepancies finement in Wave Propagation Problems

We consider the selection of a model as an uncertain input AMRClaw and GeoClaw software uses block-structured parameter and we quantify this uncertainty in the measure- adaptive mesh refinement to selectively refine around prop- theoretic framework using the BET Python Package. For agating waves. The refinement criterion is often based on example, in multi-scale models, optimal mesoscale models local estimates of error via Richardson extrapolation, or that upscale fine-scale parameters for use in the macro- some measure of solution smoothness such as the gradient. scale model are often uncertain. We describe and analyze For problems where a small region of the solution is of pri- modifications to the BET package to optimize load balanc- mary interest, solving the time-dependent adjoint equation ing taking into account the widely different computational and using a suitable inner product with the forward solu- CS15 Abstracts 273

tion allows more precise refinement of the relevant waves. built on existing codes, including Clawpack, SharpClaw, and PETSc. We describe PyClaw’s design, development, Brisa Davis and some applications. University of Washington [email protected] David I. Ketcheson CEMSE Division Randall LeVeque King Abdullah University of Science & Technology University of Washington [email protected] Applied Math [email protected] Aron Ahmadia US Army Engineer Research and Development Center [email protected] PP102 A Community-Driven Collection of Approximate Kyle T. Mandli Riemann Solvers for Hyperbolic Problems University of Texas at Austin ICES The key ingredient in modern numerical methods for hy- [email protected] perbolic problems is the Riemann solver. The same algo- rithms can then be used to solve a wide range of hyperbolic problems – water waves, fluid dynamics, elasticity, electro- PP102 magnetics, etc. We present an effort to make available a Practical Applications of GeoClaw to Tsunami large library of Riemann solvers for general use, and the Hazard Assessment development of a set of IPython notebooks that describe and interactively explain the solvers for important systems. The GeoClaw software has recently been used for several tsunami hazard assessment projects and two examples will Mauricio J. Del Razo be presented in this poster. The first is the analysis of an University of Washington elementary school site in Ocosta, WA that has since been mauricio [email protected] selected for the first ”vertical evacuation structure” to be built in the United States. The second is the development of improved probabilistic tsunami hazard assessment tech- David I. Ketcheson niques. CEMSE Division King Abdullah University of Science & Technology Randall LeVeque [email protected] University of Washington Applied Math Randall LeVeque [email protected] University of Washington Applied Math Loyce Adams [email protected] University of Washington [email protected] PP102 Frank I. Gonzalez High Resolution Tsunami Modeling at the U. Washington, Dept. of Earth and Space Sciences Mediterranean Coast of Israel Towards An Early fi[email protected] Warning Tsunami Scenarios Data Bank

A tsunami modelling investigation using the state of the PP102 art, open source tsunami model (GeoClaw a subset of the software package Clawpack), its adaptation to investigate CUDACLAW: A GPU Framework for the Solution the impact of tsunami wave generation, propagation and of Hyperbolic Pdes inundation at the Mediterranean coast of Israel using high resolution bathymetric and topographic grid, aided by ad- CUDACLAW is a data-parallel framework that allows ditional tsunami generation modelling tools simulating the users to take advantage of GPU accelerators to solve hyper- initial stages of tsunami generation by earthquake induced bolic PDEs, without being burdened by the need to write tectonic plates rupture and movement or by landslide on CUDA code, worry about thread and block details, data the coastal shelf. layout, and data movement between the different levels of the memory hierarchy. The user defines the set of PDEs Barak Galanti via a serial Riemann solver and the framework takes care Inter-University Computational Center of orchestrating the computations and data transfers to Tel Aviv University maximize arithmetic throughput. A prototype implemen- [email protected] tation shows that, on 2D and 3D acoustics wave equations and shallow water equations, the framework can achieve performance comparable to that of manually-tuned code. PP102 PyClaw: Accurate, Scalable Solution of Hyperbolic George M. Turkiyyah PDEs in Python American University of Beirut [email protected] PyClaw is a Python-based interface to fast and accurate Godunov-type numerical algorithms for modeling nonlin- H. Gorune Ohannessian ear waves. It is massively scalable and includes both 2nd- University of Wisconsin order TVD and higher-order WENO discretizations. It is [email protected] 274 CS15 Abstracts

Aron Ahmadia to support adaptive unstructured simulations on massively US Army Engineer Research and Development Center parallel computers. The in-memory integration of these [email protected] components with multiple unstructured mesh finite ele- ment and finite volume codes will be included. David I. Ketcheson CEMSE Division Brian Granzow King Abdullah University of Science & Technology Rensselaer Polytechnic Institute [email protected] [email protected]

PP103 PP103 An Overview of PETSc MueLu: Multigrid Framework for Advanced Ar- chitectures The changing landscape of scientific application needs and high-performance architectures requires continued innova- MueLu multigrid library is a part of Sandia’s Trilinos tion in mathematical algorithms for the robust solution of project. MueLu is designed to be flexible, easily exten- large-scale numerical problems. This poster provides an sible, and efficient on emerging architectures. MueLu al- overview of the Portable, Extensible Toolkit for Scientific lows users to specify preferred data (ordinal or scalar) Computing (PETSc), a suite of data structures and rou- and shared memory (”node”) types by leveraging Trilinos’ tines for the scalable (parallel) solution of scientific appli- sparse linear algebra libraries Kokkos and Tpetra. Cur- cations modeled by partial differential equations (PDEs). rent algorithms include smoothed aggregation (SA), non- We also will provide demos of a variety of PDE-based ex- symmetric SA, Maxwell solvers, and energy-minimization. amples, including advances in composable linear, nonlin- In this poster, we highlight important design features and ear, and timestepping solvers, which incorporate multiple large-scale results on DOE supercomputers. levels of nested algorithms and data models to exploit ar- chitectural features and/or problem-specific structure. Jonathan J. Hu Sandia National Laboratories Satish Balay Livermore, CA 94551 Argonne National Laboratory [email protected] [email protected] Andrey Prokopenko Jed Brown Sandia National Laboratories Mathematics and Computer Science Division [email protected] Argonne National Laboratory and CU Boulder [email protected] PP103 William D. Gropp Parallel Unstructured Mesh Infrastructure University of Illinois at Urbana-Champaign The Parallel Unstructured Mesh Infrastructure (PUMI) Dept of Computer Science supports the needs of parallel mesh-based analysis codes [email protected] to develop complete simulation workflows. This poster will focus on recent developments including array-based mesh Matthew Knepley data structures and field abstractions that provide sub- University of Chicago stantial reductions in memory usage. Component reorga- [email protected] nization via dependency inversion provides a substantial decrease in code size. The integration of PUMI with dy- Lois Curfman McInnes namic load balancing and its use in simulation workflows Mathematics and Computer Science Division will be included. Argonne National Laboratory [email protected] Dan A. Ibanez Rensselaer Polytechnic Institute Barry F. Smith SCOREC Argonne National Lab [email protected] MCS Division [email protected] E. Seegyoung Seol Rensselaer Polytechnic Institute Hong Zhang Scientific Computation Research Center MCS, Argonne National Laboratory [email protected] [email protected] Gerrett Diamond Rensselaer Polytechnic Institute PP103 [email protected] Construction of Parallel Adaptive Simulation Loops PP103 The automation of reliable large-scale simulations requires Massively Parallel Adaptive Simulations Using the integration of a number of operations that include mesh Petsc for Turbulent Boundary Layer Flows generation, equation discretization, equation solution, er- ror estimation and discretization improvement within a A set of tools and techniques are presented on adaptive loop that requires regular dynamic load balancing to main- methods for boundary layer meshes. Such meshes are use- tain scalability. This poster presents a set of components ful in wall-bounded turbulent flows. An adaptive approach CS15 Abstracts 275

for such meshes must maintain highly anisotropic, graded, [email protected], [email protected] and layered elements near the walls. Parallel procedures must account for mixed elements, i.e., in mesh modifica- tions and load balancing. Additionally, we study the ef- PP103 ficiency and scalability of the linear solvers and precondi- Dynamic Partitioning Using Mesh Adjacencies tioners available via PETSc for this class of problems. Parallel unstructured mesh-based applications running on Michel Rasquin the latest petascale systems require partitions optimizing University of Colorado Boulder specific balance metrics. Methods combining the most [email protected] powerful graph based and geometric methods with diffu- sive methods directly operating on the unstructured mesh Dan A. Ibanez are discussed. Implementation details will be provided for Rensselaer Polytechnic Institute the components comprising the direct unstructured mesh SCOREC based methods as will initial results for applications with [email protected] meshes of several billion elements on over 500k parts.

Benjamin Matthews Cameron Smith University of Colorado Boulder Scientific Computation Research Center [email protected] Rensselaer Polytechnic Institute [email protected] Cameron Smith Scientific Computation Research Center Dan A. Ibanez Rensselaer Polytechnic Institute Rensselaer Polytechnic Institute [email protected] SCOREC [email protected] Onkar Sahni Rensselaer Polytechnic Institute Gerrett Diamond [email protected] Rensselaer Polytechnic Institute [email protected] Mark S. Shephard Rensselaer Polytechnic Institute PP103 Scientific Computation Research Center [email protected] Fastmath Structured Mesh and Particle Technolo- gies Kenneth Jansen Scientific phenomenon happen over a wide range of length University of Colorado at Boulder and time scales. Chombo and BoxLib are libraries that are [email protected] developing and deploying state-of-the-art structured adap- tive mesh and particle-in-cell technologies under the aegis of FASTMath. The evolving algorithms and computational PP103 frameworks provided by these libraries allow scientific ap- Sparse Direct Solvers and Preconditioners on plication codes to capture these scales efficiently and enable Manycore Systems scientific discovery at scale currently, as well as prepare for the future architectures. We develop scalable sparse direct linear solvers and effec- tive preconditioners for the most challenging linear systems Anshu Dubey, Phillip Colella on manycore parallel machines. Our focal efforts are the Lawrence Berkeley National Laboratory developments of two types of solvers: The first is a pure di- [email protected], [email protected] rect solver, encapsulated in SuperLU software. The second is the nearly-optimal preconditioners using the HSS low- Mark Adams rank approximate factorization of the dense submatrices, Lawrence Berkeley Laboratory encapsulated in STRUMPACK software. [email protected]

Xiaoye Sherry Li Ann S. Almgren Computational Research Division Lawrence Berkeley National Laboratory Lawrence Berkeley National Laboratory [email protected] [email protected] Dan Graves, Terry J. Ligocki Pieter Ghysels Lawrence Berkeley Laboratory Lawrence Berkeley National Laboratory [email protected], [email protected] Computational Research Division [email protected] Brian Van Straalen Lawrence Berkeley National Laboratory Francois-Henry Rouet Compuational Research Division Lawrence Berkeley National Laboratory [email protected] [email protected] Milo Dorr Piyush Sao, Richard Vuduc Center for Applied Scientific Computing Georgia Institute of Technology Lawrence Livermore National Laboratory 276 CS15 Abstracts

[email protected] [email protected]

PP103 PP104 Sundials: Suite of Nonlinear and Differen- Concurrent Coupling Methods in Mesoscopic Ma- tial/algebraic Solvers terials Modeling

In this poster we present the SUNDIALS library suite, con- Mesoscopic methods with thermodynamic fluctuations, sisting of the solver libraries CVODE, CVODES, ARKode, such as dissipative particle dynamics, are powerful tools IDA, IDAS, and KINSOL. This DOE-funded solver library to study material properties at relevant spatial-temporal focuses on robust and scalable solvers for systems of ordi- scales. Concurrently coupling a mesoscopic model with a nary differential equations, systems of differential-algebraic microscopic description, such as molecular dynamics, can equations and systems of nonlinear equations. Sharing a benefit further from microscopic description with great de- common set of vector libraries and linear solvers (both tails. Concurrently coupling a mesoscopic model with a direct and iterative), these solvers are designed for algo- continuum discretization, such as smoothed particle hy- rithmic flexibility, with interfaces in C, C++ and For- drodynamics, enables to simulate real applications at large tran (some even in Matlab), and may be easily adapted scale with great computational efficiency. to application-specific and user-defined data structures. Xin Bian Brown University Daniel R. Reynolds Xin [email protected] Southern Methodist University Mathematics [email protected] PP104 Overview of Mathematics for Mesoscopic Modeling Carol S. Woodward of Materials Lawrence Livermore Nat’l Lab [email protected] The Collaboratory on Mathematics for Mesoscopic Mod- eling of Materials, or CM4, develops systematic mathe- matical foundations for understanding and controlling the PP103 fundamental mechanisms in mesoscale processes. CM4 fo- Hypre: High Performance Preconditioners cuses on the development and integration of particle-based, continuum-based, and stochastic methods, as well as the The hypre software library provides high performance pre- concurrent coupling between them. As science drivers, a conditioners and solvers for the solution of large sparse set of demonstration problems will facilitate integration of linear systems on massively parallel computers. One of CM4 mathematical models and numerical approaches in its attractive features is the provision of conceptual inter- the context of important materials modeling challenges. faces, which include a structured, a semi-structured, and a traditional linear-algebra based interface. These interfaces George E. Karniadakis give application users a more natural means for describing Brown University their linear systems, and provide access to hypre’s solvers, Division of Applied Mathematics which include structured and unstructured algebraic multi- george [email protected] grid solvers.

Robert Falgout, Tzanio V. Kolev PP104 Center for Applied Scientific Computing Hierarchical Coarse-graining and Parallelization Lawrence Livermore National Laboratory Methods for Mesoscale material Models [email protected], [email protected] We discuss information theory-based methods for the pa- rameterized coarse-graining of non-equilibrium extended Jacob B. Schroder, Ulrike M. Yang systems, typically associated with coupled physicochemical Lawrence Livermore National Laboratory mechanisms or driven systems, and where steady states are [email protected], [email protected] unknown altogether, e.g. do not have a Gibbs structure. Our pathwise information theory tools provide reliable PP104 molecular model parameterizations and rational model se- lection through suitable dynamics-based information crite- Stochastic Methods in Mesoscopic Materials Mod- ria. We also discuss connections of the developed tools to eling force-matching in a dynamics context and the transferabil- ity of coarse-graining maps. For soft materials, a central challenge is to link bulk prop- erties with the behaviours of the material mesostructures. Markos A. Katsoulakis Such interactions/kinetics often involve a subtle interplay University of Massachusetts, Amherst of enthalpic and entropic effects extending over a wide Dept of Mathematics and Statistics range of scales presenting well-known challenges for mod- [email protected] elling and simulation. We present our recent progress on dynamic implicit-solvent coarse-grained approaches that utilize a fluctuating hydrodynamics thermostat. We inves- PP104 tigate the properties of polymeric materials and biophysical Particle-Based Methods in Mesoscopic Materials questions for lipid bilayer membranes. Modeling

Paul J. Atzberger Coarse-grained particle-based method is capable of sim- University of California-Santa Barbara ulating mesoscopic phenomena with a discrete or discon- CS15 Abstracts 277

tinuous nature. Its governing equations can be obtained Maximilian S. Metti by applying the Mori-Zwanzig projection on a microscopic Penn State University dynamics. We present a bottom-up approach to quantify [email protected] the coarse-grained model via the Mori-Zwanzig formula- tion with microscopic data provided by molecular dynamics (MD) simulations. Results show that such MD-informed PP104 coarse-grained model is able to accurately reproduce its Applications in Mesoscopic Modeling of Materials underlying MD system. Recent applications in micro-/nano-technology, material Zhen Li assembly and biological systems demand robust and ac- Brown University curate computational modeling of multiphysical processes Brown University at the mesoscale. In this poster we focus on mathe- Zhen [email protected] matical models and numerical schemes that can effec- tively capture mesoscale multiphysics (hydrodynamics, transport, electrostatics and chemical reaction). Specifi- PP104 cally, we show simulation results on mixing and separa- Grid-Based Methods in Mesoscopic Materials tion processes in micro-/nano-channel, electrokinetic flow Modeling through semi-permeable membranes, and diffusive reaction on biomolecules. Our focus is on developing continuum-level simulations to describe the dynamics of colloidal systems, self-assembly Wenxiao Pan and flow transport in micro-channels. Generally the ap- Pacific Northwest National Laboratory proach is to use grid-based methods but we also work with [email protected] Lagrangian particle-based methods. Here we evaluate the electrostatic or magnetostatic moments of particles in sus- Mauro Perego pension, subject to an external field, and the resulting force CSRI Sandia National Laboratories interactions. We use both immersive methods (smoothed [email protected] profile method) and finite multipoles, and compare accu- racy and efficiency. PP104 Martin Maxey Coarse-Graining in Mesoscopic Materials Modeling Division of Applied Mathematics, Brown University The mesoscopic modeling of materials is a flourishing sub- [email protected] ject of research due to its importance for many techno- logical and societally relevant applications. By definition, mesoscopic models entail the process of coarse-graining PP104 of microscopic (molecular) models. The resulting models Fast Solvers for Mesoscopic Materials Modeling may exhibit space/time symmetry breaking. In our re- cent work as part of CM4 we have focused on the use of The Collaboratory on Mathematics for Mesoscopic Model- renormalization in order to construct coarse-grained mod- ing of Materials is developing numerical solvers designed to els which are adaptive, in the sense that the relevant co- efficiently solve systems modeling charge transport. These efficients of the model are estimated on the fly as the sys- phenomena are commonly encountered in engineering ap- tem evolves. We believe that renormalization (perturbative plications and are also of growing importance to biolog- or non-perturbative) is a viable method for constructing ical contexts as well. We conduct a numerical analysis coarse-grained models of controlled accuracy for complex of our proposed schemes to understand important aspects systems. The purpose of the current poster is to present of our solvers, such as stability, consistency, and well- our recent results on the subject as well as outline future posedness. We consider fast solvers for the Poisson-Nernst- directions and open problems. Planck (PNP) system using a finite element discretization. Panos Stinis We leverage qualitative mathematical structures and phys- University of Minnesota, Twin Cities ical properties of this system to improve the quality and [email protected] efficiency of computed solutions. Our proposed discretiza- tion scheme readily leads to an energy estimate for the computed solution that is characteristic of the continuous PP105 PNP system. Further analysis for the efficiency and robust- ness of the solvers is considered as a separate component Realizability Limiting in High-Order Numerical of the analysis. Solutions of Entropy-Based Moment Closures Entropy moment closures for kinetic equations (colloqui- Jinchao Xu ally known as MN models) have attractive theoretical prop- Pennsylvania State University erties (hyperbolicity, entropy dissipation, and positivity) [email protected] but are only defined in the set of realizable moment vec- tors, that is those which are consistent with a positive dis- Chun Liu tribution. High-order numerical solutions do not always Department of Mathematics, Penn State University stay in this set, so we investigate the use of a limiter to University Park, PA 16802 handle nonrealizable moments in the implementation of a [email protected] high-order discontinuous Galerkin method.

Xiaozhe Hu Graham Alldredge The Pennsylvania State University RWTH AACHEN University [email protected] [email protected] 278 CS15 Abstracts

Florian Schneider Jet Propulsion Laboratory TU Kaiserslautern California Institute of Technology [email protected] [email protected], [email protected], [email protected], [email protected]

PP105 Exploration and Validation of Full-Domain Mas- PP105 sively Parallel Transport Sweep Algorithms On the Hyperbolicity of Grads 13 Moment System

Scaling of discrete-ordinates transport sweep-based algo- In gas kinetic theory, lack of global hyperbolicity is a major rithms is currently of great general interest. Recent re- critique for Grad’s moment method. For the well-known search on volume-based spatial decomposition approaches Grad’s 13 moment system, I. Muller et. al.(1998) pointed shows great potential. Schedule conflict resolution and spa- out it is not globally hyperbolic for 1D flow. In this presen- tial domain overloading are essential algorithm characteris- tation, we will point out for 3D case, for each equilibrium tics for obtaining good scaling. We describe computational state, none of its neighbourhoods is contained in the hyper- experiments performed on the IBM BG/Q machine (Se- bolicity region. And a globally hyperbolic regularization quoia) at LLNL that indicate MPI based algorithms scale for it will be proposed. to the full machine with good efficiencies predicted by par- allel performance models. We also present simple studies of Yuwei Fan single node performance using task, thread and instruction School of Mathematical Sciences level parallelism for these algorithms. Peking University, Beijing, P.R.China [email protected] Teresa S. Bailey LLNL Zhenning Cai [email protected] Center for Computational Engineering Science RWTH Aachen University Peter Brown, Adam Kunen [email protected] Lawrence Livermore National Laboratory [email protected], [email protected] Ruo Li School of Mathematical Science Peking University PP105 [email protected] A New Moment Method in the Kinetic Theory of Gases Based on the L2 Function Space PP105 Recently, a framework for hyperbolic model reduction in Convergence of Filtered Spherical Harmonic Equa- the kinetic theory was proposed. Based on this framework, tions for Radiation Transport we reconsider the convergence of Grad’s expansion, and find the function space may be insufficient in some cases. We analyze the global convergence properties of the filtered To make improvements, we replace the weighted L2 space spherical harmonic (FPN ) equations for radiation trans- used in the classic moment method by the plain L2 space, port. The well-known spherical harmonic (PN )equations and special projections are used in the model recduction are a spectral method (in angle) for the radiation transport to maintain both hyperbolicity and conservation. equation and are known to suffer from Gibbs phenomena Zhenning Cai around discontinuities. The filtered equations include ad- Center for Computational Engineering Science ditional terms to address this issue that are derived via a spectral filtering procedure. We show explicitly how the RWTH Aachen University 2 [email protected] global L convergence rate (in space and angle) of the spec- tral method to the solution of the transport equation de- pends on the smoothness of the solution (in angle only) Manuel Torrilhon and on the order of the filter. The results are confirmed by RWTH Aachen University numerical experiments. Numerical tests have been imple- [email protected] mented in MATLAB and are available online.

Martin Frank PP105 RWTH Aachen University Markov Chain Formalism for Radiative Transfer Center for Computational Engineering Science in Planetary Atmospheres: Forward Modeling, In- [email protected] cluding Linearization Cory Hauck The 1D vector radiative transfer problem is solved with Oak Ridge National Laboratory a Markov chain approach. The matrix structure of that [email protected] method enables efficient numerical computation of polar- ized radiation fields throughout the atmosphere, as well as straightforward linearization to derive Jacobian matrixes Kerstin Kuepper exactly. We applied this computational forward model- RWTH Aachen University ing framework for remote sensing signals to aerosol/surface Center for Computational Engineering Science property retrievals from air- and spaceborne observations [email protected] on Earth and to analyses of polarized imagery of Titan from the Cassini probe. PP105 Anthony B. Davis, Feng Xu, Robert West, David Diner A High Order, Implicit, Hybrid Solver for Linear CS15 Abstracts 279

Kinetic Equations [email protected], [email protected], [email protected] Recently, an implicit, hybrid solver for linear kinetic equa- tions has been investigated using a backward Euler solver in time. We present a high order time discretization based PP105 on deferred corrections with respect to the backward Euler Massively Parallel Calculations of Neutronics Ex- method. Also, several numerical results are given to show periments Using Pdt the efficacy of the hybrid method for various orders of ac- curacy in time as well as streaming versus highly collisional We demonstrate efficient parallel solution algorithms for regimes. high-fidelity neutron transport calculations and thermal radiative-transfer calculations. Calculations employ spa- Michael Crockat tial grids that are structured at a coarse level but unstruc- Michigan State University tured at a fine level to accurately represent geometries of [email protected] simulated experiments. Calculations employ optimal par- allel transport sweeps and physics-based preconditioners. Charles K. Garrett, Cory Hauck Oak Ridge National Laboratory [email protected], [email protected] Marvin L. Adams, Aaron Holzaepfel,W.DarylHawkins, Michael Adams, Anthony Barbu, Timmie Smith Texas A&M University PP105 [email protected], [email protected], A High Order Time Splitting Method Based on [email protected], [email protected], Integral Deferred Correction for Semi-Lagrangian [email protected], [email protected] Vlasov Simulations

The dimensional splitting semi-Lagrangian methods with PP105 different reconstruction/interpolation strategies have been Numerical Solution of the Boltzmann Equation Us- applied to kinetic simulations in various settings. How- ing Quadrature-Based Projection Methods ever, the temporal error is dominated by the splitting er- ror. In order to have numerical algorithms that are high The lack of hyperbolicity has posed many problems for ex- order both in space and in time, we propose to use the in- isting moment models based on the Boltzmann equation. tegral deferred correction (IDC) framework to reduce the We derive globally hyperbolic and rotationally invariant splitting error. The proposed algorithm is applied to the equations using the Quadrature-Based Moment Method. Vlasov-Poisson system, the guiding center model and in- The method is explained by a newly developed framework compressible flows.We show numerically that the IDC pro- of projection operators. In order to investigate the approxi- cedure can automatically increase the order of accuracy in mation quality of the emerging non-conservative equations, time. we apply dedicated numerical methods on unstructured two-dimensional quad grids and the results are compared Wei Guo to reference solutions. Michigan State University [email protected] Julian Koellermeier, Manuel Torrilhon RWTH Aachen University [email protected], PP105 [email protected] Analysis of Discontinuous Galerkin Algorithms for Diffusion and for Energy-Conserving Hamiltonian Dynamics PP105 Positive Filtered PN Closures for Linear Kinetic We present mixed continuous/discontinuous Galerkin Transport Equations, with some Convergence Re- schemes for solution of a class of kinetic Vlasov-Boltzmann sults problems in Hamiltonian Poisson-bracket form (plus colli- sions). These schemes conserve energy, and optionally the We propose a modification to the standard spherical har- L2 norm, exactly. Application to electromagnetic gyroki- monic closure, known as PN closure, for kinetic equations. netic problems requires novel extension to avoid the Am- The modification produces smooth, nonnegative polyno- pere cancellation problem and significant time step limita- mial ansatzes by applying two-step filtering on the oscil- tions. There are subtle properties of commonly used DG latory, partially negative PN solutions, and integrates the schemes for second order derivatives, such as from diffu- closed moment system with filtered moments. We formu- sion, which we compare with a recovery-based approach. late the filtering process as a quadratic program, prove convergence of the proposed closure when the moment or- Greg Hammett der goes to infinity, and report numerical results on the Princeton Plasma Physics Laboratory linesourcebenchmark. Princeton University [email protected] Ming Tse P. Laiu Department of Electrical and Computer Engineering Ammar Hakim University of Maryland - College Park Princeton Plasma Physics Laboratory [email protected] [email protected] Cory Hauck Eric Shi, Ian Abel, Tim Stoltzfus-Dueck Oak Ridge National Laboratory Princeton University [email protected] 280 CS15 Abstracts

Dianne P. O’Leary the BGK equation in a hyperbolic scaling. Our approaches University of Maryland, College Park are based on the micro-macro formulation of the kinetic Department of Computer Science equation which involves a natural decomposition of the [email protected] problem to the equilibrium and the non-equilibrium parts. The new ingredients for the proposed methods to achieve Andr´eTits high order accuracy are the following: we introduce dis- University of Maryland at College Park continuous Galerkin discretization of arbitrary order of ac- [email protected] curacy with nodal Lagrangian basis functions in space; we employ a high order globally stiffly accurate implicit- explicit Runge-Kutta scheme as time discretization. It PP105 is demonstrated that the proposed scheme becomes a lo- Implicit, Filtered Pn Methods for Radiation Trans- cal DG discretization with an explicit RK method for port the macroscopic compressible Navier-Stokes equations, a method in a similar spirit to the ones in [Bassi & Rabey The solution of thermal radiation transport as part of 1997, Cockburn & Shu 1998]. Numerical results are pre- radiation-hydrodynamics calculations is important in the sented for a wide range of Knudsen number to illustrate simulation of astrophysical phenomenon as well as high- the effectiveness and high order accuracy. energy density physics applications such as inertial confine- ment fusion. In this work we present an implicit method Jingmei Qiu for solving the spherical harmonics (PN ) equations of ra- University of Houston diation transport using filtered expansions. Since the in- [email protected] troduction of such filtered PN methods by McClarren and Hauck, these approaches have been successful in produc- Juhi Jang ing high fidelity solutions to difficult transport problems. Math department . In this poster we present results of implicit filtered PN UC Riverside radiation transport simulations and discuss precondition- [email protected] ing strategies as well as the effect of implicit time inte- gration on the necessary filter strength. We compare the Fengyan Li results to reference Monte-Carlo calculations for several Rensselaer Polytechnic Institute standard test problems, including radiation transport in [email protected] a laser-driven shock tube experiment. Tao Xiong Ryan G. McClarren Math Department Texas A & M University of Houston [email protected] [email protected] Vincent Laboure Texas A&M University PP105 [email protected] Towards Hyperbolic Moment Approximations of Multicomponent Plasmas Cory Hauck Oak Ridge National Laboratory Travelling shock waves through initially neutral gases can [email protected] initiate ionisation reactions leading to a multicomponent plasma. The description of such shock waves poses a great modelling challenge since not only collisional processes in- PP105 cluding reactive collisions, but also the interactions of the Massively Parallel Nuclear Reactor Analysis Using gas with the macroscopic force fields have to be taken Pdt into account. In the most general case a kinetic descrip- tion of the plasma would require the numerical solution We demonstrate efficient parallel solution algorithms for of the Boltzmann equation for each species coupled to the high-fidelity neutron and gamma transport calculations in Maxwell equations. We consider hyperbolic moment ap- nuclear reactors. Calculations employ spatial grids that proximations of the Boltzmann equation, which promise an are structured at a coarse level but unstructured at a fine efficient description of the plasma components for Knudsen level to accurately represent fuel and structural geometries. numbers in the continuum and transition regime. Calculations employ optimal parallel transport sweeps and sophisticated physics-based preconditioners. Roman P. Sch¨arer, Manuel Torrilhon RWTH Aachen University Marvin L. Adams, Carolyn McGraw,W.DarylHawkins, [email protected], [email protected] Michael Adams, Timmie Smith aachen.de Texas A&M University [email protected], [email protected], [email protected], [email protected], PP105 [email protected] Ifp: An Optimal, Fully Conservative, Fully Im- plicit, Vlasov-Fokker-Planck Solver: Poster PP105 We introduce a new, exactly conservative (mass, momen- High Order Asymptotic Preserving Nodal Discon- tum, and energy), and fully nonlinearly implicit solver for tinuous Galerkin Imex Schemes for the Bgk Equa- a multi-species 1D-2V Vlasov-Rosenbluth-Fokker-Planck tion system. The new solver optimizes mesh resolution require- ments by 1) adapting the velocity-space mesh based on the We develop high-order asymptotic preserving schemes for species’ local thermal-velocity, and 2) treating the cross- CS15 Abstracts 281

species collisions exhibiting disparate thermal velocities by Kokkos library is employed to handle memory layout and an asymptotic formulation. We demonstrate the efficiency parallelization over a large number of threads in the as- and accuracy properties of the approach with challenging sembly kernel. The PDE is discretized using edge-basis numerical examples. functions for the eletric field and face-basis functions for magnetics. We also explore the memory to computation William T. Taitano tradeoffs of using these vector basis functions. Results il- Los Alamos National Laboratory lustrating the thread scalability of our approach will be [email protected] presented.

PP105 Eric C. Cyr Residual Monte Carlo Methods Within the Scalable Algorithms Department Moment-Based Acceleration Framework Sandia National Laboratotories [email protected] Over the past several years, Moment-Based Acceleration, or High-Order/Low-Order methods, have been used to Irina Demeshko solve kinetic equations efficiently and accurately. Recent Sandia National Laboratories work has adapted these methods to include Monte Carlo [email protected] transport solvers. These Monte Carlo simulations often contain a significant level of stochastic noise which can cor- rupt the low-order solver, resulting in a breakdown of the Roger Pawlowski method or inaccurate results. In this poster we demon- Multiphysics Simulation Technologies Dept. strate that a residual form of the Monte Carlo method can Sandia National Laboratories be used, producing significantly more accurate results. We [email protected] display results for both thermal radiation transport and neutronics applications. Matthew Bettencourt Sandia National Laboratories Jeffrey A. Willert [email protected] Los Alamos National Laboratory [email protected]

PP106 PP105 Asymptotic Preserving Discontinuous Galerkin Towards Exascale Implementation of the Finite El- Method for the Radiative Transfer Equation ement Based Application Development Environ- ment Many kinetic equations converge to macroscopic models, known as the asymptotic limit of the kinetic equations, when  (the ratio of mean free path over macroscopic size) → 0. Asymptotic preserving (AP) methods are It is not clear today which architecture Exascale supercom- designed to preserve the asymptotic limits from micro- puters will have, but we believe that multicore-CPUs and scopic to macroscopic models in the discrete setting. In manycore-accelerator devices, that promise improvements this poster, we consider the radiative transfer equation in both runtime performance and energy consumption, are which models isotropic particle scattering in a medium. major candidates to be used in the future HPC systems. Discontinuous Galerkin (DG) (with upwind flux and at Nowadays, the Finite Element Method is actively used in least piecewise linear polynomial) methods are known to diverse variety of scientific and industry simulations, that have such property, but require much more degree of free- require High Performance Computing (HPC) technology. dom, especially in high dimensional applications. We will In this poster we present our strategy for adapting Finite present an AP mixed DG-FV method which has com- Element-based codes for future architecture, based on us- parable computational cost and memory as FV method. ing a new Phalanx-Kokkoslocal field evaluation kernel from Rigorous analysis will be provided to show that the pro- Trilinos, specifically designed for general partial differen- posed methods are consistent with the limit equation in tial equation solvers and portable acrossdiverse multicore/ the asymptotic regimes. Some numerical examples are pre- manycore architectures.We present performance evaluation sented to demonstrate the performance of our methods. results for our strategy on the example of Finite Element Assembly in Greenland Ice-Sheet simulations code. Yulong Xing Department of Mathematics Univeristy of Tennessee / Oak Ridge National Lab Irina Demeshko, H. Carter Edwards, Michael Heroux, [email protected] ROGER P. Pawkowski Sandia National Laboratories Cory Hauck [email protected], [email protected], Oak Ridge National Laboratory [email protected], [email protected] [email protected] Eric Phipps Sandia National Laboratories PP106 Optimization and Uncertainty Quantification Department Architecture Portable Assembly for Maxwell’s [email protected] Equations Andrew Salinger This poster presents an architecture portable implemen- CSRI tation of Maxwell’s equations. To achieve portability the Sandia National Labs 282 CS15 Abstracts

[email protected] algorithms lead to improved PDE assembly performance by amortizing communication latency, improving memory ac- cess patterns, and exposing new dimensions of fine-grained PP106 parallelism. We also describe simple approaches for incor- Multicore Finite Element Assembly Via Scans porating these ideas in complex simulation codes.

Minisymposterium placeholder abstract to follow Eric Phipps Sandia National Laboratories Robert C. Kirby Optimization and Uncertainty Quantification Department Baylor University [email protected] Robert [email protected] H. Carter Edwards Sandia National Laboratories PP106 [email protected] Operator Transformation and Code Generation for Scientific Computing PP106 The present poster discusses three software components for scientific computing. ‘Pymbolic’ is an expression tree with Using Multicore Parallelism for Common Finite El- traversal and rewriting capabilities. Both its mathemati- ement Operations cal vocabulary and its traversal operations are easily ex- tended for use in mathematical abstractions. ‘PyOpenCL’ Whereas finite element assembly with MPI is well under- is a toolkit to facilitate code generation, access to massively stood, assembly using a multithreading model has been less parallel hardware, and basic parallel algorithms. ‘Loopy’ is explored. This later model becomes more important as the a code generator targeting shared-memory, massively par- number of cores on a chip, and thus in a node, increases. allel machines, that cleanly separates task specification and Using graph coloring and MapReduce on cells or sets of transformation-based optimization. cells, not only good scalability but bitwise reproducibility can be achieved for matrix assembly and other common op- Andreas Kloeckner erations such as post-processing, estimating discretization Department of Computer Science errors, etc. University of Illinois at Urbana-Champaign [email protected] Bruno Turcksin Texas A&M University [email protected] PP106 occa: A Unified Approach to Multi-Threading Martin Kronbichler Languages Technische Universitat Munchen [email protected] The inability to predict lasting languages and architec- occa tures led us to develop , a library focused on host- Wolfgang Bangerth device interactions. Using run-time compilation and macro Texas A&M University expansions, the result is a novel single kernel language [email protected] that expands to multiple threading languages. Currently, occa supports device kernel expansions for the Pthreads, OCCA OpenMP, OpenCL, CUDA and COI platforms. PP201 can be used through the front-ends provided for C++, C, Matlab, Python, Julia and C#. Forward Backward Doubly Stochastic Differential Equations and Applications to The Optimal Filter- David Medina ing Problem Rice University [email protected] We consider the filtering problem where a signal process is modeled by an SDE and the observation is perturbed Tim Warburton by a white noise. The goal is to find the best estimation Rice University of the signal process based on the observation. Kalman Department of Computational and Applied Filter, Particle Filter, Zakai Filter are some well-known [email protected] approaches to solve optimal filter problems. In this effort, we shall show the optimal filter problem can also be solved Amik St-Cyr using forward backward doubly stochastic differential equa- Computation and Modeling, tions. Shell International E&P, Inc. [email protected] Feng Bao Oak Ridge National Laboratory baof@ornlgov PP106 Assembly Algorithms for Pdes with Uncertain In- Yanzhao Cao put Data on Emerging Multicore Architectures Department of Mathematics & Statistics Auburn University In this work we explore assembly algorithms for PDEs dis- [email protected] cretized with stochastic Galerkin and sampling-based un- certainty quantification algorithms. We demonstrate that Clayton G. Webster, Guannan Zhang rearrangements of these classical uncertainty propagation Oak Ridge National Laboratory CS15 Abstracts 283

[email protected], [email protected] interpolation points that minimize the Lebesgue constant, and the treatment of uncertainty quantification for nonlo- cal diffusion equations, including fractional Laplacian mod- PP201 els. Embedded Sampling-Based Uncertainty Quantifi- cation Approaches for Emerging Computer Archi- Max Gunzburger tectures Florida State University School for Computational Sciences In this work we explore embedded sampling-based uncer- [email protected] tainty quantification approaches geared towards emerging computer architectures. These approaches improve perfor- mance by leveraging reuse of simulation information be- PP201 tween samples, improve memory access patterns, and ex- A Mathematical Environment for Quantifying Un- pose new dimensions of fine-grained parallelism. We in- certainty: Integrated and Optimized at the EX- vestigate the applicability of these ideas to relevant partial treme Scale (equinox) differential equations with uncertain input data. This poster describes a modern mathematical and sta- Eric Phipps tistical foundation that will enable next-generation, com- Sandia National Laboratories plex, stochastic predictive simulations. This is a collab- Optimization and Uncertainty Quantification Department orative effort funded by the Advanced Scientific Com- [email protected] puting Research at the US Department of Energy, fo- cused on combing novel paradigms in applied mathemat- Marta D’Elia,H.CarterEdwards ics, statistics and computational science into a unified Sandia National Laboratories framework, which we call an Environment for Quantifying [email protected], [email protected] Uncertainty: Integrated aNd Optimized at the eXtreme- scale (EQUINOX). This rigorous UQ methodology includes adaptive and quasi-optimal approximations, hierarchical Jonathan J. Hu and multilevel methods, architecture aware UQ paradigms, Sandia National Laboratories and robust experimental design strategies. Livermore, CA 94551 [email protected] Clayton G. Webster Oak Ridge National Laboratory Siva Rajamanickam [email protected] Sandia National Laboratories [email protected] PP201 Hierarchical Acceleration of Multilevel Methods PP201 for Pdes with Random Input Data A Unified Framework for Uncertainty and Sensitiv- ity Analysis of Computational Models with Many Multilevel methods seek to decrease computational com- Input Parameters plexity by balancing spatial and stochastic discretization errors. As a form of variance reduction, multilevel Monte Computational models have found wide applications in Carlo (MLMC) and multilevel stochastic collocation have simulating physical systems. Uncertainties in input pa- been developed. We present an approach to adaptively rameters of the system can greatly influence the outputs, accelerate a sequence of hierarchical interpolants required which are studied by Uncertainty Analysis (UA) and Sensi- by a multilevel method. Taking advantage of the hierar- tivity Analysis (SA). As the system becomes more complex, chical structure, we build new iterates and improved pre- the number of input parameters can be large and existing conditioners, at each level, by using the interpolant from methods for UA and SA are computationally intensive or the previous level. We provide rigorous complexity analysis prohibitive. We propose a unified framework by using a hi- of the fully discrete problem and demonstrate the increased erarchical variable selection approach to connect UA and computational efficiency. SA with one design. By incorporating the effect hierarchy principle and the effect heredity principle, the approach Guannan Zhang works well especially when the number of input parame- Oak Ridge National Laboratory ters is large. Since the whole procedure requires only one [email protected] design, it is economical in run size and computationally efficient. PP202 Li Gu,C.F.JeffWu Compatible Discrete Operator Schemes for Georgia Institute of Technology Advection-Diffusion Equations [email protected], jeff[email protected] Compatible Discrete Operator (CDO) schemes belong to the class of mimetic (or structure-preserving) schemes and PP201 can be deployed on polyhedral meshes. We extend the Florida State University Efforts Withing the analysis of CDO schemes, introduced by J. Bonelle and A. Equinox Project Ern for elliptic and Stokes equations, to advection-diffusion equations. The novelties are a discrete contraction op- We present the results of projects funded by the EQUINOX erator for the advective derivative designed using ideas grant from the Department of Energy Advanced Simulation from Friedrichs’ systems and boundary Hodge operators Computing Research program of the US Department of En- to weakly enforce Dirichlet conditions. We prove stability ergy. Included in the presentation are extensions of 1/f α and error bounds for the discrete problems. Two salient as- noise to multi-dimensions, the construction of total degree pects are P´eclet-robust error estimates and the treatment 284 CS15 Abstracts

of divergence-free advection fields in the absence of reac- rects the convective flux in the nonlinear state equation tive dissipation. Finally, we present numerical results on so as to enforce mass conservation while minimizing devia- three-dimensional polyhedral meshes. tions from the target state. The methodology is evaluated numerically. Pierre Cantin Universite Paris-Est, Ecole des Ponts, Paris Tech, Christopher Basting,DmitriKuzmin CERMICS, Dortmund University of Technology 77455 Marne La Vallee, Cedex 2, France [email protected], [email protected] [email protected]

Alexandre Ern Universite Paris-Est PP203 CERMICS, Ecole des Ponts A New Partitioned Algorithm for Explicit Elasto- [email protected] dynamics Based on Variational Flux Recovery

J´erome Bonelle We present a new partitioned algorithm for explicit elasto- EDF R&D dynamics, based on variational flux recovery. This method [email protected] works by the exchange of tractions which depend on both the known state and the unknown state at the future time step. The exchange of recovered tractions between the PP202 bodies formally involves modification of both the forcing Upwinding in the Mimetic Finite Difference term and the mass matrix on each subdomain. Reliance on Method for Richards’ Equation the future time step distinguishes our approach from tra- ditional partitioned solution algorithms, which use inter- In porous media applications, harmonic averaging of ma- face conditions between subdomains and the current time terial properties is the intrinsic property of FV, mimetic step solution to define boundary conditions for the models. FD, and mixed FE methods reflecting continuity of the Our approach offers some distinct numerical and theoreti- Darcy flux. In some cases, as as infiltration in a dry soil, cal advantages. It passes a linear patch test and is second it may lead to a strong nonlinear stability condition. To order accurate in space. Furthermore, if interface grids relax this condition, upwinding of a relative permeability match, our new partitioned method recovers the solution is often used. To preserve fundamental properties of the of a monolithic coupling scheme for the solid-solid interac- mimetic methods such as symmetry and positive definite- tion problem. ness of discrete operators, a special upwind technique is required that we present and analyze in this poster. Pavel Bochev Sandia National Laboratories Konstantin Lipnikov Computational Math and Algorithms Los Alamos National Laboratory [email protected] [email protected] Paul Kuberry PP202 Sandia National Laboratories [email protected] The Virtual Element Method

We present a generalization of the finite element methods to unstructured polygonal and polyhedral meshes. The PP203 development is based on a new paradigm, dubbed virtual Analysis of a Fluid-Structure Interaction Problem element method, or VEM. In this new framework only a Decoupled by Optimal Control part of the approximation space is constructed explicitly, while the remaining (virtual) part of the space is given only A new method is presented which allows fluid-structure in- in terms of some algebraic conditions. This new family of teraction problems to be stably decoupled. This method numerical methods is suitable to polygonal and polyhe- permits the use of existing solvers for the fluid and struc- dral unstructured meshes and is applied to the numerical ture subsystems. With existence of an optimal solution resolution of diffusion, reaction-diffusion and convection- and Lagrange multipliers proven, the optimization problem diffusion problems, the Stokes equations and compressible constrained by PDEs can be written unconstrained using and incompressible elasticity equations. the Lagrange multiplier rule. The first order optimality system is derived and and a gradient based algorithm is Gianmarco Manzini given along with numerical results. Los Alamos National Laboratory [email protected] Paul A. Kuberry Clemson University [email protected] PP203 Optimal Control for Mass Conservative Level Set Hyesuk Lee Methods Clemson University We present a conservative level set method for numerical Dep. of Mathematical Sciences simulation of evolving interfaces. A PDE-constrained op- [email protected] timization problem is formulated and solved in an itera- tive fashion. The proposed optimal control procedure con- strains the level set function to satisfy a conservation law PP203 for the corresponding Heaviside function. The control cor- Feature-Preserving Finite Element Transport CS15 Abstracts 285

Across Interfaces: Part 2, Direct Flux Recovery ements for 3D Compatible Discretizations

We present an optimization-driven approach for coupling Current tends to concentrate near material interfaces, ergo transport codes across non-coincident interfaces. Our accurate simulation of electromagnetics requires the reso- approach relies on the recently introduced methods for lution of said interfaces. Large deformations make body- optimization-based finite element transport (see Part 1). fit meshes impractical, but the continuity requirements of It uses constrained interpolation to recover and exchange physics-compatible discretizations are not satisfied with- flux variables on the interfaces, and maintains key physical out body-fitting. We propose using the existing non- properties, such as mass conservation and monotonicity. conforming node and edge element bases to dynamically construct an interface-conforming basis in 3D. We also de- Kara Peterson velop a conformal decomposition finite element method for Sandia Natl. Labs edges and demonstrate their equivalence for tetrahedral el- [email protected] ements. Pavel Bochev Christopher Siefert,RichardKramer Sandia National Laboratories Sandia National Laboratories Computational Math and Algorithms [email protected], [email protected] [email protected] Pavel Bochev Denis Ridzal Sandia National Laboratories Sandia National Laboratories Computational Math and Algorithms [email protected] [email protected]

PP203 Thomas Voth Sandia National Laboratory Feature-Preserving Finite Element Transport [email protected] Across Interfaces: Part 1, Optimization-Based Transport

We discuss an optimization framework for the design of PP204 robust feature-preserving schemes for finite element trans- Chebfun port. Our optimization models and algorithms preserve key physical features such as monotonicity and mass con- servation, and can be used to efficiently couple simulation Chebfun is an open-source MATLAB package for comput- codes for transport across non-coincident interfaces (see ing with functions instead of numbers. By overloading Part 2). common MATLAB commands to operate on function ob- jects called chebfuns, the package provides a computing Denis Ridzal experience which feels symbolic but is actually driven by Sandia National Laboratories the numerical tools of Chebyshev polynomial approxima- [email protected] tion technology. Users can do things like plot and evaluate functions, compute roots and extrema, and solve differen- Kara Peterson tial equations using a simple syntax intuitive to anyone Sandia Natl. Labs familiar with MATLAB. This poster will provide a tour of [email protected] some of Chebfun’s major features. A member of the Cheb- fun development team will be on site to present demos and discuss the software with anyone interested. Pavel Bochev Sandia National Laboratories Computational Math and Algorithms Anthony Austin [email protected] University of Oxford [email protected]

PP203 Higher Order Finite Element Methods for Interface PP204 Problems Feel++: A Versatile High Performance Finite Ele- We present a higher-order finite element method for solv- ment Embedded Library into C++ ing a class of interface problems in two dimensions. The methodisbasedoncorrectiontermsaddedtotheright- Feel++ (Finite Element method Embedded Language in hand side of the natural method. We prove optimal error C++) offers a domain specific language to partial differ- estimates of the method on general quasi-uniform meshes ential equations embedded in C++. It allows to use a in the maximum norms. In addition, we apply the method very wide range of possibly, high order, Galerkin methods, to a Stokes interface problem obtaining optimal result. and advanced numerical methods such as domain decom- position methods including h-p mortar methods, levelset Manuel A. Sanchez-Uribe methods, fictitious domain methods or certified reduced Brown University basis. We illustrate on some applications the numerical manuel sanchez [email protected] behavor up to millions and even billions of unknowns.

Vincent Chabannes PP203 Laboratoire Jean Kuntzmann Extended and Conformal Decomposition Finite El- Universit´edeGrenoble 286 CS15 Abstracts

[email protected] Lawrence Mitchell Department of Computing Imperial College London PP204 [email protected] Dolfin-Adjoint Michael Lange dolfin-adjoint automatically derives parallel, efficient ad- Department of Earth Science and Engineering joint and tangent linear models from finite-element mod- Imperial College London els written in the FEniCS environment. It also provides [email protected] high-level tools to solve PDE-constrained optimisation and generalised stability problems. This poster presents an Andrew McRae overview of dolfin-adjoint, including examples and recent Department of Mathematics developments. The dolfin-adjoint developers will live-demo Imperial College London the software and answer questions. [email protected] Simon W. Funke Center for Biomedical Computing Gheorghe-Teodor Bercea, Fabio Luporini Simula Research Laboratory Department of Computing [email protected] Imperial College London [email protected], Marie E. Rognes [email protected] Simula Research Laboratory [email protected] Paul Kelly Imperial College London Patrick E. Farrell [email protected] Department of Mathematics University of Oxford [email protected] PP204 The DEAL.II Finite Element Library David Ham Imperial College London deal.II is a C++ software library supporting the creation of [email protected] finite element codes and an open community of users and developers. In this poster session, we present an overview of deal.II, highlight some applications, and present future PP204 plans. Building Performance Transportable Codes for Ex- treme Scale Timo Heister Clemson University The goal of the Center for Exascale Simulation of Plasma- Mathematical Sciences Coupled Combustion is to explore and understand a new [email protected] approach to controlling combustion though the use of plas- mas. The computation is multiscale and multiphysics, and Wolfgang Bangerth is a challenge even with extreme scale computers. This Texas A&M University poster highlights the approach to transportable perfor- [email protected] mance being being taken by the center, including the use of a golden copy for development and source transformations Guido Kanschat, Matthias Maier for data structure and loop optimization. Universit¨at Heidelberg, Germany [email protected], [email protected] William D. Gropp heidelberg.de University of Illinois at Urbana-Champaign Dept of Computer Science [email protected] PP204 An Overview of the Trilinos Project PP204 Firedrake: Automating Finite Element by Com- Trilinos is a large collection of interoperable packages for posing Abstractions formulation, solution and analysis of large scale modeling and simulation problems. Trilinos provides libraries for Firedrake automates the portable solution of partial dif- (i) portable architecture-aware data containers and algo- ferential equations using the finite element method. Fire- rithms; (ii) geometry, meshing, discretization, load balanc- drake takes separation of concerns in automated FEM to a ing and scalable solution of linear, nonlinear and transient new level. In addition to the Unified Form Language from problems; (iii) optimization, uncertainty quantification and the FEniCS project, and PETSc’s linear algebra abstrac- analysis and (iv) scalable IO. Trilinos also provides soft- tion, Firedrake introduces the PyOP2 abstraction for mesh ware tools and processes for developing scientific software iteration and the COFFEE abstraction for kernel vectori- from inception to post-delivery maintenance, supporting sation and optimisation. The result is faster, more flexible components-based application development strategies in- and more capable automated simulation. tended to improve software quality, and reduce time to completion and cost. David Ham, Florian Rathgeber Imperial College London Michael Heroux [email protected], [email protected] Sandia National Laboratories CS15 Abstracts 287

[email protected] richer and more robust alternatives for nonlinear solves. Likewise, for small scale parallelism, we propose a system that allows different threading models to interact, avoiding PP204 resource contention and over-provisioning. We attempt to FEniCS High Performance Computing with Appli- minimize assumptions about our environment so as to max- cations in Aerodynamics, Environmental Science imize the ability to compose with other packages and users and Biomedicine that chose other models.

Adaptive finite element methods (AFEM) using unstruc- Matthew G. Knepley tured meshes pose serious challenges for the development of University of Chicago efficient algorithms and software implementations for mas- [email protected] sively parallel architectures. We describe the open source software DOLFIN-- HPC/Unicorn that implements AFEM Jed Brown for a general class of problems in computational mechanics, Mathematics and Computer Science Division as part of the software project FEniCS [1,2]. DOLFIN- Argonne National Laboratory and CU Boulder -HPC is based on a hybrid MPI+OpenMP/MPI+PGAS [email protected] programming model, and shows near optimal scaling up to tens of thousands of processing elements for applications in computational fluid dynamics (CFD) [3]. The method is PP204 based on the computation of an adjoint (or dual) problem Fenics to derive a posteriori estimates of the error in a certain out- put of interest, such as the drag or lift of an airplane, which FEniCS is a high-level, high-performance software envi- guides the mesh refinement algorithms. Since the problem ronment for automated, efficient, and intuitive solution of is nonlinear, the primal solution appears as data in the ad- partial differential equations by the finite element method. joint problem, and since the adjoint problem is solved back- In this poster session, an overview of FEniCS is presented, wards in time, the time series of the primal problem must together with explained examples and a summary of re- be stored which is a challenge for large problems. In addi- cently added new features. Live demos will be presented tion, algorithms for local mesh refinement pose challenges and FEniCS developers will be on spot to chat with users. in terms of dynamic load balancing and efficient commu- nication over the unstructured mesh data. In this poster presentation we describe the methods and software imple- Anders Logg mentation, and highlight application projects based on the Chalmers University of Technology computational technology, including simulation of the aero- [email protected] dynamics of airplanes, blood flow in the human heart, and human phonation. PP204 Johan Hoffman Sigma: Scalable Interface for Geometry and Mesh Royal Institute of Technology KTH Based Applications jhoff[email protected] SIGMA provides components to define/query geometric entities (CGM), and apply efficient mesh generation algo- PP204 rithms (MeshKit) based on relational definitions (Lasso) to create high quality unstructured mesh databases (MOAB), EMatter: A Materials Simulation Framework As a which serves as a data backplane for applications (Nuclear, Service CFD, Climate, FEA) running on desktop to petascale architectures. SIGMA tools handle several I/O formats eMatter is a fledging new computational service that aims with interfaces for visualization, solvers (PETSc) and scal- to simplify life for computational materials scientists. Built able conservative solution transfers (enabling multi-physics on top of a stack of scalable high-performance libraries, in- solvers). We will present interactive workflow demos to en- cluding PETSc, libMesh and MOOSE, eMatter presents courage further discussions with audience. their capabilities as a service, or as a platform. Library maintenance, configuration and building, as well as job Vijay Mahadevan, Iulian Grindeanu, Rajeev Jain submission, data handling and basic visualization capabil- Argonne National Laboratory ities are taken care of by the framework. eMatter demos [email protected], [email protected], will be provided and developers will be available on site for [email protected] questions and hands-on exercises.

Dmitry A. Karpeyev Navamita Ray University of Chicago Argonne National Labratory [email protected] [email protected]

Danqing Wu PP204 Argonne National Laboratory Composability in Petsc [email protected]

Composability of lower-level abstractions is crucial for Paul Wilson building large software systems while controlling complex- University of Wisconsin - Madison ity. This fact is often overlooked in computational science [email protected] since it is not emphasized in the numerical analysis. We present two examples of its role in PETSc. In the design of nonlinear solvers, we allow preconditioning of one solve by PP204 another, in analogy with the linear case, giving us much Dune - The Distributed and Unified Numerics En- 288 CS15 Abstracts

vironment In this poster, we introduce Camellia, a software frame- work whose central design goal is to enable developers to DUNE is a modular open-source framework for the solution create efficient hp-adaptive DPG solvers with minimal ef- of partial differential equations using grid-based methods, fort. written in modern C++. It offers clear abstractions at all levels of a PDE simulation, providing the user with Nathan Roberts high-level abstractions for productive development, while Argonne National Laboratory also allowing access to lower-level functionality, enabling [email protected] scalability from notebooks to HPC applications. Due to its modularity, DUNE easily integrates with legacy codes like existing grid managers and LA libraries. PP204 ViennaCL - Fast Linear Algebra for Multi and Steffen M¨uthing Many-Core Architectures Heidelberg University steff[email protected] An overview of the linear algebra functionality and solvers available in the Vienna Computing Library (ViennaCL) for multi-core CPUs as well as GPUs and Intel’s MIC architec- PP204 ture is given. Compute backends using OpenMP, CUDA, Elemental and OpenCL allow for maximum flexibility and best perfor- mance on the underlying hardware from all major vendors. Elemental is a modern C++11 implementation of distributed-memory dense linear algebra that has been ex- Karl Rupp tended to various sparse-direct solvers, preconditioners, Institute for Analysis and Scientific Computing, TU Wien optimization, and medical imaging applications. In this Institute for Microelectronics, TU Wien poster session, an overview of Elemental is presented, with [email protected] a focus on the idioms that the project has converged upon for manipulating (distributed) matrices and exposing ab- Philippe Tillet, Toby St Clere Smithe, Namik Karovic, stract interfaces without incurring performance penalties. Josef Weinbub, Florian Rudolf Institute for Microelectronics Jack L. Poulson Vienna University of Technology Computational Science and Engineering [email protected], [email protected], Georgia Institute of Technology [email protected], [email protected], [email protected] [email protected]

PP204 PP205 Jupyter Widgets: Interactive Computing Through Radical Optimization Techniques for Asynchronous the Browser in Any Programming Language Iterative Algorithms on Gpus

The Jupyter project, evolved from IPython, provides Asynchronous algorithms, with their ability to tolerate a generic architecture for interactive computing with a memory latency, form an important class of algorithms for language-independent protocol for controlling code execu- modern computer architectures. For the recently proposed tion over the network. In particular, it can be used from asynchronous iterative algorithm for computing incomplete web browsers to provide interactive graphical exploration factorizations we present non-traditional optimizations to of complex computations by combining Javascript widgets leverage the computing power of GPUs. These include con- coupled to computational kernels written in Python, Ju- trolling the order in which variables are updated, taking lia, R or any other language. This facilitates both rapid advantage of cache reuse between thread blocks, and op- exploration and illustration of computational concepts for timizing the trade-off between parallelism and algorithm education. convergence for time-to-solution performance.

Min Ragan-Kelley Hartwig Anzt UC Berkeley AS&T Innovate Computing Lab [email protected] University of Tennessee [email protected] Fernando Perez Helen Wills Neuroscience Institute Edmond Chow University of California, Berkeley School of Computational Science and Engineering [email protected] Georgia Institute of Technology [email protected]

PP204 Jack J. Dongarra Camellia: A Software Framework for Discontinu- Department of Computer Science ous Petrov-Galerkin Methods The University of Tennessee [email protected] The discontinuous Petrov-Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan minimizes the solution residual in a user-determinable energy norm and offers a PP205 built-in mechanism for evaluating error in the energy norm, Experiences in Autotuning Linear Algebra Opera- among other desirable features. However, the methodology tions for Energy Minimization on Gpus brings with it some additional complexity for researchers who wish to experiment with DPG in their computations. Approaching the Exascale computing era requires a CS15 Abstracts 289

paradigm shift from pure runtime performance to metrics University of Illinois at Urbana-Champaign accounting also for resource efficiency. In this line, we [email protected] present experiences about using the BEAST autotuning framework for optimizing the energy efficiency of GPU im- Steven Dalton plementations of basic linear algebra building blocks. We University of Illinois at Urbana-Champaign analyze the kernel metrics to correlate the pruning param- [email protected] eters to performance and resource usage.

Hartwig Anzt PP206 Innovate Computing Lab University of Tennessee Parallel Petascale Modeling of Transportation Ac- [email protected] cidents Involving High Explosives Simulations of multiple explosive devices undergoing com- Blake Haugen bustion requires algorithms and models capable of solv- Innovative Computing Lab ing fluid-structure interactions, compressible flow, and fast University of Tennessee solid-¿gas reactions. We have been developing these tools [email protected] in the Uintah:MPMICE, which is capable of scaling up to 512k. This research will give insight in to the phys- Jakub Kurzak ical mechanism of Deflagration to Detonation Transition University of Tennessee, Knoxville (DDT) for large-scale explosions and help determine safe [email protected] packaging configurations to eliminate DDT in transporta- tion accidents. Jack J. Dongarra Department of Computer Science Jacqueline Beckvermit The University of Tennessee Department of Chemsitry [email protected] University of Utah [email protected] PP205 Andrew Bezdjian CUSP: A Parallel Sparse Matrix Package for Gpus University of Utah [email protected] CUSP, an open-source C++ templated library for sparse matrix and graph operations, enables collection oriented parallel processing on modern architec- tures, such as Todd Harman GPUs. In this presentation we will discuss the Thrust- Department of Mechanical Engineering based ab- stract programming model to express highly ir- University of Utah regular computations involving sparse matrices, such as ad- [email protected] dition and multiplication, and the integration of GPU ori- ented programming systems, such as CUB, to implement John A. Schmidt high-performance routines to perform reordering, coloring, SCI Institute and maximum-ow computations on GPU architectures. University of Utah [email protected] Steven Dalton University of Illinois at Urbana-Champaign Martin Berzins [email protected] Scientific Computing and Imaging Institute University of Utah Luke Olson [email protected] Department of Computer Science University of Illinois at Urbana-Champaign Chuck Wight [email protected] Weber State University [email protected] PP205 Sparse Matrix-Matrix Multiplication on High- PP206 Throughput Architectures Radiation Modeling Using Reverse Monte Carlo Many computations in the physical and data sciences rely Ray Tracing Within the Uintah Framework on sparse matrix operations such as the sparse matrix- matrix multiplication (SpMM) operation. Yet an efficient The Uintah ARCHES component has previously used the SpMM on high-throughput architectures requires expos- Discrete Ordinates algorithm for solving the Radiative ing fine-grained parallelism in the operation while limiting Transport Equation (RTE). This approach is expensive due the use of the off-chip memory bandwidth. In this poster to the linear solves involved. We are exploring the use of we highlight an approach that decomposes the SpMM into the Reverse Monte Carlo Ray Tracing (RMCRT) technique three phases: expansion, sorting, and contraction, thereby for solving the RTE on both CPUs and GPUs to reduce allowing the use of optimized throughput-oriented kernels. this computational cost. Here we we discuss the challenges The result is a SpMM algorithm that requires low a pri- involved in moving to an RMCRT approach for solving the ori analysis of the matrix structures, yet yields substantial RTE at scale. savings for general classes of unstructured matrices. Alan Humphrey Luke Olson Scientific Computing and Imaging Institute Department of Computer Science University of Utah 290 CS15 Abstracts

[email protected] oxy-coal systems with Large Eddy Simulation (LES) in a rigorous validation and uncertainty quantification (V/UQ) Bayesian technique. The method identifies a subset of PP206 parameters that control the heat flux, temperature, and Using Uintah:mpmice for High Resolution Urban species concentrations within the boilers. Given the uncer- Flow Studies tain ranges in these variables, the V/UQ method discov- ers a range of simultaneously consistent values constrained Urban flow transport plays a critical role in investigations by the experimental data with uncertainties. The exper- of the impact of local and global climate on urban in- imental systems of interest are the 15MW Alstom Boiler habitants. We introduce Uintah:MPMICE for the simu- Simulation Facility and the 150 KW Oxy-Fired Combus- lation of fluid-structure interactions in urban flows. Uin- tor located at the University of Utah. The simulation work tah:MPMICE has been developed in a massively paral- was performedusing Arches, a large-eddy simulation com- lel computational infrastructure, uses material points to ponent with DQMOM multiphase capabilities in the Uin- represent buildings, and LES technique to represent mo- tah framework, at large scale. mentum and scalar transport. Using Uintah:MPMICE for highly turbulent flows in urban areas introduce challenges Jeremy Thornock on the implementation of appropriate boundary conditions. The University of Utah [email protected] Arash Nemati Hayati, Rob Stoll Wu Yuxin Department of Mechanical Engineering University of Utah Institute for Clean and Secure Energy [email protected], [email protected] University of Utah [email protected] Todd Harman Department of Mechanical Engineering Ben Isaac University of Utah University of Utah & Universit´e Libre de Bruxelles [email protected] [email protected] Eric Pardyjak Sean Smith Department of Mechanical Engineering University of Utah The University of Utah [email protected] [email protected]

PP206 Philip J. Smith Wasatch: A CPU/GPU-Ready Multiphysics Code University of Utah Using a Domain Specific Language [email protected] Hybrid computing poses a challenge for computational sci- ence. Legacy code is unable to leverage the benefits of PP207 CPU/GPU platforms without significant refactor. Here, The Periodic Table of the Finite Elements we present a promising approach to making computational codes architecture-proof. Our method consists of using a Since the dawn of the finite element method half a cen- Domain Specific Language to separate implementation and tury ago, increasingly sophisticated finite element spaces usage. At the outset, one can write a single code that may have been developed and applied. Even to specialists, the be executed on multiple backends. This is shown to work resulting collection of finite elements can seem a disorga- with our flagship multiphysics code, Wasatch. nized zoo of possibilities. By taking the viewpoint of finite element exterior calculus these spaces can be arranged in a Tony Saad sort of periodic table, which explains their shape functions, The Institute for Clean and Secure Energy degrees of freedom, and interrelationships, and guides im- Department of Chemical Engineering, University of Utah plementation in advanced software environments. [email protected] Douglas N. Arnold Abhishek Bagusetty School of Mathematics Chemical Engineering University of Minnesota University of Utah [email protected] [email protected] Anders Logg James C. Sutherland Chalmers University of Technology Department of Chemical Engineering [email protected] The University of Utah [email protected] PP207 Convolution-Translation and Bounded Cochain PP206 Projections for the Elasticity Complex

Applied Large Eddy Simulation: Validation and 2 Uncertainty Quantification of Lab and Pilot-Scale, Uniformly bounded projections in L which commute with Oxy-Coal Boiler Simulations the exterior derivative play an essential role in the finite element exterior calculus. The extension part of the pro- This work seeks to advance simulation capabilitiesrelat- cess limits the construction of bounded cochain projec- edto oxy-coal combustion. The approach combines ex- tions for the elasticity complex to star shaped domains. perimental and simulation data from lab and pilot-scale In this work, we avoid the extension operator by using CS15 Abstracts 291

convolution-translation. The construction is revisited from tation shall introduce the WG-FEM through some model that point of view and cochain projections without the re- problems: (1) mixed formulation for second order elliptic striction of star-shaped domains are constructed for the equations, (2) the Stokes equations, and (3) div-curl prob- elasticity complex. lems or Maxwell equations.

Gerard Awanou Junping Wang Chicago National Science Foundation [email protected] [email protected]

Chunmei Wang PP207 Georgia Institute of Technology What is a Good Linear Finite Element... On a [email protected] Generic Polytope? Xiu Ye The notion of what constitutes a ”good” linear finite el- University of Arkansas, Little Rock ement on geometries other than simplices and cubes re- [email protected] mains largely unexplored. We use harmonic coordinates as a means to investigate this question, arriving at a few key conclusions. On convex polygons, harmonic coordinates PP208 in general provide no improvement over standard interpo- Approximate Active Bayesian Inference of Nonlin- lation on the constrained Delaunay triangulation of the ear Dynamical Systems polygon. On non-convex polygons, however, harmonic co- ordinates can provide optimal interpolation estimates even This poster introduces a computationally efficient approx- when all triangulations fail to do so. We also present the imation method to design experiments for Bayesian model extension and implication of these results to finite elements selection of nonlinear dynamical systems. The methods on non-convex polyhedra in 3D. employs surrogate functions to reconstruct the total or- dering of the candidate experiments induced by the mu- Andrew Gillette tual information between the data and the models. Under University of Arizona mild assumptions, it can be shown that such approxima- Department of Mathematics tion achieves almost indistinguishable design results with [email protected] a significant computational speedup.

Alexander Rand AlbertoGiovanni Busetto CD-adapco UCSB Austin, Texas [email protected] [email protected]

PP208 PP207 Variational Reformulation of Bayesian Inverse Stokes Elements on Cubic Meshes Yielding Problems Divergence-Free Approximations Despite of its computational appeal, the classical approach Using a finite element exterior calculus framework, con- to inverse problems suffers from many shortcomings. The forming piecewise polynomial spaces with respect to cu- Bayesian formalism to inverse problems avoids most of bic meshes are constructed for the Stokes problem in ar- these difficulties, albeit at an increased computational cost. bitrary dimensions yielding exactly divergence–free veloc- In this work, we use information theoretic arguments in or- ity approximations. We first present the construction of der to cast the Bayesian inference problem in terms of an the lowest order case, its implementation, and convergence optimization problem. The resulting scheme combines the analysis. We then introduce finite element spaces with con- theoretical soundness of fully Bayesian inference with the tinuous pressure approximations leading to a system of less computational efficiency of a simple optimization. unknowns. Finally, numerical experiments are shown veri- fying the theoretical results. Ilias Bilionis Purdue University MichaelJ.Neilan [email protected] University of Pittsburgh Department of Mathematics Panagiotis Tsilifis [email protected] University of Southern California [email protected] Duygu Sap University of Pittsburgh Nicholas Zabaras [email protected] Cornell University [email protected] PP207 Weak Galerkin Finite Element Methods PP208 Bayesian Model Selection for Exploring Mecha- Weak Galerkin finite element method (WG-FEM)is a new nisms Contributing to Differential Signaling approximating technique for partial differential equations. The main idea behind the WG method is the use of discrete An important phenomenon in cytokine signaling, termed weak differential operators in the conventional variational “differential signaling,” is the ability of structurally simi- formulations for the corresponding PDEs. This presen- lar ligands with different binding affinities to elicit diverse 292 CS15 Abstracts

biological actions through the same receptor. We model signaling networks as linear steady state models for which we derive explicit signaling differentials for single cells and cell populations. We explore the capacity of candidate sig- naling mechanisms to reproduce observed differential sig- naling dose response data by employing Bayesian model selection.

Pencho Yordanov ETH Zurich [email protected]

Joerg Stelling Department of Biosystems Science and Engineering, ETH Zurich [email protected]