Central States Section Meeting | Sept 30 - Oct. 2, 2016
Society for Industrial and Applied Mathematics
2nd Annual Meeting of SIAM Central States Section
Meeting Program
University of Arkansas at Little Rock September 30, 2016 - October 2, 2016 1 Society for Industrial and Applied Mathematics
Welcome to SIAM Central States Section Second Annual Meeting
Society for Industrial and Applied Mathematics Welcome to University of Arkansas at Little Rock and the second annual meeting of the SIAM Central States Section. Organizing Committee The second meeting promises to be an excellent event for the Committee Chair and Section President growing SIAM section. The conference features presentations by four Xiaoming He plenary speakers, over 200 invited and contributed presentations Missouri University of split between 47 parallel sessions. We are honored to have Irene Science and Technology (S&T) Gamba, Weizhang Huang, Paul Martin, and Bob Pego as plenary Section Vice President speakers. Erik Van Vleck University of Kansas One of the primary goals of the new SIAM Central States Section is Section Secretary to promote communication and collaboration among SIAM members Xiu Ye in the central region, consisting of Arkansas, Colorado, Iowa, University of Arkansas at Little Rock Kansas, Mississippi, Missouri, Nebraska, and Oklahoma. We hope Section Treasurer that you take advantage of the many opportunities to network with Stephen Pankavich colleagues from the central region and many other locations. Colorado School of Mines
Committee Member We are very grateful to SIAM for the support in starting the SIAM Eric Kaufmann Central States Section. We also thank all of the individuals who University of Arkansas at Little Rock contributed to the organization of the conference, University of Committee Member Arkansas at Little Rock, Missouri S&T and SIAM for their support. Zhu Wang University of South Carolina We hope everyone enjoys the conference and finds it valuable. Conference Coordinator Thanks to everyone for attending and participating, and for Michelle Wiginton (S&T) supporting our new SIAM Central States Section. Conference Secretary Tammy Mace (S&T)
About SIAM Central States Section – siamcentral2016.mst.edu/
The SIAM Central States Section was formed in Participation in SIAM Central States Section activities will 2014 to serve SIAM members in Arkansas, Colorado, be open to all institutions and industries in the region with Iowa, Kansas, Mississippi, Missouri, Nebraska, and an interest in applied and computational mathematics. Oklahoma. The purpose of this section is to enhance the communication among the section members, promote the collaboration for both basic research and applications of mathematics to industry and science, represent applied and computational mathematics, and support the SIAM SIAM Central States Section Officers: mission in the central region of the USA. President Treasurer Xiaoming He Stephen D. Pankavich The proposed activities for the SIAM Central Section Missouri University of Colorado School of Mines Science and Technology include annual section meetings, seminars and workshops Secretary for advanced topics of common interests of the section Vice President Xiu Ye members, encouraging new SIAM student chapters and Erik S. Van Vleck University of Arkansas facilitating the SIAM student chapters in the central region University of Kansas at Little Rock to connect together, promoting collaboration in applied mathematics and its applications to industry and science, and expanding the influence of SIAM in the central states.
2 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Schedule at a Glance
Friday, September 30, 2016 Saturday, October 1, 2016 Sunday, October 2, 2016
MORNING SCHEDULE MORNING SCHEDULE MORNING SCHEDULE Stella Boyle Concert Hall-Fine Arts Building Stella Boyle Concert Hall-Fine Arts Building EIT and ETAS Buildings* Chair: Dr. Minh Nguyen Chair: Dr. Eric Kaufmann
8:00 a.m. – 3:30 p.m. 8:00 a.m. – 5:00 p.m. 8:00 a.m. – Noon Registration Desk Open Registration Desk Open Registration Desk Open
9:00 a.m. - 9:20 a.m. 9:00 a.m. - 9:20 a.m. 8:30 a.m. - 10:10 a.m. Welcome Remarks Discussion with Potential Parallel Sessions Section Officer EIT and ETAS Buildings* 9:20 a.m. - 10:10 a.m. See schedule on pages 10-11 for details. Plenary Speaker 9:20 a.m. - 10:10 a.m. Irene Gamba Plenary Speaker 10:10 a.m. - 10:40 a.m. Paul Martin Refreshment Break 10:10 a.m. - 10:40 a.m. 10:40 a.m. - 12:20 p.m. Refreshment Break 10:10 a.m. - 10:40 a.m. Parallel Sessions Group Photo & Refreshment Break EIT and ETAS Buildings 10:40 a.m. - 11:30 a.m. See schedule on page 12 for details. Plenary Speaker 10:40 a.m. - 11:30 a.m. Weizhang Huang Plenary Speaker 12:20 p.m. Bob Pego Meeting Adjourns 11:30 a.m. - 1:20 p.m. Lunch on your own 11:30 a.m. - 1:20 p.m. Lunch on your own
AFTERNOON SCHEDULE *PLEASE NOTE EIT and ETAS Buildings* Engineering and Information Technology Building AFTERNOON SCHEDULE (EIT) and the Engineering Technology and Science 1:30 p.m. - 3:10 p.m. EIT and ETAS Buildings* Building (ETAS) are connected. Parallel Sessions EIT and ETAS Buildings* 1:30 p.m. - 3:10 p.m. See schedule on pages 4-5 for details. Parallel Sessions EIT and ETAS Buildings* 3:40 p.m. - 4:20 p.m. See schedule on pages 6-7 for details Transportation to Clinton Library If you do not have a car or cannot find a ride 3:10 p.m. - 3:50 p.m. from other conference participants, please Refreshment Break let the registration desk know and wait at the registration desk for the shuttle at 3:40 p.m. 3:50 p.m. - 5:30 p.m. Parallel Sessions 5:00 p.m. - 7:00 p.m. EIT and ETAS Buildings* Social Mixer See schedule on pages 8-9 for details. (refreshments, but not a meal) Room 42, Clinton Library 6:30 p.m. - 8:00 p.m. Banquet
Donaghey Student Center
3 Society for Industrial and Applied Mathematics
Conference Schedule Friday, September 30, 2016
MORNING SCHEDULE Parallel Sessions | 1:30 p.m. - 3:10 p.m. - EIT and ETAS Buildings Stella Boyle Concert Hall – Fine Arts Building EIT 219: Recent Advances on Numerical Methods for Interface Problems 8:00 a.m. – 3:00 p.m. Registration Desk Open Organizer: Xu Zhang, James B. Collins Speakers: Long Chen, Jeb Collins, Tao Lin, Cuiyu He, Songming Hou 9:00 a.m. - 9:20 a.m. 1001 - An Interface-Fitted Mesh Generator And Virtual Element Methods Welcome Remarks For Elliptic Interface Problems 1002 - A Posteriori Error Estimation For A Cut Cell Method With Uncertain Interface Location 9:20 a.m. - 10:10 a.m. 1003 - Applications of Immersed Finite Element Methods Plenary Speaker 1004 - A Posteriori error estimation for nonconforming finite element methods Irene Gamba 1005 - Numerical Methods For Solving Linear And Nonlinear Interface Problems Conservative Solvers for Collisional Kinetic Boltzmann EIT 224: Partial Differential Equations: Analysis, Computation, and Landau-Poisson Modeling, and Applications Systems Organizer: John Singler, Weiwei Hu Speakers: Tong Li, Mathew Johnson, Samuel Walsh, Aslihan Demirkaya, Majid Bani-Yaghoub 10:10 a.m. - 10:40 a.m. 1006 - Global Wellposedness And Traveling Waves To The PDE Models Of Chemotaxis. Refreshment Break 1007 - Dynamics and Stability of Viscous Roll Waves 1008 - Existence And Qualitative Theory Of Stratified Solitary Water Waves 1009 - Numerical Results On Existence And Stability Of Standing And Traveling Waves For The Fourth 10:40 a.m. - 11:30 a.m. Order Beam Equation Plenary Speaker 1010 - Stability Of Travelling And Stationary Waves Arising From A Delayed Hyperbolic–Parabolic Weizhang Huang Population Model A New Implementation of the MMPDE Moving EIT 318: Highly Accurate and Effective Numerical Methods Mesh Method and for Partial Differential Equations Applications Organizers: Qin Sheng, Abdul Q.M. Khaliq, JaEun Ku Speakers: Aaron Benham, Matthew Beauregard, Nick Kosmatov, Josh Padgett 11:30 a.m. - 1:20 p.m. 1011 - Multiple Positive Solutions Of A Semipositone Fourth-Order Boundary Value Problem Lunch on your own 1012 - A Nonlinear Splitting Algorithm for Systems of Partial Differential Equations with self-Diffusion 1013 - The Sturm-Liouville Boundary Value Problem With Impulsive Effects On The Half-Line 1014 - Solving The Degenerate Stochastic Kawarada Equation Via An Adaptive AFTERNOON SCHEDULE Crank-Nicolson Method
1:30 p.m. - 3:10 p.m. EIT 319: No Talks Scheduled Parallel Sessions See schedule on right. EIT 321: No Talks Scheduled 3:20 p.m. - 4:20 p.m. Transportation to Clinton Library EIT 323: Applied and Computational Topology 5:00 p.m. - 7:00 p.m. Organizers: Henry Adams, Patrick Shipman Social Mixer Speakers: Eric Hanson, Jose Perea, Douglas Heisterkamp, Sara Kalisnik (refreshments, but not a meal) 1015 - Persistence Images: Representing Persistent Homology for Machine Learning Room 42, Clinton Library 1016 - Directional Features, Projective Coordinates and Classification 1017 - Thin Position Inspired Algorithms For Machine Learning And Data Analysis 1018 - Tropical Coordinates on the Space of Persistence Barcodes
4 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Conference Schedule Friday September 30, 2016 (Location: EIT and ETAS Buildings for Parallel Sessions)
Parallel Sessions | 1:30 p.m. - 3:10 p.m. Session Abstracts on pages 15-20
EIT 325: New Numerical Advances ETAS 480: Some Novel Computational on Wave Propagation Problems Methods For PDEs Organizer: Yassine Boubendir Organizer: Huiqing Zhu Speakers: Yassine Boubendir, Lise-Marie Imbert-Gerard, Wangtao Lu Speakers: Jiangguo Liu, Zhimin Zhang, Zhiyun Yu, Xinxiang Li, Huiqing Zhu 1019 - Asymptotic Expansions of the Helmholtz Equation Solutions in the Case of Convex Obstacles 1031 - THex Algorithm and Its Applications in Finite Element Methods 1020 - Volume Integral Methods For Wave Propagation In 1032 - Polynomial Preserving Recovery for Gradient and Hessian Inhomogeneous Media 1033 - Nonconforming Mixed Finite Elements Method For The Three- 1021 - Babich-Like Ansatz For Three-Dimensional Point-Source Dimensional Incompressible Magnetohydrodynamics Equation Maxwell’s Equations In An Inhomogeneous Medium 1034 - Superconvergence and Extrapolation of Quasi-Wilson Element for At High Frequencies Nonsymmetric and Indefinite Problem 1035 - Method Of Fundamental Solutions Using Transformed Angular Basis Functions ETAS 229: Recent Advances in Fractional PDEs
Organizer: Yanzhi Zhang ETAS 483: Contributed presentations Speakers: Hong Wang, Mohsen Zayernouri, Xiaofan Li, Joseph E. Pasciak, Siwei Duo Speakers: Necmettin Aggez, Kyle Claassen, Tania Hazra, Michelle 1022 - A Fast Numerical Method for a Bond-Based Linear Peridynamic Maiden, Zhihan Wei Model 1036 - A Note on Finite Difference Method for NBVP of the Hyperbolic 1023 - Unified Petrov-Galerkin Spectral Methods for High-Dimensional Type FPDEs 1037 - Antiperiodic Ground State Theory for Fractional Schr\ 1024 - Numerical Schemes For Integro-Differential Equations 1038 - Stable Operator Splitting Method For Free Energy Calculations Of Related To Alpha-Stable Processes One Atom Model 1025 - Numerical Approximation of a Variational Problem on a Bounded Domain involving the Fractional Laplacian 1039 - Soliton Envelopes in Viscous Conduits 1026 - A Fast Algorithm For Solving The Space-Time Fractional 1040 - Three-Dimensional Matched Alternating Direction Implicit (ADI) Diffusion Equation Schemes for Solving the Heat Equation with Complex Interface
ETAS 230: Numerical Approximation And Analysis For Time Dependent PDEs Organizers: Cheng Wang, Steve Wise Speaker order: Cheng Wang, Wen-Qiang Feng, Zhen Guan, Lili Ju 1027 - Energy-Stable Pseudo-Spectral Numerical Scheme For The Cahn-Hilliard Equation And The Homogeneous Linear Iteration Algorithm 1028 - Efficient Finite-Difference Geometric Multigrid Solvers for the Cahn-Hilliard Equation 1029 - Unconditional Stable Method for the Amplitude Description of the Phase-Field Crystal model 1030 - Energy Stability and Error Estimates of Exponential Time Differencing Schemes for the Epitaxial Growth Model without Slope Selection
5 Society for Industrial and Applied Mathematics
Conference Schedule Saturday, October 1, 2016
MORNING SCHEDULE Parallel Sessions | 1:30 p.m. - 3:10 p.m. Stella Boyle Concert Hall – Fine Arts Building EIT 219: Recent Advances on Numerical Methods for Interface Problems 8:00 a.m. – 3:00 p.m. Organizers: Xu Zhang, James B. Collins Registration Desk Open Speakers: Xu Zhang, Marcus Sarkis, Xiaoming He, Ruchi Guo, Nishant Panda 1041 - Superconvergence of Immersed Finite Element Methods. 9:00 a.m. - 9:20 a.m. 1042 - Multiscale Variational FETI-DP Discretization For High-Contrast Problems Discussion with Potential 1043 - Multi-Physics Domain Decomposition Method For Coupled Porous Media Flow And Free Flow Section Officer 1044 - A Class of Immersed Finite Element Spaces Defined by the Actual Interface 1045 - Stochastic Inverse Problem For Internal Boundaries: A Measure Theoretic Solution 9:20 a.m. - 10:10 a.m. Plenary Speaker Paul Martin EIT 224: Partial Differential Equations: Analysis, Computation, Solving the Wave Modeling, and Applications Equation: Acoustic Organizers: John Singler, Weiwei Hu Scattering in the Speakers: John Singler, Weiwei Hu, Taige Wang, Ning Ju Time Domain 1046 - Model Reduction of a Nonlinear Cable-Mass PDE System with Dynamic Boundary Input 1047 - Boundary Control for Optimal Mixing by Stokes Flows 1048 - A Thixotropic Flow Dynamics Under Large Amplitude Oscillatory Shearing 10:10 a.m. - 10:40 a.m. 1049 - Global Regularity And Long-Time Behavior For The Solutions To 2D Boussinesq Group Photo & Refreshment Break EIT 318: Highly Accurate and Effective Numerical Methods 10:40 a.m. - 11:30 a.m. for Partial Differential Equations Plenary Speaker Bob Pego Organizers: Qin Sheng, Abdul Q.M. Khaliq, JaEun Ku Euler Sprays Speakers: Weizhang Huang, Tiffany Jones, Haiyan Tian, Ruihua Liu and Optimal 1050 - Conditioning Of Finite Element Equations With Arbitrary Nonuniform Meshes Transportation 1051 - Asymptotic Stability of a Decomposed Compact Method for Highly Oscillatory Wave Problems 1052 - The Method Of Fictitious Time Integration And Approximate Fundamental Solutions For Nonlinear Elliptic PDEs 1053 - Numerical Methods for Option Pricing in Regime-Switching Jump Diffusion Models
11:30 a.m. - 1:20 p.m. Lunch on your own EIT 319: Operator Splitting Methods For Numerical PDEs And Their Applications AFTERNOON Organizers: Shan Zhao, Qin Sheng Speakers: Lili Ju, Wenyuan Liao, Chuan Li, Qin Sheng SCHEDULE 1054 - Efficient and Stable Exponential Time Differencing Runge-Kutta Methods for Phase Field Elastic 1:30 p.m. - 3:10 p.m. Bending Energy Models Parallel Sessions 1055 - An ADI preconditioner for solving discrete Helmholtz equation EIT and ETAS Buildings 1056 - Improvements On A Matched Interface And Boundary (MIB) Method For Solving Parabolic See full schedule on right. Interface Problems 1057 - The Legacy Of ADI And LOD Methods And Their Application In Solving Highly Oscillatory Wave 3:10 p.m. - 3:50 p.m. Problems Refreshment Break
6 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Conference Schedule Saturday, October 1, 2016 (Location: EIT and ETAS Buildings for Parallel Sessions)
Parallel Sessions | 1:30 p.m. - 3:10 p.m. Session Abstracts on pages 20-27
EIT 321: Modeling and Computations for General 1075 - On The Ground States And Dynamics Of Space Fractional Nonlinear Schro ̈Dinger/Gross-Pitaevskii Equations With and Chaotic Biological Systems Rotation Term And Nonlocal Nonlinear Interactions Organizers: Majid Bani-Yaghoub, Naveen K. Vaidya, Xianping Li, Noah Rhee Speakers: Noah Rhee, Peter Uhl, Minh Nguyen, Jiu Ding ETAS 230: Numerical Approximation And Analysis 1058 - Biological Systems And Chaos For Time Dependent PDEs 1059 - Some Properties Of A One Parameter Family Of Solutions To The Inverse Frobenius- Perron Problem Organizer: Cheng Wang, Steve Wise 1060 - Monotone Traveling Waves In A General Discrete Speaker order: Amanda Diegel, Yulong Xing, Fei Yu, Jue Yan Model For Populations 1076 - A Second Order in Time Finite Element Scheme for 1061 - A Picewise Linear Maximum Entropy Method for the Cahn-Hilliard-Navier-Stokes Equations Invariant Measures of Random Maps 1077 - High Order Finite Volume WENO Methods For The Euler Equations With Gravitation 1078 - High Order Diffuse-Domain Methods for Partial Differential EIT 323: Applied and Computational Topology Equations in Complex Geometries 1079 - Fourier Type Error Analysis On The Solution Gradient’s Super Organizers: Henry Adams, Patrick Shipman Convergence Of Direct DG Methods Speakers: Michael Lesnick, Matthew Wright, Mateusz Juda, Leyda Almodóvar Velázquez 1062 - Interactive Visualization of 2-D Persistence Modules ETAS 480: Some Novel Computational 1063 - Computing Multidimensional Persistent Homology Methods For PDEs 1064 - Combinatorial Multivector Fields Organizers: Huiqing Zhu 1065 - Hclust Barcodes Speakers: Sheng-Wei Chi, Balaram KhatriGhimire, Jun Liu, Sheldon Wang, Daniel Waston EIT 325: Interactions Among Analysis, 1080 - High Order Gradient Reproducing Kernel Collocation Optimization And Network Science Method for Phase Field Fracture Model 1081 - Hybrid Chebyshev Polynomial Scheme For The Numerical Organizers: Pietro Poggi-Corradini, Nathan Albin Speakers: Pietro Poggi-Corradini, Mario Bonk, Brian Benson, Solution Of Elliptic PDEs David Aristoff, Nathan Albin 1082 - Multilevel Discretize-then-Optimize Algorithms for PDE-Constrained Optimizations 1066 - The Probabilistic Interpretation Of 2-Modulus On Networks 1083 - Mixed Finite Element Formulations and Resonance Frequency 1067 - Discretizations And Analytic Structure Predictions for Acoustoelastic Fluid-Structure Interactions 1068 - Curvature of Discrete Graphs 1084 - A Matrix Decomposition RBF Differential Quadrature Algorithm 1069 - Structure Of Large Graphs With Constraints for Solving Elliptic Boundary Value Problems 1070 - Spanning Tree Modulus: Homogeneous Graphs and Deflation
ETAS 483: Recent Advance on High Order Numerical ETAS 229: Recent Advances in Fractional PDEs Methods for Partial Differential Equations Organizers: Yanzhi Zhang Speakers: Janna Lierl, Pablo Stinga, Zhu Wang, Nan Jiang, Yong Zhang Organizers: Yuan Liu, Yingda Cheng Speakers: Weitao Chen, Yingda Cheng, Huijing Du, Wei Guo 1071 - Boundary Harnack Principle For Nonsymmetric Stable-Like 1085 - Semi-Implicit Integration Factor Methods On Sparse Grids For Operators On Smooth Open Sets High-Dimensional Systems 1072 - Extension Problem For Fractional Powers Of Parabolic 1086 - An Adaptive Multiresoluton Discontinuous Galerkin Method for Operators And Applications Time-Dependent Transport Equations in Multi-dimensions 1073 - POD Reduced-Order Modeling of Time-Fractional Partial 1087 - Multiscale Computational Models of Complex Biological Systems Differential Equations with Applications in Parameter 1088 - An Asymptotic Preserving Maxwell Solver Resulting in the Identification Darwin Limit of Electrodynamics 1074 - A Fractional Laplacian-Based Closure Model for Turbulent Fluid Flows
7 Society for Industrial and Applied Mathematics
Conference Schedule Saturday, October 1, 2016
AFTERNOON Parallel Sessions | 3:50 p.m. - 5:30 p.m. SCHEDULE EIT 219: Mesh Adaption for Numerical Simulations 3:50 p.m. - 5:30 p.m. Organizers: Xianping Li, Weizhang Huang Parallel Sessions Speakers: Runchang Lin, Cuong Ngo, Brandon Reyes, Dongmi Luo, Xianping Li EIT and ETAS Buildings See full schedule on right, 1089 - A Discontinuous Galerkin Least-Squares Finite Element Method For Solving Coupled Singularly Perturbed Reaction-Diffusion Equations 1090 - An Adaptive Moving Mesh Numerical Solution To The Porous Medium Equation 6:30 p.m. - 8:00 p.m. 1091 - An Efficient Power-Aware Algorithm For A Class Of Stochastic Models Banquet 1092 - A Moving Mesh Discontinuous Galerkin Method For Hyperbolic Conservation Laws Donaghey Student Center 1093 - Anisotropic Mesh Adaptation For Image Scaling
EIT 224: Partial Differential Equations: Analysis, Computation, Modeling, and Applications Organizers: John Singler, Weiwei Hu Speakers: Jiahong Wu, Wenqing Hu, Yang Yang, Walter Rusin 1094 - The Two-Dimensional Boussinesq Equations With Partial Or Fractional Dissipation 1095 - On 2-D Incompressible Euler Equations With Partial Damping 1096 - Thermo-Acoustic Tomography With Reflectors 1097 - Localized Anisotropic Regularity Conditions For The Navier-Stokes Equations
EIT 318: Highly Accurate and Effective Numerical Methods for Partial Differential Equations Organizers: Qin Sheng, Abdul Q.M. Khaliq, JaEun Ku Speakers: JaEun Ku, Songming Hou, Qin Sheng, Wenyuan Liao 1098 - Hybrid Finite Element Methods 1099 - Improved Imaging Methods for Extended Targets 2000 - An Asymptotic Stability of an Eikonal Splitting Method for Solving Paraxial Helmholtz Equations on Arbitrary Transverse Grids 2001 - An Accurate Numerical Method For Solving 3D Elastic Equation Using Helmholtz Decomposition
EIT 319: Operator Splitting Methods For Numerical PDEs And Their Applications Organizers: Shan Zhao, Qin Sheng Speakers: Shan Zhao, Alexey Sukhinin, Xinfeng Liu, JaEun Ku, Cheng Wang 2002 - Fast Operator Splitting Algorithms For The Electrostatic Analysis Of Solvated Biomolecules 2003 - Spatio-Temporal Modeling of Two-Color Filamentation 2004 - Integration Factor Methods For A Class Of High Order Differential Equations 2005 - An Efficient Solver For A System Of Finite Element Methods For Flux Variable 2006 - A Second Order Operator Splitting Numerical Scheme For The ``Good” Boussinesq Equation And Its Convergence Analysis
8 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Conference Schedule Saturday, October 1, 2016 (Location: EIT and ETAS Buildings for Parallel Sessions)
Parallel Sessions | 3:50 p.m. - 5:30 p.m. Session Abstracts on pages 27-33
EIT 321: Modeling and Computations for ETAS 230: Recent Developments in Discontinuous General and Chaotic Biological Systems Galerkin Methods for Partial Differential Equations Organizers: Majid Bani-Yaghoub, Naveen K. Vaidya, Xianping Li, Organizer: Mahboub Baccouch Noah Rhee Speakers: Yang Yang, Mahboub Baccouch, Bo Dong, Yulong Xing Speakers: Naveen Vaidya, Libin Rong, Songnian Zhao, Maia Martcheva 2024 - Superconvergence Of Discontinuous Galerkin Methods For 2007 - Modeling Movements Of HIV In Vaginal Mucus Nonlinear Hyperbolic Equations 2008 - Modeling Viral Control by CD8+ T Cells 2025 - \emph{A posteriori} error analysis of the discontinuous Galerkin 2009 - Optimal Control in Transmission Dynamics of Zoonotic Visceral method for two-dimensional linear hyperbolic conservation laws Leishmaniasis on Cartesian grids 2010 - Structural And Practical Identifiability Issues Of Immuno- 2026 - Superconvergent HDG Methods For Third-Order Equations In One- Epidemiological Vector-Host Model Space Dimension 2027 - A Posteriori Error Estimates Of Local Discontinuous Galerkin Methods For The Generalized Korteweg-De Vries Equations EIT 323: Applied and Computational Topology Organizers: Henry Adams, Patrick Shipman ETAS 480: Some Advances In Finite Element Methods Speakers: Francis Motta, Hamza Ghadyali, Chad Giusti, Henry Adams Organizers: Yuchuan Chu, Feng Shi 2011 - A Zoo Of Data And Questions Speaker order: Feng Shi, Xiaozhe Hu, Ju Ming, Yuchuan Chu, Keyu Gong 2012 - Topological Patterns in Climatic Data 2028 - A space-time discretization method for solving flow problems 2013 - Topological Methods In Neuroscience based on the partition of unity and adaptivity strategy 2014 - The Theory Of Vietoris-Rips Complexes: What Is Known 2029- Weak Galerkin Finite Element Method for the Biot’s Consolidation And What Is Open? Model 2030 - Multi-Level Monte Carlo Finite Element Method for A Stochastic Optimal Control Problem 2031 - A Dynamic Interface Immersed-Finite-Element Particle-In-Cell EIT 325: Interactions Among Analysis, Method For Modeling Plasma-Wall Interactions Optimization and Network Science 2032 - A Modified Weighting Algorithm for Immersed Finite Element Particle-In-Cell (IFE-PIC) Method Organizers: Pietro Poggi-Corradini, Nathan Albin Speakers: Nages Shanmugalingam, Lukas Geyer, Michael Higgins, Caterina Scoglio, Daniela Ferrero ETAS 483: Recent Advance on High Order Numerical 2015 - Uniformly Perfect Cantor Sets And Analysis On Trees Methods for Partial Differential Equations 2016 - Conformal Dimension Of Sierpinski Carpets Organizers: Yuan Liu, Yingda Cheng 2017 - Threshold Partitioning Problems and Applications in Statistics Speakers: Yang Jiang, Qi Tang, He Yang, Yuan Liu 2018 - Network-Centric Partner Notification Strategies to Contain Epidemics 2033 - A WENO-based Method of Lines Transpose Approach for Vlasov 2019 - Lower Bounds For The Power Domination Number Of A Graph Simulations 2034 - An Added-Mass/Added-Damping Partitioned Algorithm For Rigid Bodies And Incompressible Flows 2035 - Local Discontinuous Galerkin Methods for Khokhlov- ETAS 229: Recent Developments of High Order Zabolotskaya-Kuznetzov Equation Numerical Methods 2036 - A Simple Bound-Preserving Sweeping Technique For Conservative Numerical Approximations Organizer: Ying Wang Speaker order: Mustafa Aggul, Dilek Erkmen, Ming-jun Lai, S. Lakshmivarahan
2020 - High Accuracy Approach To Turbulence Modeling 2021 - Defect-Deferred Correction Method For The Two-Domain Convection-Dominated Convection-Diffusion Problem 2022 - Bivariate Spline Solution of Reaction-Diffusion Equations and Its Application 2023 - On The Structure Of Energy Conserving Low-Order Models
9 Society for Industrial and Applied Mathematics
Conference Schedule Sunday October 2, 2016 (Location: EIT and ETAS Buildings for Parallel Sessions)
MORNING SCHEDULE Parallel Sessions | 8:30 a.m. - 10:10 a.m.
8:00 a.m. – Noon EIT 219: Mesh Adaption for Numerical Simulations Registration Desk Open Coffee Station Organizers: Xianping Li, Weizhang Huang EIT Building Speakers: Stefano Micheletti, Cuiyu He, Avary Kolasinski, Junbo Cheng, Fei Zhang 2037 - Anisotropic mesh adaptation for crack propagation in brittle materials 8:30 a.m. - 10:10 a.m. 2038 - Improved ZZ A Posterior Error Estimation For Diffusion Problem Parallel Sessions 2039 - A New Functional For Variational Mesh Generation And Adaption Based On Equidistribution And EIT and ETAS Buildings Alignment Conditions See full schedule on right 2040 - A Four-Rarefaction Approximate Riemann Solver With Elastic Wave And Von Mises’ Yielding Condition For Two-Dimension Elastic-Plastic Flows 2041 - A Moving Mesh Method For The Numerical Simulation Of Fracture Propagation 10:10 a.m. - 10:40 a.m. Refreshment Break EIT 224: Partial Differential Equations: Analysis, Computation, 10:40 a.m. - 12:20 p.m. Modeling, and Applications Parallel Sessions EIT and ETAS Buildings Organizers: John Singler, Weiwei Hu See full schedule on page 12 Speakers: Michael Schmidt, Siwei Duo, Hans-Werner van Wyk, Yangwen Zhang 2042 - Novel Lagrangian Methods for Imperfectly Mixed Chemical Reactions 12:20 p.m. 2043 - Numerical Methods For Solving The Fractional Schrodinger Equation Meeting Adjourns 2044 - Spatial Adaptivity For Numerical PDEs In The Presence Of Parametric Uncertainty 2045 - Group Finite Element Method For 2D And 3D Navier-Stokes And Boussinesq Equations
EIT 318: Methods Of Applied And Numerical Complex Analysis Organizers: Anna Zemlyanova, Thomas DeLillo Speakers: Anna Zemlyanova, Yuri Antipov, Aditi Ghosh 2046 - Two-Dimensional Fluid Flows Around Multiple Cylinders In The Presence Of Vortices 2047 - A Crack Induced By A Thin Rigid Inclusion Partly Debonded From The Matrix 2048 - A Fast Fourier Recursive Relation Method To Evaluate Singular Integrals In A Complex Plane
EIT 319: Nonlinear Analysis Organizer: Matt Insall Speakers: Giles Auchmuty, Shibin Dai, Youngjoon Hong, Ning Ju, Matt Insall 2049 - Nonlinear Boundary Value Problems for Harmonic Functions 2050 - Phase-Field Free Energy and Boundary Force for Molecular Solvation 2051 - Theoretical And Numerical Analysis Of Singularly Perturbed Problems 2052 - Solution Regularity for the Primitive Equations 2053 - Advances in the Mathematical Analysis of the Complete Iterative Inversion Method
EIT 321: Modeling and Computations for General and Chaotic Biological Systems Organizers: Majid Bani-Yaghoub, Naveen K. Vaidya, Xianping Li, Noah Rhee Speakers: Majid Bani-Yaghoub, James Moore, Jin Wang, Joe Tien 2054 - Optimal Control Policies For Reducing Johne’s Disease In Dairy Farms 2055 - Modeling the Acceleration and Delay of Type 1 Diabetes by Viral Infection 2056 - Modeling Cholera In Heterogeneous Environments 2057 - Modeling The Trade-Off Between Transmission And Contact In Disease Dynamics
10 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Conference Schedule Sunday, October 2, 2016 (Location: EIT and ETAS Buildings for Parallel Sessions)
Parallel Sessions | 8:30 a.m. - 10:10 a.m. Session Abstracts on pages 33-39
EIT 323: Applied and Computational Topology ETAS 230: Recent Developments in Discontinuous Organizers: Henry Adams, Patrick Shipman Galerkin Methods for Partial Differential Equations Speakers: Rachel Neville, Patrick Shipman, Pawel Dlotko, David Organizer: Mahboub Baccouch Letscher Speakers: Joshua Buli, Ari Stern, James Rossmanith, Bahaudin Hashmi 2058 - Topological Measure of Order on Lattice Patterns 2070 - A Local Discontinuous Galerkin Method for the Coupled BBM- 2059 - The Soft Mode Plays A Role In Defect Persistence In Pattern- BBM System Forming Systems 2071 - Multisymplectic HDG methods 2060 - Computational topology and computational electromagnetism 2072 - High-order DG-FEM for Micro-Macro Partitioned Kinetic Models 2061 - Persistent Homotopy: An Overview 2073 - Modeling of Important Vapor-to-Particle Reactions
EIT 325: Interactions Among Analysis, ETAS 480: Some Advances in Finite Element Methods Optimization And Network Science Organizers: Yuchuan Chu, Feng Shi (Special Time 8:05 a.m. - 10:10 a.m.) Speaker order: Fatma Songul Ozesenli Tetikoglu, Lulu Quan, Fatih Sabahattin Tetikoglu, Yingwei Wang Organizers: Pietro Poggi-Corradini, Nathan Albin Speakers: Jason Clemens, Jim Gill, Thiwanka Fernando, 2074 - Numerical Solution of an Elliptic-Hyperbolic Equation with an Hrant Hakobyan, Paul Horn Unknown Parameter 2075 - Time-domain Immersed Finite Element Methods for 2062 - Blocker Duality for Modulus Electromagnetic Scattering and Radiation in Composite Material 2063 - Modulus and Spaces Without Walks 2076 - The positivity of the difference operator with periodic conditions 2064 - An Investigation Of Node-Based Metrics On Networks and its application Arising From P-Modulus 2077 - Muntz-Galerkin Methods And Applications To Mixed Dirichlet- 2065 - Quasisymmetric Embeddings Of Metric Spaces Neumann Boundary Value Problems 2065A - A Hamilton Type Gradient Estimate For Solutions To The Heat Equation On Graphs ETAS 483: Contributed presentations ETAS 229: Recent Developments of Speakers: Adelaide Akers, Dennis Brewer, Rong Fan, S. Lakshmivarahan, Hung Le High Order Numerical Methods 2078 - Existence and Symmetry of Small-amplitude Solitary Water Waves Organizer: Ying Wang with Discontinuous Vorticity Speaker order: Songting Luo, Lin Mu, Jin-song Pei, Ran Zhang 2079 - An Introductory Course in Partial Differential Equations Using Mathematica 2080 - A Squared Correlation Coefficient of the Correlation Matrix 2066 - High-Order Methods For Traveltime And Amplitude In Fast Huygens 2081 - Data Ming, Data Assimilation and Prediction - Parts of a Sweeping Method For High Frequency Helmholtz Equation Continuum 2067 - Weak Galerkin Finite Element Methods and Implementations 2082 - The Transmission Problem for Elliptic Equations with Wentzel 2068 - A Brief Introduction to “Mem-Models” in Engineering Mechanics Boundary Condition Applications 2069 - Maximum Principles For P1-P0 Weak Galerkin Finite Element Approximations Of Quasi-Linear Second Order Elliptic Equations
11 Society for Industrial and Applied Mathematics
Conference Schedule Sunday October 2, 2016 (Location: EIT and ETAS Buildings for Parallel Sessions)
MORNING SCHEDULE Parallel Sessions | 10:40 a.m. - 12:20 p.m.
8:00 a.m. – Noon EIT 219, 224, 229, 230, 480, 483: No scheduled talks Registration Desk Open Coffee Station EIT Building EIT 318: Methods Of Applied And Numerical Complex Analysis
8:30 a.m. - 10:10 a.m. Organizers: Anna Zemlyanova, Thomas DeLillo Speakers: Tom DeLillo, Justin Mears, Mehran Mehrabi Parallel Sessions EIT and ETAS Buildings 2083 - A Comparison of Some Numerical Conformal Mapping Methods for Simply and Multiply See full schedule on pages 10-11 Connected Domains 2084 - Computation of Stokes Waves Using Conformal Mapping Session Abstracts on pages 39-42 2085 - Analytical Analysis of Gas Diffusion into Noncircular Pores of Shale Organic Matter 10:10 a.m. - 10:40 a.m. Refreshment Break EIT 319: Contributed talks Speakers: Lasanthi Pelawa Watagoda, Liangya Pi, Changxin Qiu, 10:40 a.m. - 12:20 p.m. Hasthika Rupasinghe Arachchige Don Parallel Sessions EIT and ETAS Buildings 2086 - Inference After Variable Selection See full schedule on right 2087 - An Investigation on the Data Assimilation with Kalman Filter and Finite Elements for Subsurface Flows 12:20 p.m. 2088 - A Multi-Physics Domain Decomposition Method for Navier-Stokes-Darcy Model Meeting Adjourns 2089 - Bootstrapping Analogs of the Two Sample Hotelling’s T^2 Test}
EIT 321: Modeling and Computations for General and Chaotic Biological Systems Organizers: Majid Bani-Yaghoub, Naveen K. Vaidya, Xianping Li, Noah Rhee Speakers: Xianping Li, Weijiu Liu, Gayla Olbricht, Yi Sun 2090 - Mathematical Modeling and Computation of Spatio-temporal Dynamics of Dengue Epidemics 2091 - Asymptotic Tracking and Disturbance Rejection of the Blood Glucose Regulation System 2092 - Modeling Sleep Patterns In The Fruit Fly To Investigate The Link Between Sleep And Alzheimer’s Disease 2093 - Kinetic Monte Carlo Simulations of Multicellular Aggregate Self-Assembly in Biofabrication
EIT 323: Applied and Computational Topology Organizers: Henry Adams, Patrick Shipman Speakers: Amit Patel, Lori Ziegelmeier, Isabel Darcy, Iuliana Oprea 2094 - Semicontinuity of Persistence Diagrams 2095 - Persistent Homology on Grassmann Manifolds for Analysis of Hyperspectral Movies 2096 - Studying Knots Via Heat Maps 2097 - Topological Measures of Snow Surface Roughness
EIT 325: Interactions Among Analysis, Optimization And Network Science Organizers: Pietro Poggi-Corradini, Nathan Albin Speakers: Dominique Zosso, Lizaveta Ihnatsyeva, Heman Shakeri, Kevin Wildrick 2098 - Primal-Dual Methods for p-Modulus on Graphs 2099 - Functions Of Fractional Smoothness On Metric Measure Spaces 3000 - Analyzing Loop Structures In Networks 3001 - Metric Spaces of Small Cotype
12 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Conference Plenary Speakers Friday, September 30, 2016
9:20 a.m. - 10:10 a.m. Irene Gamba University of Texas-Austin
Conservative Solvers for Collisional Kinetic Boltzmann and Landau-Poisson Systems
ABSTRACT: These computational models are at the core of collisional plasma theories. In particular we will discuss several aspects of conservative solvers for the kinetic transport equations of particle interactions that involve either linear or non-linear Boltzmann as well as the non-linear Landau equations, by means of stagger conservative DG schemes for the transport part and DG or spectral solvers for the collisional part, linked by a projection method that is conservative. In addition we will discuss the computational aspects of boundary layer formation due to rough boundary effects for insulating conditions.
9:20 a.m. - 10:10 a.m. Weizhang Huang University of Kansas
A New Implementation of the MMPDE Moving Mesh Method and Applications
ABSTRACT: The MMPDE moving mesh method is a dynamic mesh adaptation method for use in the numerical solution of partial differential equations. It employs a partial differential equation (MMPDE) to move the mesh nodes continuously in time and orderly in space while adapting to evolving features in the solution of the underlying problem. The MMPDE is formulated as the gradient flow equation of a meshing functional that is typically designed based on geometric, physical, and/or accuracy considerations. In this talk, I will describe a new discretization of the MMPDE which gives the mesh velocities explicitly, analytically, and in a compact matrix form. The discretization leads to a simple, efficient, and robust implementation of the MMPDE method. In particular, it works for convex or nonconvex domains and is guaranteed to produce nonsingular meshes. Some applications of the method will be discussed, including mesh smoothing (to improve mesh quality), generation of anisotropic polygonal meshes, and the numerical solution of the porous medium equation and the regularized long-wave equation.
13 Society for Industrial and Applied Mathematics
Conference Plenary Speakers Saturday, October 1, 2016
9:20 a.m. - 10:10 a.m. Paul Martin Colorado School of Mines
Solving the Wave Equation: Acoustic Scattering in the Time Domain
ABSTRACT: Transient acoustic waves are generated or scattered by an obstacle. This leads to initial-boundary value problems for the wave equation. Recent studies usually assume that solutions are smooth. However, many interesting physical problems lead to non-smooth solutions: there are moving wavefronts. These situations are usually handled by seeking weak solutions, but care is needed to ensure that constraints imposed by the underlying continuum mechanics are respected. We investigate some of the consequences, with a focus on the benchmark problem of scattering by a sphere.
10:40 a.m. - 11:40 a.m. Robert Pego Carnegie Mellon University
Euler Sprays and Optimal Transportation
ABSTRACT: We describe a striking connection between Arnold’s least-action principle for incompressible Euler flows and geodesic paths for Wasserstein distance. A connection with a variant of Brenier’s relaxed least-action principle for generalized Euler flows will be outlined also. This is joint work with Jian-Guo Liu and Dejan Slepcev.
14 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Session Abstracts | Friday, September 30, 2016 | 1:30 p.m. - 3:10 p.m.
Friday, September 30, 2016 1003 - Applications of Immersed EIT 224: Partial Differential 1:30 p.m. - 3:10 p.m. Finite Element Methods Equations: Analysis, Tao Lin, Department of Mathematics, Virginia Tech ______Computation, Modeling, and Interface problems often appear in numerical EIT 219: Recent Advances simulations over domains consisting of Applications multiple materials leading to discontinuous Organizers: John Singler, Weiwei Hu on Numerical Methods for coefficients in the involved partial differential Speakers: Tong Li, Mathew Johnson, Samuel Walsh, Interface Problems equations whose solutions are inevitably less Aslihan Demirkaya, Majid Bani-Yaghoub Organizers: Xu Zhang, James B. Collins smooth around the material interfaces. This Speakers: Long Chen, Jeb Collins, Tao Lin, presentation will start from a brief description 1006 - Global Wellposedness Cuiyu He, Songming Hou of recently developed immersed finite element And Traveling Waves To The PDE (IFE) methods that can use a Cartesian mesh to solve interface problems even with non- Models Of Chemotaxis 1001 - An Interface-Fitted Mesh trivial interface geometry. We will then present Tong Li, University of Iowa Generator And Virtual Element a few application problems to demonstrate We investigate global existence and long Methods For Elliptic Interface where IFE methods can be advantageous. The time behavior of solutions for PDE models of presentation will conclude with a few research chemotaxis. These models include the classical Problems topics in IFE methods. Long Chen, University of California at Irvine Keller-Segel model and its variations such as a Solving the Wave Equation: Acoustic Scattering in the Time Domain model reflecting rotational chemotactic motion. In this work, we develop a simple and efficient 1004 -A Posteriori error estimation for Moreover, we establish the existence and the interface-fitted mesh algorithm which can nonlinear stability of large-amplitude traveling produce an interface-fitted mesh in two and nonconforming finite element methods Cuiyu He, Purdue University wave solutions to the system of nonlinear three dimension quickly. Elements in such conservation laws derived from Keller-Segel interface-fitted mesh are not restricted to In this talk, we derive and analysis a robust model. simplex but can be polygons or polyhedron. residual-based A Posteriori error estimation We thus apply Virtual Element Methods to without the Quasi-monotone assumption for 1007 - Dynamics and Stability solve the elliptic interface problem in two nonconforming FEM on interface problems and three dimensions. We present some whose diffusion coefficients could possibly of Viscous Roll Waves numerical results to illustrate the effectiveness possess large jumps across interfaces. Using Mathew Johnson, University of Kansas of our method and prove an optimal order a new and more direct approach, we derive Roll waves are well observed hydrodynamic convergence of our method. This is a joint work a new residual-based error estimator for CR instabilities occurring in inclined thin film flow, with Huayi Wei and Min Wen. element that can be proved both robustly occurring from the competition of gravitational reliable and efficient in the sense that both forces pulling the fluid down the ramp and the 1002 - A Posteriori Error Estimation constants are indecent of the ratio of the jump frictional forces exerted on the fluid along the of diffusion coefficients. Numerical results are For A Cut Cell Method With surface of the ramp. Although the observation also provided. of roll waves is a common experience (I’ll try to Uncertain Interface Location convince you of this!), and while a great deal Jeb Collins, West Texas A&M University 1005 - Numerical Methods For Solving of effort has been devoted to studying these We study a simple diffusive process in which Linear And Nonlinear Interface waves experimentally, numerically, and through the diffusivity is discontinuous across an formal calculations, a complete mathematical interface interior to the domain. In many Problems understanding of the existence of such Songming Hou, Louisiana Tech University situations, the location of the interface is structures that are “physically observable”, We present numerical methods for solving measured at a small number of locations and in the sense that they persist when subject to linear and nonlinear interface problems. The these measurements contain error. Thus the small perturbations, is still lacking. In this talk, key idea of these methods is to use different location of the interface and the solution itself I will discuss recent progress in this direction. basis functions for test and trial functions and are subject to uncertainty. A Monte Carlo This is joint work with Blake Barker (Brown), Euler Sprays and Optimal Transportation to use non-body-fitted grids. approach is employed which requires solving Pascal Noble (University of Toulouse), L. Miguel a large number of sample problems, each Rodrigues (University of Rennes), and Kevin with a different interface location. An efficient Zumbrun (Indiana University) adjoint-based a posteriori technique is used to estimate the error in a quantity of interest 1008 - Existence And Qualitative for each sample problem. This error has a component due to the numerical approximation Theory Of Stratified Solitary of the diffusive process and a component Water Waves arising from the uncertainty in the interface Samuel Walsh, University of Missouri, Columbia location. A recognition of these separate In this talk, we will report some recent results sources of error is necessary in order to concerning two-dimensional gravity solitary construct effective adaptivity strategies. water waves with hereogeneous density. The fluid domain is assumed be bounded below by an impenetrable flat ocean bed, while the interface between the water and vacuum above is a free boundary. Our main existence result states that, for any smooth choice of upstream velocity and streamline density
15 Society for Industrial and Applied Mathematics
Session Abstracts | Friday, September 30, 2016 | 1:30 p.m. - 3:10 p.m. function, there exists a path connected set of numerically explored for different time lag 1014 - Solving The Degenerate such solutions that includes large-amplitude values. Stochastic Kawarada Equation Via surface waves. Indeed, this solution set can be continued up to (but does not include) an An Adaptive Crank-Nicolson Method ``extreme wave`` that possess a stagnation EIT 318: Highly Accurate and Josh Padgett, Baylor University point. We will also discuss a number of results This talk concerns the use of a nonuniform characterizing the qualitative features of Effective Numerical Methods for finite difference method for solving a solitary stratified waves. In part, these include degenerate Kawarada quenching-combustion bounds on the Froude number from above and Partial Differential Equations Organizers: Qin Sheng, Abdul Q.M. Khaliq, JaEun Ku equation with a vibrant stochastic source term. below that are new even for constant density Speakers: Aaron Benham, Matthew Beauregard, Arbitrary grids are introduced in both space flow; an a priori bound on the velocity field and Nick Kosmatov, Josh Padgett and time to accommodate the uncertainty lower bound on the pressure; a proof of the and singularities involved. It is shown that nonexistence of monotone bores for stratified under proper constraints on mesh step sizes, surface waves; and a theorem ensuring that all 1011 - Multiple Positive Solutions the positivity and monotonicity of the solution supercritical solitary waves of elevation have Of A Semipositone Fourth-Order are maintained. The numerical stability of an axis of even symmetry. This is joint work Boundary Value Problem the scheme is studied in the classical von with R. M. Chen and M. H. Wheeler. Aaron Benham, University of Arkansas at Little Rock Neumann sense by freezing the nonlinear source term and then the analysis is further We consider a nonlinear fourth-order boundary 1009 - Numerical Results On improved by including the contributions of the value problem. Our method is based on a source term. Numerical experiments are given Existence And Stability Of Standing cone-theoretic method which is used to to illustrate our conclusions and further explore And Traveling Waves For The obtain existence and multiplicity results which the possible effects of the stochastic term on improve those in several previously published solution profile and quenching times. Fourth Order Beam Equation papers. Aslihan Demirkaya, University of Hartford In this work, we study numerically the 1012 - A Nonlinear Splitting Algorithm EIT 319: No Talks Scheduled existence and stability of some special for Systems of Partial Differential solutions of the nonlinear beam equation: EIT 321: No Talks Scheduled $u_{tt}+u_{xxxx}+u-|u|^{p-1} u=0$ when $p=3$ Equations with self-Diffusion and $p=5$. For the standing wave solutions Matthew A. Beauregard, Stephen F. Austin $u(x,t)=e^{i\omega t}\varphi_{\omega}(x)$ we State University EIT 323: Applied and numerically illustrate their existence using Systems of reaction-diffusion equations are variational approach. Our numerics illustrate Computational Topology commonly used in biological models of food Organizers: Henry Adams, Patrick Shipman the existence of both ground states and exited chains. The populations and their complicated Speakers: Eric Hanson, Jose Perea, Douglas Heister- states. We also compute numerically the interactions present numerous challenges kamp, Sara Kalisnik threshold value $\omega^*$ which separates in theory and in numerical approximation. In stable and unstable ground states. Next, we particular, self-diffusion is a nonlinear term 1015 - Persistence Images: study the existence and linear stability of that models over-crowding of a particular periodic traveling wave solutions $u(x,t)=\ species. The nonlinearity complicates attempts Representing Persistent Homology varphi(x+ct)$. We present numerical illustration to construct efficient and accurate numerical for Machine Learning of the theoretically predicted threshold value of approximations of the underlying systems of Eric Hanson, Texas Christian University the speed $c$ which separates the stable and equations. In this talk, a new nonlinear splitting unstable waves. algorithm is designed for a partial differential If we consider a data set as a noisy sampling equation that incorporates self-diffusion. We of an underlying topological space, then the 1010 - Stability Of Travelling And present a general model that incorporates tools of topological data analysis (TDA) can be used to understand the structure of the data. Stationary Waves Arising From self-diffusion and develop a numerical approximation. The numerical analysis of the One of these tools is persistent homology (PH), A Delayed Hyperbolic–Parabolic approximation provides criteria for stability and which provides a multiscale description of Population Model convergence. Numerical examples are used to the homological features, often represented Majid Bani-Yaghoub, University of illustrate the theoretical results. by a persistence diagram (PD). A desire to Missouri-Kansas City analyze data using the homological features captured by PH, in combination with machine We consider a hyperbolic–parabolic population 1013 - The Sturm-Liouville Boundary learning (ML) techniques, has led to numerous model which takes into account the time lag in Value Problem With Impulsive approaches to adapting the PD representation spread of invasive species. In the absence of for this purpose. Certainly, the space of PDs time lag, the model is reduced to a parabolic Effects On The Half-Line Nickolai Kosmatov, University of Arkansas can be given a metric structure, but often equation, whose traveling and stationary wave at Little Rock additional structure is valuable to machine solutions have been extensively studied. Using learning tasks. We convert a PD to a finite- the perturbation methods, when the time lag Using a cone-theoretic theorem, we obtain dimensional vector representation, and prove is sufficiently small, we show that the stability the existence of positive solutions of the the stability of this transformation with respect of wave solutions of the hyperbolic-parabolic semipositone Sturm-Liouville boundary value to small perturbations in the inputs. This talk model and the reduced model are concurrent. problem on the half-line subject to nonlinear will begin with an introduction to PH, describe Furthermore, formation of the traveling and functional impulsive conditions. this new representation, which we call a stationary wave solutions of the hyperbolic- persistence image, and discuss how it can be parabolic model to the wave solutions is used with ML techniques.
16 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Session Abstracts | Friday, September 30, 2016 | 1:30 p.m. - 3:10 p.m.
1016 - Directional Features, Projective EIT 325: New Numerical 1021 - Babich-Like Ansatz For Three- Coordinates and Classification Advances on Wave Dimensional Point-Source Maxwell’s Jose Perea, Michigan State University Propagation Problems Equations In An Inhomogeneous Directional features in images have been Organizer: Yassine Boubendir Medium At High Frequencies shown to be fundamental in digit recognition Speakers: Yassine Boubendir, Lise-Marie Wangtao Lu, Michigan State University and texture classification tasks. We will show Imbert-Gerard, Wangtao Lu in this talk how projective spaces can be used We propose a novel Babich-like ansatz to model distributions of said features, and how consisting of an infinite series of dyadic data can be mapped onto these spaces. 1019 - Asymptotic Expansions of coefficients (three-by-three matrices) the Helmholtz Equation Solutions and spherical Hankel functions for solving point-source Maxwell’s equations in an 1017 - Thin Position Inspired in the Case of Convex Obstacles inhomogeneous medium so as to produce Algorithms For Machine Learning Yassine Boubendir, New Jersey Institute the so-called dyadic Green’s function. Using of Technology And Data Analysis properties of spherical Hankel functions, we Douglas Heisterkamp, Oklahoma State University In this talk, we will review some of the well- derive governing equations for the unknown known asymptotic expansions of solutions asymptotics of the ansatz including the This presentation introduces the algorithms of of the Helmholtz equation. Then, we will traveltime function and dyadic coefficients. By topologically intrinsic lexicographic ordering present some new expansions based on proposing matching conditions at the (TILO), pinch ratio clustering (PRC), and thin local approximations of the Dirichlet to point source, we rigorously derive asymptotic tree position (TTP) which are inspired by thin Neumann operator. The goal is the derivation behaviors of these geometrical-optics position for knots and 3-dimensional manifolds. of appropriate ansatz that can be used in the ingredients near the source so that their initial An overview will be given of the benefits design of high-frequency integral equation data at the source point are well-defined. To and limitations of applying the algorithms to solvers. verify the feasibility of the proposed ansatz, clustering, feature selection, manifold learning, we truncate the ansatz to keep only the first and data visualization. 1020 - Volume Integral Methods two terms, and we further develop partial- differential-equation based 1018 - Tropical Coordinates on the For Wave Propagation In Eulerian approaches to compute the resulting Space of Persistence Barcodes Inhomogeneous Media asymptotic solutions. Since the system of governing equations for each dyadic coefficient Sara Kalisnik Verovsek, Brown University Lise-Marie Imbert-Gerard, NYU is strongly coupled, we introduce auxiliary In the last two decades applied topologists We will discuss high order accurate numerical variables to transform these strongly coupled have developed numerous methods for methods for scattering by a penetrable systems into decoupled scalar equations. ‘measuring’ and building combinatorial obstacle in an homogeneous background. In Furthermore, we develop high-order Lax- representations of the shape of the data. the penetrable case, as opposed to obstacle Friedrichs weighted essentially non-oscillatory The most famous example of the former scattering case, a volume integral formulation schemes for computing these auxiliary is persistent homology. This adaptation of is required. The volume integral equation variables so that the Green’s function can be classical homology assigns a barcode, i.e. a corresponding to the Helmholtz equation is constructed. Numerical examples demonstrate collection of intervals with endpoints on the called the Lippmann-Schwinger equation. It that our new ansatz yields a uniform asymptotic real line, to a finite metric space. Unfortunately, is derived by representing the scattered field solution in the region of space containing a barcodes are not well-adapted for use by as the convolution of the background Green’s point source but no other caustics. This is practitioners in machine learning tasks. We can function for the exterior homogeneous medium a joint work with Jianliang Qian and Robert circumvent this problem by assigning numerical with an unknown density. We developed an Burridge. quantities to barcodes and these outputs can automatically adaptive, high-order accurate then be used as input to standard algorithms. discretization method that provides rapid I will talk about max-plus polynomials and access to arbitrary elements of the system tropical rational functions that can be used as matrix. This method relies on the identification ETAS 229: Recent Advances coordinates on the space of barcodes. All of of two different regimes of interactions with in Fractional PDEs these are stable with respect to the standard respect to the singularity of the Green’s Organizer: Yanzhi Zhang distance functions (bottleneck, Wasserstein) function. The system itself is solved using Speakers: Hong Wang, Mohsen Zayernouri, used on the barcode space. a hierarchical fast direct solver (HODLR), Xiaofan Li, Joseph E. Pasciak, Siwei Duo by constructing a compressed version of the inverse matrix. Applications to waves in plasmas will be described. Radio frequency 1022 - A Fast Numerical waves are used to heat and probe plasmas. Method for a Bond-Based Time harmonic equations model these waves, Linear Peridynamic Model with variable coefficients depending of the Hong Wang, University of South Carolina plasma density. Our numerical method is particularly convenient to study the influence We develop a fast numerical method for of the incident angle : the compression of a two-dimensional bond-based linear the inverse matrix is performed only once peridynamic model, which provides an independently of the incident angle. appropriate description of the planar deformation of a continuous elastic body involving discontinuities or other singularities. The method reduces the computational cost of evaluating and assembling the stiffness matrix from O(N^2) to O(N), where N is the
17 Society for Industrial and Applied Mathematics
Session Abstracts | Friday, September 30, 2016 | 1:30 p.m. - 3:10 p.m. number of unknowns in the discrete system. homogeneous Dirichlet boundary conditions. ETAS 230: Numerical The method also reduces the computational Although it is conceptually feasible to study the work from O(N^2) to O(N log N) and the memory Galerkin approximation based on a standard Approximation And Analysis requirement from O(N^2) to O(N). All of this is finite element space, such a direct approach For Time Dependent PDEs achieved by carefully exploring the structure of is not viable as the exact computation of the Organizers: Cheng Wang, Steve Wise the stiffness matrix of the collocation scheme, resulting stiffness matrix entries is not possible Speaker order: Cheng Wang, Wen-Qiang Feng, without any lossy compression involved. (at least in two or more spatial dimensions). Zhen Guan, Lili Ju Instead, we will develop a non-conforming 1023 - Unified Petrov-Galerkin method by approximating the action of the stiffness matrix on a vector (sometimes 1027 - Energy-Stable Pseudo- Spectral Methods for High- referred to as a matrix free approach). The Spectral Numerical Scheme Dimensional FPDEs bilinear form is written as an improper integral For The Cahn-Hilliard Equation Mohsen Zayernouri, Michigan State University involving the solution of parameter dependent elliptic problems on $R^d$. We compute And The Homogeneous Linear We present a series of unified spectral methods an approximate action of stiffness matrix Iteration Algorithm of Petrov-Galerkin sense for a general class of by applying a SINC quadrature rule to the Cheng Wang, University of Massachusetts linear fractional partial differential equations improper integral, replacing the problems on Dartmouth (FPDEs) in any $(d+1)$ dimensions, $d\geq 1$. $R^d$ by problems on parameter dependent To efficiently solve the corresponding linear A second order energy stable numerical bounded domains, and the application of systems, we also develop a unified fast solver scheme is presented for the two and three the finite element method to the bounded with optimal complexity. The proposed scheme dimensional Cahn-Hilliard equation, with domain problems. The entire procedure can works with the same ease and efficiency for Fourier pseudo-spectral approximation in be implemented using standard finite element parabolic, elliptic, and hyperbolic problems. space. The convex splitting nature assures its tools, e.g., the DEAL-II library. The analysis of unique solvability and unconditional energy the resulting algorithm is discussed. In addition, 1024 - Numerical Schemes For stability. Meanwhile, the implicit treatment of the results of numerical computations on a the nonlinear term makes a direct nonlinear Integro-Differential Equations model problem with known solution are given. solver not available, due to the global nature Related To Alpha-Stable Processes of the pseudo-spectral spatial discretization. Xiaofan Li, Illinois Institute of Technology 1026 - A Fast Algorithm For In turn, a linear iteration algorithm is proposed to overcome this difficulty, in which a Douglas- The mean first exit time, escape probability Solving The Space-Time Dupont-type regularization term is introduced. and transitional probability density are utilized Fractional Diffusion Equation As a consequence, the numerical efficiency to quantify dynamical behaviors of stochastic Siwei Duo, Missouri University of has been greatly improved, since the highly differential equations with non-Gaussian, $\ Science and Technology nonlinear system can be decomposed as an alpha$-stable type L\’evy motions. Taking In this talk, we present a fast and accurate iteration of purely linear solvers. Moreover, a advantage of the Toeplitz matrix structure algorithm to solve the space-time fractional careful nonlinear analysis shows a contraction of the time-space discretization, a fast and diffusion equation with spectral fractional mapping property of this linear iteration. A few accurate numerical algorithm is proposed to Laplacian in space and Caputo fractional numerical examples are also presented in this simulate the nonlocal Fokker-Planck equations derivative in time. The central finite difference talk. on either a bounded or infinite domain. Under scheme combine with the matrix transfer a specified condition, the scheme is shown to technique is used for the space discretization, satisfy a discrete maximum principle and to 1028 - Efficient Finite-Difference and the Laplace transform is used for time be convergent. The numerical results for two integration. Because of the nonlocality, Geometric Multigrid Solvers prototypical stochastic systems, the Ornstein- numerical discretization of the spectral for the Cahn-Hilliard Equation Uhlenbeck system and the double-well system fractional Laplacian results in a large dense Wenqiang Feng, The University of Tennessee, are shown. matrix, which causes considerable challenges Knoxville in not only storing the matrix but also 1025 - Numerical Approximation We present two geometric multigrid solvers computing the matrix-vector products. By using with finite difference discretization for the of a Variational Problem on a the compact structure of the discrete system Cahn-Hilliard equation. One is preconditioned Bounded Domain involving the and the sine transform, our algorithm avoids steepest descent with multigrid method as to store the large matrix therefore significantly preconditioner and the other one is using Fractional Laplacian reduces the computational costs, especially Joseph Pasciak, Texas A&M University multigrid method as a direct solver. In the in higher spatial dimensions. Varies numerical preconditioned method, we minimize the The mathematical theory and numerical examples will be presented to demonstrate the corresponding convex energies with the analysis of non-local operators has been a accuracy and efficiency of the algorithm. proposed method in stead of solving the topic of intensive research in recent years. nonlinear system directly. Moreover, by using One class of applications come from replacing the energy dissipation property, we derive the Brownian motion diffusion by diffusion coming discrete $\ell^p$ bound for the solution, as well from a symmetric $\alpha$-stable Levy process, as the upper-bound for the second derivative i.e., the Laplace operator is replaced by a of the energy, and investigate the convergence fractional Laplacian. In this talk, we propose properties. Various numerical simulations are a numerical approximation of equations with carried out to demonstrate the efficiency and this type of diffusion terms posed on bounded robustness of the proposed methods. domains. We focus on the simplest example of an elliptic variational problem coming from the fractional Laplacian on a bounded domain with
18 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Session Abstracts | Friday, September 30, 2016 | 1:30 p.m. - 3:10 p.m.
1029 - Unconditional Stable Method ETAS 480: Some Novel 1034 - Superconvergence and for the Amplitude Description of the Computational Methods Extrapolation of Quasi-Wilson Phase-Field Crystal model Element for Nonsymmetric and Zhen Guan, University of California, Irvine For PDEs Organizer: Huiqing Zhu Indefinite Problem The amplitude description of the Phase- Speakers: Jiangguo Liu, Zhimin Zhang, Zhiyun Yu, Xinxiang Li, Shanghai University Field Crystal model is widely used coarse- Xinxiang Li, Huiqing Zhu The quasi-Wilson finite element method will be grained approach for studying polycrystalline discussed to pproximate the nonsymmetric and solidification. In addition to the obvious 1031 - THex Algorithm and Its indefinite problem. Applying the characteristics computational advantages over the atomistic Applications in Finite Element of this element, the known high accuracy models, the amplitude description allows analysis results of bilinear element and for isolating variables associated with Methods averaging technique, the super-close property macroscopic description of continuum media Jiangguo Liu, Colorado State University and global superconvergence result with such as order parameter or displacement In this talk, we present the THex algorithm that O(ℎ^2 )order are obtained. Furthermore, a new fields. Here we present an unconditional refines a tetrahedral mesh into a hexahedral asymptotic error expansion is deduced and energy stable method with parallelogram mesh. mesh. Based on this, we discuss finite element the extrapolation solution with O(ℎ^3 ) order The resulting nonlinear scheme is handled by methods on hexahedral meshes. is derived which is two order higher than the highly efficient nonlinear multigrid method. traditional error estimate. 1030 - Energy Stability and Error 1032 - Polynomial Preserving Recovery for Gradient and Hessian 1035 - Method Of Fundamental Estimates of Exponential Time Zhimin Zhang, Beijing Computational Science Solutions Using Transformed Angular Differencing Schemes for the Research Center; Wayne State University Basis Functions Epitaxial Growth Model without Post-processing techniques are important in Huiqing Zhu, The University of Southern Mississippi Slope Selection scientific and engineering computation. One In this talk, we introduce transformed angular Lili Ju, University of South Carolina of such technique, Superconvergent Patch basis function-s(ABFs) that can be used in Recovery (SPR) proposed by Zienkiewicz-Zhu In this talk, we present a class of exponential the method of fundamental solutions (MFS) as in 1992, has been widely used in finite element time differencing (ETD) schemes for solving the basis functions. The idea of ABF was proposed commercial software packages such as epitaxial growth model without slope selection. by Young et al. in 2015, but its implementation Abaqus, ANSYS, Diffpack, etc.; another one, A linear convex splitting is first applied to was limited by the selection of source points. Polynomial Preserving Recovery (PPR) has the energy functional of the model, and then By the transformation we designed, the source been adopted by COMSOL Multiphysics since Fourier collocation and ETD-based multistep points can be selected in a similar way to 2008. In this talk, I will discuss some resent approximations are used respectively for traditional MFS using radial basis functions. development of PPR in obtaining the Hessian spatial discretization and time integration of the Numerical experiments on solving interior matrix (second derivatives) from the computed corresponding gradient flow equation. Energy and exterior potential potential flow problems data. stabilities and error estimates of the first and governed by the 2-D Laplace equation will be second order ETD schemes are rigorously presented. established in the fully discrete sense. We 1033 - Nonconforming Mixed Finite also numerically demonstrate the accuracy Elements Method For The Three- of the proposed schemes and simulate the Dimensional Incompressible ETAS 483: Contributed coarsening dynamics with small diffusion coefficients. The results show the logarithm Magnetohydrodynamics Equation presentations law for the energy decay and the power laws Zhiyun Yu, Zhongyuan University of Technology Speakers: Necmettin Aggez, Kyle Claassen, Tania Hazra, Michelle Maiden, Zhihan Wei for growth of the surface roughness and the Nonconforming mixed finite element method is mound width, which are consistent with the established for the stationary incompressible existing theories in the literature. magnetohydrodynamics equation which 1036 - A Note on Finite Difference couples Navier-Stokes equations with Method for NBVP of the Hyperbolic Maxwell’s equations in a bounded domain Type in 3D. The lowest order finite elements on Necmettin Aggez, Fatih University Allaberen tetrahedral or hexahedra are chosen to Ashyralyev, Fatih University approximate the pressure, the velocity field In this work, the nonlocal boundary value and the magnetic field. The hydrodynamic problem for the semilinear hyperbolic equation unknowns are discretized by inf-sup stable in a Hilbert space is considered. The second finite element pairs and the magnetic field order of accuracy difference scheme is by H^1-conforming element and H(curl)- presented for obtaining approximate solution conforming element, respectively. Through of the nonlocal boundary value problem. The applying the prior estimates of the exact and convergence estimate for the solution of this approximated solutions, and choosing the difference scheme is obtained. Theoretical appropriate parameters Re, Rm and S in the results are supported by a numerical example. MHD equation considered, we obtain the optimal order error estimates of H^1-norm and L^2-norm for the velocity field, L^2-norm for the pressure and the broken H^1-norm and H(curl)- norm for the magnetic field, respectively.
19 Society for Industrial and Applied Mathematics
Session Abstracts | Saturday, October 1, 2016 | 1:30 p.m. - 3:10 p.m.
1037 - Antiperiodic Ground State formable pipe forms. The long wave interfacial Saturday, October 1, 2016 Theory for Fractional Schr\”odinger dynamics are well-described by a dispersive nonlinear partial differential equation called 1:30 p.m. - 3:10 p.m. Operators the conduit equation. In this talk, numerical and ______Kyle Claassen, University of Kansas; asymptotic analysis as well as experiments Mathew Johnson (University of Kansas) of the viscous fluid conduit system will be EIT 219: Recent Advances Schr\”odinger operators with periodic presented. Of particular interest are modula- potentials acting on antiperiodic function tions of periodic traveling wave solutions of on Numerical Methods for spaces present special challenges, as the the conduit equation. Approximate dark and Interface Problems ground state eigenvalues of such operators bright envelope soliton solutions have been Organizers: Xu Zhang, James B. Collins need not be simple, and the corresponding predicted and observed numerically to persist Speakers: Xu Zhang, Marcus Sarkis, Xiaoming He, eigen functions are not sign-definite. With for long times; these are well approximated Ruchi Guo, Nishant Panda an eye toward proving (orbital) stability of by a cubic Nonlinear Schrodinger equation in the weakly nonlinear regime, and move with antiperiodic standing waves in a class of 1041 - Superconvergence of fractional nonlinear Schr\”odinger equations, the group velocity of linear waves to leading we provide a general theory for characterizing order. The bright envelope solitons move with Immersed Finite Element Methods the $T$-antiperiodic ground states of linear negative velocity, so they are difficult to create Xu Zhang, Mississippi State University fractional Schr\”odinger operators having $T$- in a viscous conduit that is controllable only at Immersed finite element method (IFEM) is a periodic potentials. the bottom boundary. However, dark envelope class of finite element methods (FEM) that solitons exhibit positive velocity, so they should can solve interface problems with unfitted be accessible in an experimental setup. 1038 - Stable Operator Splitting meshes. Superconvergence is a phenomenon Method For Free Energy Calculations that the order of convergence at certain 1040 - Three-Dimensional Matched points is higher than the maximum order of Of One Atom Model Alternating Direction Implicit (ADI) convergence of numerical solutions. In this Tania Hazra, Department of Mathematics, University talk, we introduce some superconvergence of Alabama, Tuscaloosa, AL; Shan Zhao, Department Schemes for Solving the Heat properties of IFEM for one dimensional of Mathematics, University of Alabama, Tuscaloosa, Equation with Complex Interface interface problems. The key step in our analysis AL Zhihan Wei; Shan Zhao is constructing the so-called generalized The work explores the stability impact of the The Douglas alternating direction implicit orthogonal polynomials with discontinuous novel unconditionally stable operator splitting (ADI) method is a powerful finite difference weight function. We will show that IFE methods for solving the time dependent nonlin- method for solving parabolic equations, due to functions perfectly fit into the framework of ear Poisson-Boltzmann (NPB) equation for the its unconditional stability and high efficiency. generalized orthogonal polynomials. Finally, electrostatic analysis of solvated biomolecules. However, accuracy reduction is a serious issue we will demonstrate that IFE solutions inherit In a pseudo-transient continuation solution for the interface problem with jumps on the all desired superconvegence properties from of the NPB equation, the nonlinear term is interface and non-smooth solutions, especially standard FEM. In particular, on interface analytically integrated, so that the difficulties for three-dimensional (3D) problems. If the elements, superconvergence occurs at roots of in direct treatment of the strong nonlinearity jumps and its derivatives are given in a function generalized orthogonal polynomials. can be bypassed. There are several methods along the interface, we propose a novel tensor to solve the NPB equations. We are interested product decomposition to decouple 3D jump 1042 - Multiscale Variational in Alternating Direction Implicit (ADI) schemes conditions into essentially one-dimensional (1D) FETI-DP Discretization For High- and Locally-One Dimensional schemes (LOD). ones. Then, by combining with the matched The ADI methods are known to be conditionally interface and boundary (MIB) technique, the Contrast Problems stable, although being fully implicit. On the 1D conditions can be incorporated into the Marcus Sarkis, Worcester Polytecnic Institute other hand, LOD scheme is computationally ADI central difference discretization. Fast We combine the multiscale variational less expensive and LOD scheme based on im- algebraic solvers for perturbed tridiagonal method and adaptativeFETI-DP preconditioner plicit Euler integration is more stable than ADI systems are developed to maintain the techniques to design and rigorous analyze schemes. It has been observed that there is a computational efficiency. The proposed discretizations for the Darcy’s equations with noticeable difference between the linearized matched ADI approaches not only maintain high-contrast permeability. We establish a Poisson Boltzmann Equation result and ADI- both the unconditional stability property and priori second-order error estimates with hidden based NPB results in steady state solutions. the efficiency of Thomas algorithm, but also constants independently of the permeability. That motivated us to analyze the ADI schemes achieve spatially second order accuracy in This is a joint work with Prof. Alexandre and later on LOD schemes to detect the factor resolving complex geometries due to the MIB Madureira from LNCC, Petropolis, Brazil. for which the stability is getting affected. technique.
1039 - Soliton Envelopes in Viscous Conduits Michelle Maiden, University of Colorado Boulder; Mark Hoefer, University of Colorado Boulder Viscous fluid conduits provide an ideal system for the study of dissipationless, dispersive hydrodynamics. A dense, viscous fluid serves as the background medium through which a lighter, less viscous fluid buoyantly rises. If the interior fluid is continuously injected, a de-
20 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Session Abstracts | Saturday, October 1, 2016 | 1:30 p.m. - 3:10 p.m.
1043 - Multi-Physics Domain EIT 224: Partial Differential 1049 - Global Regularity And Long- Decomposition Method For Coupled Equations: Analysis, Time Behavior For The Solutions Porous Media Flow And Free Flow To 2D Boussinesq Equations Xiaoming He, Missouri University of Science and Computation, Modeling, and Ning Ju, Oklahoma State University Technology Applications New results recently obtained by the speaker Organizers: John Singler, Weiwei Hu The Navier-Stokes-Darcy and Stokes-Darcy about global regularity and long-time behavior Speakers: John Singler, Weiwei Hu, Taige Wang, models have attracted significant attention in for solutions to 2D Boussinesq equations will be Ning Ju the past fifteen years since it arises in many presented and discussed. applications such as surface water flows, groundwater flows in karst aquifers, petroleum 1046 - Model Reduction of a Nonlinear EIT 318: Highly Accurate and extraction and industrial filtration. It has higher Cable-Mass PDE System with fidelity than either the Darcy or Navier-Stokes Dynamic Boundary Input Effective Numerical Methods systems on their own for the coupled flow John Singler, Missouri University of Science and problem. But coupling the two constituent for Partial Differential Equations Technology Organizers: Qin Sheng, Abdul Q.M. Khaliq, JaEun Ku models leads to a very complex system. Speakers: Weizhang Huang, Tiffany Jones, Haiyan This presentation discusses a multi-physics We perform balanced truncation model Tian, Ruihua Liu domain decomposition method for solving the reduction of a nonlinear PDE system modeling Navier-Stokes-Darcy system. Convergence the motion of a flexible cable attached to a is demonstrated and computational results mass-spring system at each end. The input to 1050 - Conditioning Of Finite Element are presented to illustrate the features of the the system is the driving force to the mass- Equations With Arbitrary Nonuniform proposed method. spring system at the left end, and the output Meshes of interest is the displacement and velocity Weizhang Huang, University of Kansas 1044 - A Class of Immersed of the mass at the right end. We present (1) theoretical results for the PDE system and (2) Mesh adaptation has become an indispensable Finite Element Spaces Defined numerical results comparing the input-output tool for use in the numerical solution of partial by the Actual Interface response of the nonlinear PDE system and the differential equations to improve computation- Ruchi Guo, Virginia Tech nonlinear reduced order model. al accuracy and efficiency. However, mesh adaptation often leads to nonuniform meshes In this talk, we present a new class of and their nonuniformity can have significant immersed finite element (IFE) spaces defined 1047 - Boundary Control for Optimal impacts on the conditioning and the efficient by the actual interface for solving the second Mixing by Stokes Flows solution of the underlying algebraic systems. order elliptic interface problems on Cartesian Weiwei Hu, Oklahoma State University In this talk we will present some new results meshes. Functions in these IFE spaces are in the studies of those impacts for the finite locally piecewise polynomials and constructed We discuss the optimal boundary control element approximation of boundary value and with either linear polynomials, or bilinear problem for mixing an inhomogeneous initial-boundary value problems of linear diffu- polynomials, or rotate-Q1 polynomials, or distribution of a passive scalar field in an sion equations. Crouzeix-Raviart polynomials. We will discuss unsteady Stokes flow. The problem is the unisolvence, boundedness and optimal motivated by mixing the fluids within a cavity approximation capability of these IFE spaces by or vessel at low Reynolds numbers by moving 1051 - Asymptotic Stability of a a new unified framework. the walls or stirring at the boundaries. It is Decomposed Compact Method for natural to consider the velocity field induced by a control input tangentially acting on the Highly Oscillatory Wave Problems 1045 - Stochastic Inverse Problem boundary of the domain through the Navier Tiffany Jones, Baylor University For Internal Boundaries: A Measure slip boundary conditions. Our main objective is The paraxial Helmholtz equation describes Theoretic Solution to design an optimal Navier boundary control the propogation of electromagnetic waves Nishant Panda, Colorado State University that optimizes mixing at a given final time. A in the form of either paraboloidal waves or rigorous proof of the existence of an optimal Gaussian beams. Becuase most lasers emit In this talk, we present a measure theoretic controller is presented and the first-order beams of this form, this equation is used framework to infer internal boundaries, the necessary conditions for optimality are derived. frequently in beam propagation computations, initial configuration of which is uncertain. This particularly within focal regions. This paper is a typical scenario in modeling geophysical concerns a decomposed compact scheme quantities like flow through porous rocks, 1048 - A Thixotropic Flow for solving a highly oscillatory paraxial where distinct rock regions form an interface Dynamics Under Large Amplitude Helmholtz problem with a large wave number in whose precise description is difficult to obtain. Oscillatory Shearing radially symmetric fields. We are particularly We first present an abstract model in which Taige Wang, Virginia Tech interested in decomposition schemes that the random interface is parametrized in finite are highly accurate in transverse directions dimensions, for example piecewise linear, The PEC (partially extending strand convection) as well as highly efficient and effective for piecewise spline etc. Then, given a distribution model of Larson is able to describe thixotropic practical applications. The decomposition is on some observed quantity we determine a yield stress behavior in the limit where the utilized in the transverse direction to eliminate distribution on the parametrized interface. A relaxation time is large. In this talk, we discuss the singularity of the differential equation in partition of unity is then used to reconstruct the the dynamic behavior of the model under an polar coordinates. Special attention is paid random interface. imposed periodic shear force τ (t) = B sin(ωt). We identify regimes of fast, slow and yielded to the numerical stability of the proposed dynamics. The multiscale analysis turns out decomposition algorithm. It is shown that the to be mathematically crucial for the analysis numerical method introduced is proven to be among the dynamics. stable in an asymptotic sense. The method
21 Society for Industrial and Applied Mathematics
Session Abstracts | Saturday, October 1, 2016 | 1:30 p.m. - 3:10 p.m. is also highly accurate and efficient due to the shape transformation of biological lipid 1056 - Improvements On A Matched its straightforward algorithmic structure. vesicles. In this talk, we present some efficient Interface And Boundary (MIB) Method Computational examples are presented to and stable numerical methods for simulating illustrate our conclusions. the unconstrained phase fi eld Willmore For Solving Parabolic Interface dynamics and the phase fi eld Willmore Problems 1052 - The Method Of Fictitious dynamics with fixed volume and surface Chuan Li, West Chester University of Pennsylvania area constraints. The proposed methods can Time Integration And Approximate be high-order accurate and are completely Many computational biophysics applications Fundamental Solutions For explicit in nature, by combining exponential can all be mathematically modeled as the time differencing Runge-Kutta approximations parabolic interface problems. The standard Nonlinear Elliptic PDEs numerical methods for solving partial Haiyan Tian, The University of Southern Mississippi for time integration with spectral discretizations for spatial operators on regular meshes. We differential equations (PDEs) often perform Through a fictitious time approach, a nonlinear also incorporate novel linear operator splitting poorly for the parabolic interface problems elliptic-type PDE problem is converted into a techniques into the numerical schemes to due to the fact that the physical solutions are time-dependent quasilinear problem. This is improve the discrete energy stability. In order usually non-smooth or even discontinuous further approximated by a sequence of time- to avoid extra numerical instability brought by across the arbitrarily shaped interface of dependent linear nonhomogeneous modified use of large penalty parameters in solving the two media. In this talk, I will present our most Helmholtz boundary value problems, which are constrained phase fi eld Willmore dynamics recent work of developing of a matched solved by the method of particular solutions of problem, a modified augmented Lagrange interface and boundary (MIB) method in the Delta-shaped basis functions and approximate multiplier approach is proposed and adopted. direction of improving the scheme for handling fundamental solutions. Numerical results are Various numerical experiments are performed more complex 2D geometries and interface provided to show the accuracy and validity of to demonstrate accuracy and stability of the conditions. This work is collaborated with Dr. the computational method. proposed methods. Shan Zhao from the University of Alabama.
1053 - Numerical Methods for 1055 - An ADI preconditioner for 1057 - The Legacy Of ADI And LOD Option Pricing in Regime-Switching solving discrete Helmholtz equation Methods And Their Application In Jump Diffusion Models Wenyuan Liao, University of Calgary Solving Highly Oscillatory Wave Ruihua Liu, University of Dayton Numerical solution of multi-dimensional Problems This presentation is concerned with numerical Helmholtz equation with high wave number Qin Sheng, Baylor University methods for pricing options in regime- is a challenging computational task, mainly Different operator splitting methods have been switching jump diffusion models. Option because of two reasons. First, due to the high playing an important role in computations values are computed by solving a system of m wave number, it is required that the continuous of numerical solutions of partial differential coupled partial integro-differential equations Helmholtz equation should be discretized by equations. Modern numerical strategies (PIDE), where m>1 is the number of regimes a very fine grid, which leads to a huge linear including mesh adaptations, linear and considered for the market. We develop algebraic system. It is even worse for the high nonlinear transformations are also utilized a tree method based on the probabilistic wave number case, as a fixed number grid together with splitting algorithms in representation of the option values as an points per wavelength is required. The large applications. This will be a brief survey talk expectation of discounted payoff under a size of the linear algebraic system makes it for two cornerstones of the operator splitting, risk-neutral probability measure. The proposed difficult to use direct method, in particular in that is, Alternating Direction Implicit (ADI) and trees grow linearly as the number of tree steps higher-dimensional cases. Second, the discrete Local One-Dimensional (LOD) methods, as well increases, and can be used for both European Helmholtz equation is a highly indefinite linear as their applications together with an eikonal and American options. Numerical results are algebraic system which is extremely hard to mapping for solving highly oscillatory paraxial reported and compared with a finite-difference be solved by classical iterative methods. For optical wave equations in slowly varying (FD) method. example, many classical iterative methods envelope approximations of active laser beams. such as conjugate method converges slowly The resulted finite difference scheme is not or not even converge. In this work an operator only oscillation-free, but also asymptotically EIT 319: Operator Splitting splitting technique is used to factorize the 2D stable. This ensures the high efficiency and or 3D Helmholtz equation into a sequence of applicability in industrial applications. Methods For Numerical PDEs 1D Helmholtz equations, which is then directly solved by efficient tridiagonal solver. This ADI And Their Applications solver is then used a preconditioner which is Organizers: Shan Zhao, Qin Sheng combined with the regular iterative methods Speakers: Lili Ju, Wenyuan Liao, Chuan Li, to form an efficient preconditioned iterative Qin Sheng method. Numerical experiments are conducted and numerical results are compared with other 1054 - Efficient and Stable Exponential popular methods, which demonstrated that the Time Differencing Runge-Kutta new method is accurate, efficient and efficient in solving the Helmholtz equation with high Methods for Phase Field Elastic wave number. Bending Energy Models Lili Ju, University of South Carolina The Willmore flow formulated by phase field dynamics based on the elastic bending energy model has been widely used to describe
22 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Session Abstracts | Saturday, October 1, 2016 | 1:30 p.m. - 3:10 p.m.
EIT 321: Modeling and the non-compactness of the evolution operator experimental data sets. In particular we show by using the monotone iteration method. our recent application for diffusion tensor Computations for General and imaging (DTI) of the human brain. Chaotic Biological Systems 1061 - A Picewise Linear Maximum Organizers: Majid Bani-Yaghoub, Naveen K. Vaidya, Entropy Method for Invariant 1065 - Hclust Barcodes Xianping Li, Noah Rhee Leyda Almodóvar Velázquez, Stonehill College Speakers: Noah Rhee, Peter Uhl, Minh Nguyen, Jiu Measures of Random Maps In persistent homology, a barcode keeps track Ding Jiu Ding, The University of Southern Mississippi of the birth and death of cycles. In the case We present a numerical method for the of the H_0 barcode, if all 0-cycles are born 1058 - Biological Systems And Chaos approximation of absolutely continuous at time 0 (which is usually the case when Noah Rhee, University of Missouri-Kansas City invariant measures of one dimensional analyzing data), the H_0 barcode can be position dependent random maps, based on In this paper, given a chaotic map, we show obtained from the single linkage hierarchical the maximum entropy principle and piecewise clustering dendrogram where the death time that Ulam’s method generate a sequence linear moment functions. Numerical results of density functions in L^1-space that may of a component corresponds to a merge point are presented to show the convergence of the in the dendrogram. In a similar way, we can converge weakly to a function in L^1-space. In method. such a case we show that the limiting function create hclust barcodes using any method of generates an absolutely continuous invariant hierarchical clustering. We compare single, measure. This fact can be used to analyze average, complete, and Ward’s linkage some biological systems that may exhibit EIT 323: Applied and hclust barcodes. This work was performed chaotic behavior. in collaboration with Isabel Darcy and Paul Computational Topology Samuel Ignacio. Organizers: Henry Adams, Patrick Shipman 1059 - Some Properties Of A One Speakers: Michael Lesnick, Matthew Wright, Ma- Parameter Family Of Solutions To The teusz Juda, Leyda Almodóvar Velázquez Inverse Frobenius- Perron Problem EIT 325: Interactions Among Peter Uhl, University of Missouri- Kansas City 1062 - Interactive Visualization Analysis, Optimization And In this paper we give a review of the Inverse of 2-D Persistence Modules Michael Lesnick, Princeton University Network Science Frobenius- Perron problem (IFPP) developed Organizers: Pietro Poggi-Corradini, Nathan Albin by Rogers et al: how to create chaotic maps Matthew Wright and I have designed a Speakers: Pietro Poggi-Corradini, Mario Bonk, Brian with the desired piecewise constant invariant tool for the interactive visualization of 2-D Benson, David Aristoff, Nathan Albin density. While this method provides infinitely persistent homology. In this talk, I’ll discuss the many chaotic map solutions, we study three mathematical foundations of this tool. properties of one parameter family of chaotic 1066 - The Probabilistic Interpretation map solutions. First, we show that the desired 1063 - Computing Multidimensional Of 2-Modulus On Networks invariant density can be approximated by each Pietro Poggi-Corradini, Kansas State University truncated orbit generated from these solutions. Persistent Homology Matthew Wright, St. Olaf College I will present on overview of ongoing research Then we numerically develop the average error being done by the NODE research group formula that depends on the parameter. We Multidimensional persistent homology is (https://node.math.ksu.edu/) at Kansas State also show that individual errors are distributed highly relevant in applications that require University. The theory of modulus was normally. Second, we show that the fixed point the analysis of data which is simultaneously originally developed in complex analysis and iteration using the Frobenius- Perron operators filtered by two or more parameters. However, was then used to extend the notion of (quasi) associated with these solutions converge to the algebraic complexity of multidimensional conformal maps to higher dimensional real the desired invariant density starting from any persistence modules makes it difficult to extract Euclidean spaces and, in fact, to abstract piecewise constant density and also show useful invariants in this setting. In this talk, I metric measure spaces. On networks, modulus how the rate of convergence of the fixed point will describe recent work with Mike Lesnick provides a method for quantifying the richness iteration depends on the parameter . Finally, to efficiently compute and visualize both the of a family of objects. Some examples of we study the autocorrelation of each orbit bigraded Betti numbers and the rank invariant families of objects that we have studied are: generated by these solutions, and show how of two-dimensional persistence modules. I will families of walks, families of spanning trees, the autocorrelation with finite time lag depends focus on computational challenges and current families of simple loops, etc. Using convex on the parameter, and also present numerical work to overcome such obstacles. duality, we have shown that modulus has a simulations. probabilistic interpretation. Namely, modulus 1064 - Combinatorial Multivector tries to minimize the expected overlap among 1060 - Monotone Traveling Waves Fields the objects in the family and as a result it In A General Discrete Model For Mateusz Juda, Jagiellonian University spreads the expected edge-usage the family makes of each edge in the network. Populations In this talk we introduce theory, algorithms, Minh Nguyen, University of Arkansas at Little Rock and software for analysis of vector fields given 1067 - Discretizations And In this talk we consider the existence of by finite sample. We generalize combinatorial monotone traveling waves for a class vector fields proposed by Forman. We show Analytic Structure Mario Bonk, UCLA of general integral difference model for definitions of attractors, repellers, and Morse populations that allows the dispersal probability sets in combinatorial setting using Lefschetz How much of the analytic structure of a to have no continuous density functions but the complexes and partial orders. We show metric space can be captured by its discrete fecundity functions to generate a monotone examples constructed by the algorithms approximations? In my talk I will discuss this dynamical systems. In this setting we deal with for: flows given by differential equations, problem in two related contexts, namely for
23 Society for Industrial and Applied Mathematics
Session Abstracts | Saturday, October 1, 2016 | 1:30 p.m. - 3:10 p.m.
Sobolev functions on the space (joint work with providing deeper insight into the optimal pmfs model (FOM) over a long-term simulation while E. Saksman) and for moduli of path families for the graph. greatly reducing the computational cost. The (work by J. Lindquist). proposed ROM is then regarded as a surrogate of FOM and is applied to an inverse problem 1068 - Curvature of Discrete Graphs ETAS 229: Recent Advances for identifying the order of the time-fractional Brian Benson, Kansas State University derivative of the TFPDE model. Based on the in Fractional PDEs Levenberg--Marquardt regularization iterative There are several approaches to interpreting Organizers: Yanzhi Zhang method with the Armijo rule, we develop a the concept of curvature, as defined on a Speakers: Janna Lierl, Pablo Stinga, Zhu Wang, ROM-based algorithm for solving the inverse Riemannian manifold, on a discrete graph. In Nan Jiang, Yong Zhang problem. For cases in which the observation 1985, Bakry and Emery suggested an invariant data is either uncontaminated or contaminated on the graph based on a Markov semigroup. 1071 - Boundary Harnack Principle For by random noise, the proposed approach is Specifically, this invariant replaces a bound able to achieve accurate parameter estimation on curvature for estimates on graphs which Nonsymmetric Stable-Like Operators efficiently. are analogues of those on manifolds. In 2007, On Smooth Open Sets Ollivier used a more geometric observation to Janna Lierl, University of Connecticut define a notion of curvature on graphs which is 1074 - A Fractional Laplacian- not equivalent to that of Bakry-Emery. Ollivier’s Consider a nonsymmetric stable-like operator Based Closure Model for curvature is related to solving transport with jump intensities $\kappa(x,y)|x-y|^{-d-\ alpha}$ for $x,y \in R^d$, where $\alpha \in Turbulent Fluid Flows problems on the graph. I will discuss work in Nan Jiang, Missouri University of Science (0,2)$. I will show that under mild assumptions progress related to these topics which is joint and Technology with Peter Ralli and Prasad Tetali. on $\kappa$, a boundary Harnack principle holds on any $C^{1,1}$-open set $D$ with Nonlocal Models have attracted intensive explicit boundary decay rate dist$(\cdot,\partial research interests in recent years due to their 1069 - Structure Of Large Graphs With D)^{\alpha/2}$. ability to model phenomena that can not be Constraints correctly described by classical local PDE David Aristoff, Colorado State University 1072 - Extension Problem For models. In particular, fractional derivative models have been found to be very effective We consider large graphs with a finite number Fractional Powers Of Parabolic in modeling anomalous diffusion processes. In of constraints on subgraph densities. What Operators And Applications this talk, we will present a new closure model is the “most likely” structure of such graphs? Pablo Raúl Stinga, Iowa State University based on the fractional Laplacian operator The answer can be obtained by solving a that accounts for the anomalous diffusion that certain variational problem. We conjecture By using the semigroup language approach arises in fully-developed turbulent fluid flows. that all solutions correspond to multipodal we show that the fractional powers of any Both theoretical aspect of the turbulence model graphs -- that is, graphs in which the vertex uniformly parabolic operator with time- and the numerical algorithms to implement the set can be divided into finitely many groups, dependent coefficients can be realized as a model will be discussed. with a constant connection probability any two Dirichlet-to-Neumann map through a parabolic groups. extension problem in one more dimension. In particular, the fractional powers of the 1075 - On The Ground States And heat operator are considered. Using this 1070 - Spanning Tree Modulus: characterization we obtain regularity estimates Dynamics Of Space Fractional Homogeneous Graphs and Deflation for nonlocal space-time equations, like the Nonlinear Schro ̈Dinger/Gross- Nathan Albin, Kansas State University master equation from continuous time random Pitaevskii Equations With Rotation walks, as the one considered by L. Caffarelli The concept of modulus of curve families Term And Nonlocal Nonlinear and L. Silvestre. These results are based on originated in the field of complex analysis as a a joint work with J. L. Torrea. As a particular Interactions conformally invariant way to describe the size case, we recover the extension problem for Yong Zhang, IRMAR, University of Rennes 1, France of a family of curves. The natural extension the Marchaud fractional derivative, which to discrete graphs provides a method for In this paper, we propose some efficient and was previously obtained in joint work with A. describing the size of a family of objects on a robust numerical methods to compute the Bernardis, F. J. Martín-Reyes and J. L. Torrea graph. This notion of size is more expressive ground states and dynamics of Fractional than simply counting the number of objects; it Schrodinger Equation (FSE) with a rotation is also sensitive to individual object size and to 1073 - POD Reduced-Order Modeling term and nonlocal nonlinear interactions. In the diversity of edge use within the family. of Time-Fractional Partial Differential particular, a newly developed Gaussian-sum (GauSum) solver is used for the nonlocal This talk will focus on the modulus of the family Equations with Applications in of spanning trees on an unweighted, undirected interaction evaluation [31]. To compute the graph. Through standard techniques of Parameter Identification ground states, we integrate the preconditioned Lagrangian duality, the modulus problem can Zhu Wang, University of South Carolina Krylov subspace pseudo- spectral method [4] and the GauSum solver. For the dynamics be shown to be equivalent to the problem of In this paper, a reduced-order model (ROM) simulation, using the rotating Lagrangian choosing a probability mass function (pmf) on based on the proper orthogonal decomposition coordinates transform [14], we first reformulate the family of spanning trees that minimizes (POD) method is proposed for efficiently the FSE into a new equation without rotation. the expected overlap of two independently simulating time-fractional partial differential Then, a time-splitting pseudo-spectral scheme selected random trees. This view of the equations (TFPDEs). We demonstrate the incorporated with the GauSum solver is modulus problem leads to a Deflation Theorem, effectiveness of the POD-ROM by several proposed to simulate the new FSE. In parallel which describes the spanning tree modulus numerical examples, in which the ROM to the numerical schemes, we also prove structure of a graph through a sequence of achieves the same accuracy of the full-order simple “subgraph deflation” steps, ultimately some existence and nonexistence results for
24 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Session Abstracts | Saturday, October 1, 2016 | 1:30 p.m. - 3:10 p.m. the ground states. Dynamical laws of some atmospheric problems. Improper treatment of super convergence property is not observed standard quantities, including the mass, energy, the gravitational force can lead to a solution with the classical SIPG method. [1] Yekaterina angular momentum and the center of mass, which oscillates around the equilibrium. In this Epshteyn and Alexander Kurganov. New are stated. The ground states properties with presentation, we propose a recently developed interior penalty discontinuous Galerkin methods respect to the fractional order and/or rotating well-balanced finite volume WENO method for the Keller-Segel chemotaxis model. SIAM frequencies, dynamics involving decoherence for the Euler equations under gravitational J. Numer. Anal., 47(1):386–408, 2008/09. [2] and turbulence together with some interesting fields, which can maintain the isothermal Yekaterina Epshteyn, Discontinuous Galerkin phenomena are reported. and polytropic hydrostatic equilibrium states methods for the chemotaxis and haptotaxis exactly. Some numerical tests are performed models. J. Comput. Appl. Math., 224(1):168–181, to verify the well-balanced property, high-order 2009. [3] Shu-C.-W. Li, X. H. and Y. Yang. Local accuracy, and good resolution for smooth and discontinuous Galerkin methods for the Keller- ETAS 230: Numerical discontinuous solutions. Segel chemotaxis model. Approximation And Analysis For Time Dependent PDEs 1078 - High Order Diffuse-Domain Organizer: Cheng Wang, Steve Wise Methods for Partial Differential ETAS 480: Some Novel Speaker order: Amanda Diegel, Yulong Xing, Equations in Complex Geometries Fei Yu, Jue Yan Computational Methods Fei Yu, University of California, Irvine For PDEs 1076 - A Second Order in Time Recently, Li et al. (Comm. Math. Sci., 7:81-107, Organizers: Huiqing Zhu 2009) developed a diffuse domain method Speakers: Sheng-Wei Chi, Balaram KhatriGhimire, Finite Element Scheme for the Cahn- (DDM) in order to solve partial differential Jun Liu, Sheldon Wang, Daniel Waston Hilliard-Navier-Stokes Equations equations (PDE) on complex geometries. .In Amanda Diegel, Louisiana State University this approach the complex geometry was 1080 - High Order Gradient embedded into a larger, regular domain. The In this talk, we present a second order in original PDE was reformulated with a phase Reproducing Kernel Collocation time mixed finite element method for the field function, which smoothly approximates the Cahn-Hilliard equation coupled with a Navier- Method for Phase Field Fracture characteristic function of the original domain, Stokes flow that models phase separation Model plus additional source terms that approximate and coupled fluid flow in immiscible binary Sheng-Wei Chi, University of Illinois at Chicago the boundary conditions. Later Lerv{\aa} fluids in two and three dimensions. We will g and Lowengrub (Comm. Math. Sci., 2014) The Reproducing Kernel approximation in discuss the main results of the numerical performed a matched asymptotic analysis of conjunction with the Collocation Method scheme including the following. We show that general diffuse domain methods for Neumann (RKCM) was introduced for solutions of PDEs our scheme is unconditionally energy stable and Robin boundary conditions and showed and engineering problems for some time. with respect to a spatially discrete analogue that for certain choices of boundary condition Although it offers only algebraic convergence, of the continuous free energy of the system. approximations the DDM is second-order being less sensitive to the nodal distribution Additionally, we show that the discrete phase accurate in \(\epsilon\), which characterizes and of compact structure, thus better variable is bounded in L^\infty(0,T;L^2) and the the width of the region over which the conditioning, make it an attractive method discrete chemical potential is bounded in L^\ characteristic function is smoothed. We extend for engineering applications. However, taking infty(0,T;L^2), for any time and space step sizes, this analysis to PDEs with Dirichlet boundary direct derivatives of the reproducing kernel in two and three dimensions, and for any finite conditions and show that by perturbing the approximation is computationally expensive, final time T. We subsequently prove that these reformulated equation in a certain way, we are in comparison to other commonly used variables converge with optimal rates in the able to achieve second-order accuracy in \(\ approximations for collocation methods, appropriate energy norms in both two and three epsilon\). Our analytic results are confirmed such as RBFs. In this work, we address the dimensions. Hydrodynamical evolution in a numerically in the \(L^2\) norm for selected test high computational cost in the RKCM while gravitational field arises in many astrophysical cases. achieving optimal convergence by adopting and atmospheric problems. Improper treatment gradient reproduction kernel approximations of the gravitational force can lead to a solution for all derivatives involved in a PDE. In which oscillates around the equilibrium. In this 1079 - Fourier Type Error Analysis contrast to the earlier work, both first order presentation, we propose a recently developed On The Solution Gradient’s Super and second order derivatives involved in the well-balanced finite volume WENO method Convergence Of Direct DG Methods approximation for a second order PDE are for the Euler equations under gravitational Jue Yan, Iowa State University expressed by gradient reproducing kernels fields, which can maintain the isothermal in the present method, termed High order and polytropic hydrostatic equilibrium states Different to [1] [2] and [3], we develop direct Gradient Reproducing Kernel Method (HG- exactly. Some numerical tests are performed discontinuous Galerkin method with interface RKCM). We show that the same number of to verify the well-balanced property, high-order correction(DDGIC) and symmetric DDG collocation points and source points can be accuracy, and good resolution for smooth and methods to directly solve chemotaxis Keller- used in the HG-RKCM for optimal convergence. discontinuous solutions. Segel equations. Numerically we observe no The numerical studies show that the present order loss and obtain optimal convergence with method is roughly 10 times faster than the 1077 - High Order Finite Volume WENO $P^k$ polynomial approximations. The reason RKCM. The method is applied to fracture behind is that DDGIC and symmetric DDG modeling based on the phase field model. Methods For The Euler Equations With methods have the hidden super convergence Gravitation property on the solution’s gradient. With Fourier Yulong Xing, University of California Riverside analysis technique, we prove the polynomial solution’s spatial derivative is super convergent Hydrodynamical evolution in a gravitational to the exact solutions spatial derivative in the field arises in many astrophysical and weak sense or in some momentum sense. The
25 Society for Industrial and Applied Mathematics
Session Abstracts | Saturday, October 1, 2016 | 1:30 p.m. - 3:10 p.m.
1081 - Hybrid Chebyshev Polynomial be reconstructed with model reduction derivatives in space and stiff reactions, remain. Scheme For The Numerical Solution techniques. The incentive of this seemingly Here, we incorporate the sparse grids with the opposite approach is to utilize existing implicit integration factor method (IIF) that is Of Elliptic PDEs computational fluid dynamics (CFD) and advantageous in terms of stability conditions Balaram KhatriGhimire, Delta State University finite element method (FEM) packages in for systems containing stiff reactions and In this talk, we propose hybrid Chebyshev engineering practice and to provide guidance diffusions. We combine IIF, in which the polynomial scheme (HCPS), which combines on the importance of accurate prediction of reaction is treated implicitly and the diffusion two matrix systems of Chebyshev polynomial resonance frequency in turbulent induced is treated explicitly and exactly, with various scheme into a single matrix system. This hybrid sound production for example vocal tracks. sparse grid techniques based on the finite formulation requires solving only one system We also explore the effects of noise on these element and finite difference methods and a of equations and opens up the possibilities predictions. multi-level combination approach. The overall of solving large class of partial differential method is found to be efficient in terms of both equations (PDEs). We consider problems 1084 - A Matrix Decomposition RBF storage and computational time for solving a wide range of PDEs in high dimensions. governed by the Poisson equation and the Differential Quadrature Algorithm inhomogeneous Cauchy-Navier equations. In particular, the IIF with the sparse grid The solution is approximated by the sum for Solving Elliptic Boundary Value combination technique is flexible and of particular solution and homogeneous Problems effective in solving systems that may include solution. Chebyshev polynomials are used to Daniel Watson, University of Southern MIssissippi cross-derivatives and non-constant diffusion approximate a particular solution of a PDE. The coefficients. Extensive numerical simulations This talk discusses a differential quadrature Laplacian or biharmonic operator is kept on in both linear and nonlinear systems in high (DQ)-radial basis function (RBF) method for the left hand side and all the other terms are dimensions, along with applications of diffusive the numerical solution of elliptic boundary moved to the right hand side and treated as a logistic equations and Fokker-Planck equations, value problems in circular domains. With an forcing term. Numerical results show that our demonstrate the accuracy, efficiency, and appropriate selection of collocation points, for approach is highly accurate and stable. robustness of the new methods, indicating any choice of RBF, the matrices in the systems potential broad applications of the sparse grid- appearing in this discretization possess block based integration factor method. 1082 - Multilevel Discretize-then- circulant structures. These linear systems Optimize Algorithms for PDE- can thus be solved efficiently using matrix 1086 - An Adaptive Multiresoluton Constrained Optimizations decomposition algorithms (MDAs) and fast Fourier transforms (FFTs). In particular, we Discontinuous Galerkin Method for Jun Liu, Jackson State University consider problems governed by the Poisson Time-Dependent Transport Equations In this talk, we first review some multigrid/ equation, the inhomogeneous biharmonic multilevel algorithms that have been equation and the inhomogeneous Cauchy- in Multi-dimensions Yingda Cheng, Michigan State University proposed for solving discretized optimization Navier equations of elasticity. In addition to (or optimal control) problems governed by its simplicity, the proposed method can both In this talk, we present an adaptive PDEs, in particular within the context of \ achieve high accuracy and solve large-scale multiresolution DG method for time-dependent textit{discretize-then-optimize} approach. Some problems. The feasibility of the proposed transport equations. The scheme is constructed numerical comparison and new perspectives techniques is illustrated by several numerical based on the standard weak form of DG method will be presented. Moreover, to illustrate an examples. for hyperbolic equations and the multiwavelets interesting counter-intuitive phenomenon, of Alpert. We show that our scheme can an inconsistent discretization based on naturally go back to a sparse grid DG method, Simpson’s rule for the objective functional saving computational cost, when the solution will be discussed. Numerically, the observed ETAS 483: Recent Advance on possess sufficient smoothness. When the convergence failure can be recovered by solution is no longer smooth, the adaptive adding a suitable H1 regularization/penalty term High Order Numerical Methods algorithm that uses the hierarchical surplus with very little extra costs. for Partial Differential Equations as the refinement or coarsening indicator, can Organizers: Yuan Liu, Yingda Cheng automatically capture the local structures. 1083 - Mixed Finite Element Speakers: Weitao Chen, Yingda Cheng, Huijing Du, We use the Hash table as the underlying Wei Guo data structure and can deal with equations Formulations and Resonance in arbitrary dimensions. By using the DG Frequency Predictions for 1085 - Semi-Implicit Integration Factor framework, many nice properties are retained Acoustoelastic Fluid-Structure for the transport equations. The numerical Methods On Sparse Grids For High- scheme is validated by benchmark tests with Interactions Dimensional Systems smooth and nonsmooth solutions, and the Sheldon (Xiaodong) Wang, Midwestern State Weitao Chen, Department of Math, University of standard Vlasov-Poisson (VP) system and University California, Irvine oscillatory VP system. It is very important to have a reliable finite Numerical methods for partial differential element formulation for the prediction of equations in high-dimensional spaces are resonance frequencies within fluid-solid often limited by the curse of dimensionality. interaction systems in which compressibility Though the sparse grid technique, based on for both fluid and solid media as well as their a one-dimensional hierarchical basis through interactions are important. In this work, we tensor products, is popular for handling review two mixed finite element formulations challenges such as those associated with proven to be reliable for this type of systems spatial discretization, the stability conditions on and relate them to transient analysis data time step size due to temporal discretization, from which the resonance frequency might such as those associated with high-order
26 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Session Abstracts | Saturday, October 1, 2016 | 3:50 p.m. - 5:30 p.m.
1087 - Multiscale Computational Saturday, October 1, 2016 1092 - A Moving Mesh Discontinuous Models of Complex Biological 3:50 p.m. - 5:30 p.m. Galerkin Method For Hyperbolic Systems ______Conservation Laws Huijing Du, University of Nebraska, Lincoln Dongmi Luo, Xiamen University Computational biology is concerned with EIT 219: Mesh Adaption for A moving mesh discontinuous Galerkin method the modeling and simulation of biological is developed for the numerical solution of phenomena, processes and systems. A Numerical Simulations hyperbolic conservation laws. The method is Organizers: Xianping Li, Weizhang Huang large number of discrete and continuous a combination of the discontinuous Galerkin Speakers: Runchang Lin, Cuong Ngo, Brandon Reyes, models have made remarkable progresses method and the mesh movement strategy Dongmi Luo, Xianping Li for the description of subcellular systems, which is based on the moving mesh partial physiological dynamics, developmental and differential equation approach and moves the population biology. Almost always, these 1089 - A Discontinuous Galerkin Least- mesh continuously in time and orderly in space traditional models are focused on single Squares Finite Element Method For using a system of mesh partial differential biological scales. As the need for a detailed Solving Coupled Singularly Perturbed equations. It not only can achieve the high mechanistic understanding of biological order in smooth regions, but also capture function grows, the single-scale limitation of Reaction-Diffusion Equations shocks well in nonsmooth regions. For the conventional models is no longer adequate. Runchang Lin, Texas A&M International University same number of grid points, the numerical To setup an approach spanning multiple levels A discontinuous Galerkin least-squares finite solution with the moving mesh method is much of biophysical reality, I will describe a new 3D element method is proposed to solve coupled better than ones with the uniform mesh method. hybrid framework which includes three major reaction-diffusion equations with singular Numerical examples are presented to show the submodels: the discrete stochastic Subcellular perturbations. This method produces solutions accuracy and shock-capturing features of the Element Model for individual cellular activity; without numerical oscillations when uniform method. continuum reaction-diffusion-advection meshes are used. Numerical examples are partial differential equations of extracellular provided to demonstrate the efficiency of the 1093 - Anisotropic Mesh Adaptation biomolecules; a stochastic decision-making method. model for cell lineage transition. Our results For Image Scaling demonstrate how a modeling approach Xianping Li, University of Missouri-Kansas City 1090 - An Adaptive Moving Mesh coupling biologically relevant scales can We present the results using anisotropic mesh provide new insights into the complex Numerical Solution To The Porous adaptation in image scaling. A 2D image is biological problems related to intestinal Medium Equation represented by an anisotropic triangular mesh. crypt structure, embryonic development and Cuong Ngo, The University of Kansas Then the image information on the mesh is epidermal tissue regeneration. saved in a compressed file (encoding). The We present an adaptive moving mesh method image can be reconstructed (decoding) to any 1088 - An Asymptotic Preserving for a numerical solution to the porous medium desired scale. Linear and higher order finite equation with and without variable exponents element interpolation methods are investigated Maxwell Solver Resulting in the and absorption. It is based on the moving mesh for image reconstruction. The results show Darwin Limit of Electrodynamics partial differential equation approach, and that anisotropic mesh adaptation provides Wei Guo, Michigan State University shows a first-order convergence for uniform good quality for image scaling, especially for and arclength-based adaptive meshes and a upscaling. In plasma simulations, where the speed of second-order convergence for Hessian-based light divided by a characteristic length is at adaptive meshes. The method is applicable a much higher frequency than other relevant for solutions where the free boundaries have parameters in the underlying system, such as complex shapes and behaviors, and also the plasma frequency, implicit methods begin for porous medium equations with variable EIT 224: Partial Differential to play an important role in generating efficient exponents and absorption. Numerical results in Equations: Analysis, solutions in these multi-scale problems. Under two dimensions will be presented. conditions of scale separation, one can rescale Computation, Modeling, Maxwell’s equations in such a way as to give a magneto static limit known as the Darwin 1091 - An Efficient Power-Aware and Applications approximation of electromagnetics. In this Algorithm For A Class Of Stochastic Organizers: John Singler, Weiwei Hu talk, we present a new approach to solve Speakers: Jiahong Wu, Wenqing Hu, Yang Yang, Models Walter Rusin Maxwell’s equations based on a Method of Brandon Reyes, Colorado School of Mines Lines Transpose formulation, combined with We consider a class of partial differential a fast summation method with computational equation models with non-deterministic 1094 - The Two-Dimensional complexity O(NlogN), where N is the number parameters and develop an efficient parallel Boussinesq Equations With Partial of grid points. Under appropriate scaling, algorithm to compute, analyze, and quantify we show that the proposed schemes result Or Fractional Dissipation uncertainties in stochastic quantities of Jiahong Wu, Oklahoma State University in asymptotic preserving methods that can interest (QoI) induced by the parameters recover the Darwin limit of electrodynamics. dependent model. In addition to implementing The Boussinesq equations concerned here the parallel multilevel Monte Carlo based model geophysical flows such as atmospheric algorithm, we analyze the associated power fronts and ocean circulations. In addition, consumption while running the parallel code on they play an important role in the study of a cluster of high-performance computing nodes Rayleigh-Benard convection. Mathematically and hence develop efficient power-aware the 2D Boussinesq equations serve as a lower- strategies for simulating the QoI. dimensional model of the 3D hydrodynamics
27 Society for Industrial and Applied Mathematics
Session Abstracts | Saturday, October 1, 2016 | 3:50 p.m. - 5:30 p.m. equations. The global regularity problem on EIT 318: Highly Accurate and grid adaptations are frequently essential. It is the 2D Boussinesq equations with partial shown that the oscillation-free decomposition or fractional dissipation has attracted Effective Numerical Methods for method on arbitrary adaptive grids is considerable attention in the last few years. Partial Differential Equations asymptotically stable with a stability index one. This talk presents recent developments in Organizers: Qin Sheng, Abdul Q.M. Khaliq, JaEun Ku The result can be extended to multidimensional this direction. In particular, we detail the Speakers: JaEun Ku, Songming Hou, Qin Sheng, applications. Simulation experiments are given global regularity result on the 2D Boussinesq Wenyuan Liao to illustrate our concerns and conclusions. equations with vertical dissipation as well as some recent work on the 2D Boussinesq 2001 - An Accurate Numerical Method equations with general critical dissipation. If 1098 - Hybrid Finite Element Methods time permits, we will also briefly discuss the JaEun Ku, Oklahoma State University For Solving 3D Elastic Equation Using regularity problem on the partially dissipated A new hybrid mixed finite element method Helmholtz Decomposition Boussinesq equations in a bounded domain. will be introduced for efficient and accurate Wenyuan Liao, University of Calgary computations of flux variables. The method In an elastic migration or inversion problem, 1095 - On 2-D Incompressible Euler is a two--step method, based on a system of the P and S waves are trated separately, first-order equations for second-order elliptic thus efficient numerical solver is required to Equations With Partial Damping partial differential equations. On a coarse Wenqing Hu, Missouri University of Science and compute P and S wavefields. Direct solution mesh, the primary variable is approximated by Technology of an Elastic wave equation is computationally the standard Galerkin method. Then, on a fine costly, as it is a coupled system of partial We consider various questions about the mesh, an $H({\rm div})$ projection is sought differential equations (PDE). Numerical solution 2d incompressible Navier-Stokes and Euler as an accurate approximation for the flux of such model is of great interests to both equations on a torus when dissipation is variables. The computation on a finer mesh Mathematicians and Geophysicists working removed from or added to some of the Fourier can be carried out very efficiently using well on a variety of applications, geophysical modes. developed preconditioners for the $H({\rm div})$ exploration for instance. In particular numerical projection. Also, it will be shown that the mesh modeling of Elastic wave equation is an integral 1096 - Thermo-Acoustic Tomography size $h$ for the finer mesh can be taken as the part of full waveform inversion and other wave square of the coarse mesh size $H$, or a higher equation based seismic inversion methods. With Reflectors order power with a proper choice of parameter. Yang Yang, Purdue University Here we propose a new method, in which This means that the computational cost for the we first use the Helmholtz decomposition to Thermo-Acoustic tomography (TAT) is coarse-grid solution is negligible compared decouple the Elastic wave equation system a recently developed coupled physics to that for the fine-grid solution. This is a joint into four scalar acoustic wave equations, imaging modality. In this talk we discuss the work with Dr. Young Ju Lee and Dr. Dongwoo which are then efficiently solved by compact mathematical model of TAT with the presence Sheen. higher-order finite difference method with high of sound-hard reflectors. We propose an accuracy. Some novel boundary treatments averaged sharp time reversal algorithm which 1099 - Improved Imaging Methods for have been developed for the new equations. leads to an exponentially convergent Neumann Extended Targets The numerical solution of the Elastic wave series reconstruction. This is joint work with Songming Hou, Louisiana Tech University equation is reconstructed from the previously Plamen Stefanov. obtained numerical solutions of the four scalar The MUSIC algorithm is an efficient and robust PDEs. Finally numerical examples are solved to numerical method for imaging. However, some 1097 - Localized Anisotropic demonstrate the efficiency and effectiveness of numerical artifacts are observed around the the newly proposed numerical method. Regularity Conditions For The target(s). We proposed an improved imaging Navier-Stokes Equations method to generate imaging results better Walter Rusin, Oklahoma State University than those from the MUSIC algorithm. We also present some work on the forward solver for EIT 319: Operator Splitting In this talk, we present a sufficient regularity domains with multiple corners. condition for local solutions of the Navier- Methods For Numerical PDEs Stokes equations. We prove that for a suitable And Their Applications weak solution $(u,p)$ on a domain $D$, if $\ 2000 - An Asymptotic Stability of an Eikonal Splitting Method for Solving Organizers: Shan Zhao, Qin Sheng partial_3 u$ belongs to the space $L_t^{s_0} Speakers: Shan Zhao, Alexey Sukhinin, Xinfeng Liu, L_x^{r_0}(D)$ where $ 2/s_0 + 3/r_0 \le 2 $ and Paraxial Helmholtz Equations on JaEun Ku, Cheng Wang $9/4 \le r_0\le 5/2$, then the solution is regular. Arbitrary Transverse Grids Qin Sheng, Baylor University 2002 - Fast Operator Splitting This talk concerns the asymptotic stability Algorithms For The Electrostatic of an eikonal, or ray, transformation based Analysis Of Solvated Biomolecules splitting method for solving the paraxial Shan Zhao, University of Alabama Helmholtz equation with high wave numbers. The Poisson-Boltzmann (PB) equation is an Arbitrary grids are considered in transverse effective model for the electrostatics analysis directions. The differential equation targeted of solvated biomolecules. The nonlinearity has been used for modeling propagations of associated with the PB equation is critical high intensity laser pulses over a long distance when the underlying electrostatic potential without diffractions. Self-focusing of high is strong, but is extremely difficult to solve intensity beams may be balanced with the numerically. Recently, we have developed de-focusing effect of created ionized plasma an operator splitting framework, in which the channel in the situation, and applications of nonlinear subsystem is analytically integrated 28 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Session Abstracts | Saturday, October 1, 2016 | 3:50 p.m. - 5:30 p.m. so that the nonlinear instability is completely 2006 - A Second Order Operator 2008 - Modeling Viral Control by suppressed. For the linear subsystem, we Splitting Numerical Scheme For The CD8+ T Cells have explored the electrostatic solution by Libin Rong, Oakland University considering finite difference, finite element, ``Good” Boussinesq Equation And Its and discontinuous Galerkin methods. Fully Convergence Analysis CD8+ T cells play an important role implicit alternating direction implicit (ADI) and Cheng Wang, University of Massachusetts in controlling HIV or SIV (simian unconditionally stable locally one-dimensional Dartmouth immunodeficiency viruses) replication. The (LOD) methods have been developed for solving most convincing evidence comes from the the parabolic equation efficiently. The resulting The nonlinear stability and convergence experiment of CD8+ T cell depletion in SIV- PB solver scales linearly with respect to the analysis is presented for a second order infected nonhuman primates. Despite an number of atoms, and is promising for studying operator splitting scheme applied to the ``good” obvious temporal relationship between CD8 large macromolecules. Boussinesq equation, coupled with the Fourier decrease (increase) and viral load increase pseudo-spectral approximation in space. Due (decrease), there are still debates about the to the wave equation nature of the model, we 2003 - Spatio-Temporal Modeling of underlying explanation for the experimental have to rewrite it as a system of two equations, data. In this talk, I will use a mathematical Two-Color Filamentation for the original variable and its temporal model to study the dynamics of both T cells Alexey Sukhinin, SMU derivative, respectively. In turn, the second and virus during CD8+ T cell depletion and order operator splitting method could be In this talk, I will describe the basic subsequent recovery. The relative contributions efficiently designed. A careful Taylor expansion mathematical model of the simultaneous to viral control by the target cell availability and indicates the second order truncation error co-propagation of high intensity pulses with specific CD8+ T cell immune responses (direct of such a splitting approximation, and a different wavelengths and different temporal cell killing vs. non-killing) will be evaluated. linearized stability analysis for the numerical widths. Spatial and temporal effects will be error function yields the desired convergence presented based on analysis and numerical estimate in the energy norm. And also, 2009 - Optimal Control in Transmission simulations. Extension to the two-color the presented convergence analysis is Dynamics of Zoonotic Visceral filamentation model will be given and unconditional for the time step in terms of the discussed. Leishmaniasis spatial grid size, in comparison with a severe Songnian Zhao, Department of Industrial and restriction time step restriction required in Manufacturing Systems Engineering, Kansas State 2004 - Integration Factor Methods many existing works. University For A Class Of High Order Visceral Leishmaniasis (VL), a vector-borne Differential Equations disease caused by protozoan flagellates of Xinfeng Liu, University of South Carolina EIT 321: Modeling and the genus Leishmania, is transmitted by sand In this talk, we will present an efficient high- Computations for General and flies. After malaria, VL is the second-largest order integration factor method for solving a parasitic killer, responsible for an estimated family of high order differential equations, in Chaotic Biological Systems 500,000 infections and 51,000 deaths annually Organizers: Majid Bani-Yaghoub, Naveen K. Vaidya, which the linear high order derivatives are worldwide. Mathematical models proposed Xianping Li, Noah Rhee explicitly handled and the computational cost for VL have included the impact of dogs Speakers: Naveen Vaidya, Libin Rong, Songnian and storage remain the same as to the classic versus wild canids in disease dissemination Zhao, Maia Martcheva integration factor methods for second-order and models developed to assist in control problems. In particular, the proposed method approaches. However, quantitative conditions can deal with not only stiff nonlinear reaction 2007 - Modeling Movements Of which are required to control or eradicate terms but also various types of homogeneous HIV In Vaginal Mucus VL transmission are not provided and there or inhomogeneous boundary conditions. Also Naveen Vaidya, University of Missouri - Kansas City are not mathematical methods proposed such method has recently been extended to to quantitatively calculate optimal control solve a hydrodynamic phase field model for a The majority of all female Human strategies for VL transmission. The research binary fluid mixture of two immiscible viscous Immunodeficiency Virus (HIV) infections are the objective of this work was to model VL disease fluids. result of heterosexual intercourse with infected transmission system (Zoonotic VL in special), male partners. To establish infection, viruses perform bifurcation analysis to discuss control in semen from HIV-infected partner must 2005 - An Efficient Solver For A System conditions, and calculate optimal control penetrate the mucus barrier, which coats and strategies. Of Finite Element Methods For Flux adheres to vaginal epithelia, before they meet Variable underlying CD4+ target cells. In this talk, I will 2010 - Structural And Practical JaEun Ku, Oklahoma State University present mathematical models for movements of HIV in vaginal mucus. Using our models, Identifiability Issues Of Immuno- In this talk, a numerical method solving second- we will study the spatial-temporal distribution Epidemiological Vector-Host Model order elliptic PDEs is presented. The main of virus in vaginal mucus and time required Maia Martcheva, University of Florida goal is obtaining an accurate and efficient for the viruses to penetrate mucus layer, and approximation for the flux (gradient) variables. explore how pH level affects these phenomena. We discuss the structural and practical A differential equation for the flux variable Finally, we evaluate the potential nanoparticle- identifiability of a nested immuno- is obtained from the original equations. The based preventive therapy to control the virus in epidemiological model of arbovirus diseases. resulting algebraic equation involves solving vaginal mucosa. We show that the immunological model is not nearly singular system. An iterative scheme structurally identifiable for the measurements using well-conditioned matrix is presented for of time-series viremia concentrations. We the approximation of the solutions for the nearly study a scaled version of the immunological singular system. This is a joint work with Dr. model and prove that it is structurally globally Lothar Reichel. identifiable. After fixing estimated parameter
29 Society for Industrial and Applied Mathematics
Session Abstracts | Saturday, October 1, 2016 | 3:50 p.m. - 5:30 p.m. values for the immunological model derived demand for new quantitative tools which can 2017 - Threshold Partitioning Problems from the scaled model, we develop a numerical address the unique challenges present in this and Applications in Statistics method to fit observable Rift Valley Fever domain. We argue that tools from algebraic Michael Higgins, Kansas State University epidemiological data to the nested model topology seem, surreptitiously, ideally suited to for the remaining parameter values of the address these needs and in this talk describe a Many statistical problems benefit from the use multi-scale system. For the given CDC data collection of recent applications in both human of networks. Experimental or observational set, Monte Carlo simulations indicate that only and animal neuroscience. units comprise the nodes. Edge weights three parameters of the epidemiological model measure the pair-wise dissimilarity between are practically identifiable when the immune 2014 - The Theory Of Vietoris-Rips prognostically important covariates. A model parameters are fixed. Alternatively, particularly useful class of network optimization we fit the multi-scale data to the multi-scale Complexes: What Is Known And What problems are threshold partitioning problems--- model simultaneously. Monte Carlo simulations Is Open? those that impose a constraint on the minimum for the simultaneous fitting suggest that the Henry Adams, Colorado State University number of nodes to be contained within a parameters of the immunological model and block. Though these problems are often NP- Given a metric space X and a scale parameter the parameters of the immuno-epidemiological hard, approximate solutions may be found very r > 0, the Vietoris-Rips simplicial complex model are practically identifiable. efficiently. We examine approximate solutions has as its simplices the finite subsets of X of to these problems and show their usefulness in diameter less than r. These complexes have problems of statistical blocking and matching. been applied to problems in computational EIT 323: Applied and topology and topological data analysis, but what is known about their theoretical 2018 - Network-Centric Partner Computational Topology properties? When scale parameter r is small, Organizers: Henry Adams, Patrick Shipman Notification Strategies to Contain results by Jean-Claude Hausmann and Janko Speakers: Francis Motta, Hamza Ghadyali, Chad Epidemics Latschev show that Vietoris-Rips complexes Giusti, Henry Adams Caterina Scoglio, Kansas State University are well-behaved. However, very little is known about Vietoris-Rips complexes at larger scales. In this talk, I will present some recent 2011 - A Zoo Of Data And Questions We will discuss Vietoris-Rips complexes of simulation results on the use of network Francis Motta, Duke University circles, ellipses, and spheres, argue that infinite centrality measures to design new partner In this talk I will discuss nascent inquiries into Vietoris-Rips complexes should be equipped notification strategies aiming at containing the applicability of TDA methods to datasets with a different topology (which is a thickening sexually transmitted infectious diseases. The derived from complex dynamical systems of the metric on X), and survey open questions standard partner notification strategy consists including measurements and simulations of about larger scale parameters. Joint work on the notification of the infectious status of both Earth’s atmosphere and solid surfaces as with Michal Adamaszek, Florian Frick, and an individual to all his partners (neighbors they are eroded by broad ion beams. Samadwara Reddy. in the sexual network). Through partner notification, sexual partners are informed of the high risk of being infected and take 2012 - Topological Patterns EIT 325: Interactions Among preventive measures. Using the susceptible- in Climatic Data Analysis, Optimization and alert-infected-susceptible (SAIS) model of Hamza Ghadyali, Duke University Sahneh et al., we show the effectiveness of Network Science new partner notification strategies through Analyzing the rich dynamic structure of Organizers: Pietro Poggi-Corradini, Nathan Albin extensive simulation. In these new strategies, climatic data, we find novel patterns using Speakers: Nages Shanmugalingam, Lukas Geyer, in addition to notifying the partners of an TDA methods. We use persistent homology Michael Higgins, Caterina Scoglio, Daniela Ferrero infected individual about the infection state of to explore the geometry of high-dimensional the individual self, if the individual belongs to sliding-window curves derived from time- 2015 - Uniformly Perfect Cantor Sets a small set of nodes with the highest network series. We will discuss a novel sliding-window centrality, his infection status is notified to a construction, similar to time-delay embeddings, And Analysis On Trees large group of individuals in the network. With which reveal some structures that are expected Nageswari Shanmugalingam, this strategy, the infection prevalence can be and some that are unexpected. For example, University of Cincinnati reduced up to 1/3 when the infection status we can detect annual periodicity, but we also In this talk we will present results connecting of only 3% of the total individuals is shared. find oscillations which have connections to Newtonian spaces of functions on trees with These results suggest the development of an other climatic dynamics. These insights may Besov function spaces on Cantor sets. This is application for mobile phones to broadcast an help us to not only further understand climatic joint work with Anders Bjorn, Jana Bjorn and anonymous alert message when these central patterns, but also to predict climatic quantities James T. Gill. individuals are detected to be infected. of interest. 2016 - Conformal Dimension 2013 - Topological Methods In 2019 - Lower Bounds For The Power Of Sierpinski Carpets Domination Number Of A Graph Neuroscience Lukas Geyer, Montana State University Daniela Ferrero, Texas State University Chad Giusti, University of Pennsylvania We will present a numerical scheme to Electric power companies need to monitor the Modern neuroscience can in large part calculate conformal dimension of Sierpinski state of their networks continually in order to be characterized by the explosion of new carpets and related fractals. The main tool prevent power surges and black-outs. One techniques for gathering data from neural is the use of discrete p-modulus on graph method to accomplish this task is to place systems. Unfortunately, the development approximations, based on a similar algorithm Phase Measurement Units (PMUs) at selected of methods for analysis of that data and Oded Schramm introduced for the special case network locations. The synchronized readings for understanding the underlying complex p=2. This is joint work with Rob Malo. provided by these PMUs, in conjunction with systems has not kept pace, creating a strong
30 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Session Abstracts | Saturday, October 1, 2016 | 3:50 p.m. - 5:30 p.m.
Kirchhoff’s laws, permit to determine the state it is a partitioned time stepping method, yet it have derived a simple algorithm to show that of the network at any location. Because of the is of high order accuracy in both space and every LOM satisfying these conditions can be high cost of a PMU, it is important to minimize time (the two-step algorithm considered in rewritten as a system of coupled gyrostats their number while maintaining the ability of this report provides second order accuracy); it monitoring the entire system. This problem allows for the usage of the legacy codes (which translates into the power domination problem is a common requirement when resolving flows in graph theory. A standard approach to the in complex geometries), yet it can be applied to ETAS 230: Recent Developments power domination problem consist of finding the problems with very small viscosity/diffusion power dominating sets and proving they are coeffcients. This is achieved by combining in Discontinuous Galerkin best possible. However, proving that a set is an the defect correction technique for increased Methods for Partial Differential optimal power dominating set is usually hard. In spatial accuracy (and for resolving the issue this talk we will present the only known lower of high convection-to-diffusion ratio) with the Equations Organizer: Mahboub Baccouch bound for the power domination problem, with deferred correction in time (which allows for Speakers: Yang Yang, Mahboub Baccouch, Bo Dong, illustrates the connection between the power the usage of the computationally attractive Yulong Xing domination problem in graph theory and the partitioned scheme, yet the time accuracy is zero-forcing problem in linear algebra. The increased beyond the usual result of partitioned results are joint work with several colleagues. methods being only first order accurate) into 2024 - Superconvergence Of the defect-deferred correction method (DDC). Discontinuous Galerkin Methods For The results are readily extendable to the Nonlinear Hyperbolic Equations higher order accuracy cases by adding more Yang Yang, Michigan Technological University ETAS 229: Recent Developments correction steps. Both the theoretical results of High Order Numerical and the numerical tests provided demonstrate In this talk, we will focus on the that the computed solution is unconditionally superconvergence of discontinuous Methods stable and the accuracy in both space and time Galerkin methods for nonlinear hyperbolic Organizer: Ying Wang is improved after the correction step. equations. We will demonstrate (2k+1)th order Speaker order: Mustafa Aggul, Dilek Erkmen, Ming- superconvergence rate for problem with fix jun Lai, S. Lakshmivarahan 2022 - Bivariate Spline Solution of wind direction. If the wind direction is not fixed, (k+3/2)th order superconvergence rate will be 2020 - High Accuracy Approach To Reaction-Diffusion Equations and Its proved. Numerical experiments will be given to Turbulence Modeling Application demonstrate the optimality of the rates. Mustafa Aggul, Michigan Technological Univeirsity Ming-Jun Lai, University of Georgia A method is presented, that combines the This is a joint work with G. Slavov, based on 2025 - \emph{A posteriori} error defect and deferred correction approaches his dissertation study. We introduce a discrete analysis of the discontinuous Galerkin to approximate solutions of Navier-Stokes weak solution to a reaction-diffusion equation method for two-dimensional linear equations at high Reynolds number. The method with Allee affect. We use a minimization is of high accuracy in both space and time, approach and establish the nonnegativity of hyperbolic conservation laws on and it allows for the usage of legacy codes the solution.Then we use bivariate splines Cartesian grids. – a frequent requirement in the simulation of degree 5 or more to solve the PDE. An Mahboub Baccouch, University of Nebraska at of turbulent flows in complex geometries. In application to malaria study will be explained. Omaha. order to obtain a regularization that is second In this talk, we provide the first \emph{a order accurate in space and time, the method 2023 - On The Structure Of Energy posteriori} error analysis of the discontinuous computes a low-order accurate, stable and Conserving Low-Order Models Galerkin (DG) method for solving the two- computationally inexpensive approximation dimensional linear hyperbolic conservation S. Lakshmivarahan, University of Oklahoma (Backward Euler with artificial viscosity) laws on Cartesian grids. The key ingredients twice. The two-step method is considered Starting with the pioneering work of Lorenz in our error analysis are the recent optimal here; the results are readily extendable to the in 1963 great strides have been made in the superconvergence results proved in [W. Cao, higher order accuracy cases by adding more analysis of complex fluid dynamical system. C.-W. Shu, Y. Yang, and Z, Zhang, \emph{SIAM correction steps. Both the theoretical results The basic idea behind this approach is to J. Numer. Anal.}, 53 (2015), pp. 1651-1671]. We and the numerical tests provided demonstrate apply Galerkin-type projection technique to a first prove that the DG solution converges that the computed solution is stable and second system of partial differential equations to obtain in the $L^2$-norm to a Radau interpolating order accurate in space and time. a system of ordinary differential equations polynomial under mesh refinement. The order (ODE) describing the time evolution of a set of convergence is proved to be $p+2$, when 2021 - Defect-Deferred Correction of n Fourier amplitudes. The resulting class of tensor product polynomials of degree at most ODE has come to be known as the low-order $p$ are used. Then we show that the actual Method For The Two-Domain models, LOM(n). Despite the wide spread error can be divided into a significant part and Convection-Dominated Convection- popularity of this approach, apparently there a less significant part. The significant part of Diffusion Problem is no guide lines for the choice of the order n the DG error is spanned by two $(p+1)$-degree Dilek Erkmen, Michigan Technological University in LOM(n) that would guarantee conservation right Radau polynomials in the $x$ and $y$ of energy in the system. It has been observed directions. The less significant part converges We present a method for solving a fluid-fluid that lack conservation often leads to non- to zero at $\mathcal{O}(h^{p+2})$. These results interaction problem (two convection-dominated physical solution for LOM(n). There has been are used to construct simple, efficient and convection-diffusion problems adjoined by a number attempts to examine the relation asymptotically exact \emph{a posteriori} error an interface), which is a simplifed version of between energy conserving LOM(n) and estimates. Superconvergence towards the the atmosphere-ocean coupling problem. The couple gyrostats. Following this lead the right Radau interpolating polynomial is used to method resolves some of the issues that can be present authors have derived a set of sufficient prove that, for smooth solutions, our \emph{a crucial to the fluid-fluid interaction problems: conditions of LOM(n) to conserve energy and posteriori} DG error estimates converge at a 31 Society for Industrial and Applied Mathematics
Session Abstracts | Saturday, October 1, 2016 | 3:50 p.m. - 5:30 p.m. fixed time to the true spatial errors in the $L^2$- ETAS 480: Some Advances In the computational error subject to a given norm at $\mathcal{O}(h^{p+2})$ rate. Finally, we computational cost or minimizing the prove that the global effectivity indices in the Finite Element Methods computational cost subject to a given error $L^2$-norm converge to unity at $\mathcal{O} Organizers: Yuchuan Chu, Feng Shi tolerance. A gradient-based optimization (h)$ rate. Our proofs are valid for arbitrary Speaker order: Feng Shi, Xiaozhe Hu, Ju Ming, algorithm using MLMC was proposed and regular Cartesian meshes using tensor product Yuchuan Chu, Keyu Gong compared to the results obtained by classical polynomials of degree at most $p$ and for both Monte Carlo method. The computational results the periodic and Dirichlet boundary conditions. 2028 - A space-time discretization show the effectiveness MLMC for obtaining Several numerical experiments are performed method for solving flow problems accurate optimal solutions that are needed to to validate the theoretical results. construct statistical moments associated with based on the partition of unity and the quantity of interest (QoI) of the stochastic 2026 - Superconvergent HDG Methods adaptivity strategy control problem at low cost. For Third-Order Equations In One- Feng Shi, Department of Mathematics, University of Houston 2031 - A Dynamic Interface Space Dimension Bo Dong, University of Massachusetts Dartmouth In this talk, we present a fully discrete (space- Immersed-Finite-Element Particle- time) method for solving the flow problems. In-Cell Method For Modeling Along the time advancing, the current method We design and analyze hybridizable Plasma-Wall Interactions discontinuous Galerkin methods for third- firstly computes a global problem by standard finite element method on the prescribed regular Yuchuan Chu, Missouri University of order equations in one-space dimension. The Science and Technology methods are defined as discrete versions coarse grid; then based on the coarse grid, of characterizations of the exact solution in derives the partition of unity and its associated The evolution of wall surface is an unavoidable terms of local problems and transmission overlapping subdomains; and solve a series issue in engineering plasma applications. In conditions. They provide approximations to of local residual problems on fine grids of this article an iterative method for modeling the exact solution $u$ and its derivatives the subdomains which are automatically plasma-wall interactions with dynamic $q:=u_x$ and $p:=u_{xx}$ which are piecewise- determined by a adaptivity strategy; finally, interface is proposed and validated. In this polynomials of degree $k_u$, $k_q$ and $k_p$, obtains the globally continuous finite element method, the plasma dynamics is simulated by respectively. We prove that these methods solution by assembling all the local solutions an immersed finite element particle-in-cell have superconvergence properties and together using the partition of unity. The new (IFE-PIC) method, and the evolution of wall numerical results are displayed to validate our method can capture the moving boundary surface is modeled by the Huygens wavelet error estimates. layers in the interior of the fluid domain, which method which is coupled with the iteration of will be demonstrated by several numerical the IFE-PIC method. Numerical experiments, experiments. including prototypical engineering applications 2027 - A Posteriori Error Estimates such as the erosion of Hall thruster channel Of Local Discontinuous Galerkin 2029- Weak Galerkin Finite Element wall, are presented to demonstrate features Methods For The Generalized of this dynamic interface IFE-PIC method Method for the Biot’s Consolidation Korteweg-De Vries Equations for simulating the dynamic plasma-wall interactions. Yulong Xing, University of California Riverside Model Xiaozhe Hu, Tufts University The Korteweg-de Vries (KdV) equation is 2032 - A Modified Weighting Algorithm a nonlinear mathematical model for the Poroelasticity models the processes of unidirectional propagation of waves in a variety coupled deformable porous media flow which for Immersed Finite Element Particle- of nonlinear, dispersive media. Recently it is essential in many applications. In this talk, In-Cell (IFE-PIC) Method has attracted increasing attention as test- we consider the discretizations for the Biot’s Keyu Gong, Harbin Institue of Technology bed for the competition between nonlinear model using weak Galerkin finite elements and Shenzhen Graduate School and dispersive effects leading to a host of address the issue related to the non-physical In the plasma simulation community, the analytical issues such global existence and oscillations in the pressure approximation for Particle-In-Cell (PIC) scheme has been widely finite time blowup, etc. In this presentation, we low permeabilities and/or small time steps. We used since its noise-reduction capability and construct, analyze, and numerically validate show that weak Galerkin method provides an moderate computational expense. Immersed a class of discontinuous Galerkin schemes oscillation-free scheme numerical and study finite elements (IFEs) are relatively new and for the generalized KdV equation. We will the well-posedness and convergence of the efficient tools to handle interface problems with provide a posteriori error estimate through the scheme theoretically. This is a joint work with Cartesian meshes independent of the interface concept of dispersive reconstruction, i.e. a Lin Mu and Xiu Ye. which are required by PIC scheme. Based piecewise polynomial function which satisfies on immersed finite element (IFE) methods the GKdV equation in the strong sense but with 2030 - Multi-Level Monte Carlo Finite and Particle-In-Cell methods, the recently a computable forcing term enabling the use of Element Method for A Stochastic developed immersed finite element Particle- a priori error estimation techniques to obtain In-Cell method (IFE-PIC method) provides an computable upper bounds for the error. Both Optimal Control Problem outstanding approach to simulate plasma semi-discrete and fully discrete approximations Ju Ming, Beijing Computational Science particles with complex interface boundary. are studied. Research Center However, in current IFE-PIC method, the charge We consider the application of multi-level deposit algorithm does not work very well Monte Carlo (MLMC) finite element method by depositing the particle charge onto mesh to an elliptic optimal control problem with nodes located inside the object described by uncertain coefficients. Sample size formulae the interface surface. Also, the process of at each level of MLMC were derived from obtaining the electric field on mesh nodes with an optimization perspective, by minimizing
32 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Session Abstracts | Sunday, October 2, 2016 | 8:30 a.m. - 10:10 a.m. the potential of those nodes which locate inside viscous incompressible flow and rigid bodies. flows. Extensive numerical tests in 1D and the object has the same drawback. This paper The algorithm remains stable, without sub- 2D are provided to verify the accuracy of the is to present a modified weighting algorithm iterations, even for light rigid-bodies when sweeping procedure. to improve the accuracy of plasma simulation added-mass and viscous added-damping with IFE-PIC method. Numerical examples effects are large. A fully second-order accurate are provided to demonstrate the accuracy of implementation of the scheme is developed Sunday, October 2, 2016 IFE-PIC method with new modified weighting based on a fractional-step method for the 8:30 a.m. - 10:10 a.m. algorithm. incompressible Navier-Stokes equations using finite difference methods and overlapping grids ______to handle the moving geometry. We will first present two models problems to ETAS 483: Recent Advance on motivate and evaluate the properties of the High Order Numerical Methods AMP scheme. Then we will present simulations EIT 219: Mesh Adaption for of more complicated FSI problems with some Numerical Simulations for Partial Differential Equations interesting geometry. Organizers: Yuan Liu, Yingda Cheng Organizers: Xianping Li, Weizhang Huang Speakers: Yang Jiang, Qi Tang, He Yang, Yuan Liu Speakers: Stefano Micheletti, Cuiyu He, Avary 2035 - Local Discontinuous Galerkin Kolasinski, Junbo Cheng, Fei Zhang 2033 - A WENO-based Method of Methods for Khokhlov-Zabolotskaya- 2037 - Anisotropic mesh adaptation for Lines Transpose Approach for Vlasov Kuznetzov Equation He Yang, The Ohio State University crack propagation in brittle materials Simulations Stefano Micheletti, Politecnico di Milano, Italy Yan Jiang, Michigan State University Khokhlov-Zabolotskaya-Kuznetzov (KZK) equation is a model that describes the Quasi-static brittle fracture can be modeled A high order implicit Method of Lines propagation of the ultrasound beams in the by the Francfort-Marigo model. A suitable Transpose (MOLT ) method based on a thermoviscous fluid. It contains a nonlocal diff approximation to this model can be obtained weighted essentially non-oscillatory (WENO) raction term, an absorption term and a by the Ambrosio-Tortorelli functional, where methodology is developed for one-dimensional nonlinear term. Accurate numerical methods the crack is identified by a smooth phase- linear transport equations and further applied to simulate the KZK equation are important to field, instead of a lower-dimensional set, as in to the Vlasov-Poisson (VP) simulations via its broad applications in medical ultrasound the case of the Francfort-Marigo model. The dimensional splitting. In the MOLT framework, simulations. In this paper, we propose local minimization of the new functional can be found the time variable is rst discretized by a discontinuous Galerkin methods to solve the by solving elliptic boundary value problems via diagonally implicit strong-stability-preserving KZK equation. We prove the L2 stability of our a finite element method. Crack propagation Runge-Kutta method, resulting in a boundary scheme and conduct a series of numerical exhibits two main length scales, one related to value problem (BVP) at the discrete time levels. experiments including the focused circular the domain size and the other characterizing Then an integral formulation coupled with a short tone burst excitation and the propagation the fracture thickness. Mesh adaptation, driven high order WENO methodology is employed of unfocused sound beams, which show that by an a-posteriori error estimator, allows one to to solve the BVP. As a result, the proposed our scheme leads to accurate solutions and refine the grid only in a thin neighborhood of the scheme is high order accurate in both space performs better than the benchmark solutions crack path. In previous works, an anisotropic and time and free of oscillations even though in the literature. error estimator and a new minimization the solution is discontinuous or has sharp algorithms are proposed and applied to the gradients. Moreover, the scheme is able to classical Ambrosio-Tortorelli approximation. take larger time step evolution compared with 2036 - A Simple Bound-Preserving Several numerical tests assess the reliability an explicit MOL WENO scheme with the same Sweeping Technique For Conservative of the whole adaptation procedure. In this order of accuracy. The desired positivity- Numerical Approximations communication, we extend our previous preserving (PP) property of the scheme is Yuan Liu, Mississippi State University approach to the generalized Ambrosio-Tortorelli further attained by incorporating a newly model. Moreover, we address the extension proposed high order PP limiter. We perform In this talk, we introduce a simple bound- including thermal inelastic effects, which numerical experiments on several benchmarks preserving sweeping procedure for can model the genesis and the propagation including linear advection, solid body rotation conservative numerical approximations. of cracks in brittle materials. The numerical problem; and on the Landau damping, two- Conservative schemes are of importance in verification performed on standard benchmarks stream instabilities, bump-on-tail, and plasma many applications, yet for high order methods, in the literature confirms the good accuracy sheath by solving the VP system. The efficacy the numerical solutions do not necessarily guaranteed by anisotropic grids which yield a and efficiency of the proposed scheme is satisfy maximum principle. This paper significant computational saving. numerically verified . constructs a simple sweeping algorithm to enforce the bound of the solutions. It has a very 2038 - Improved ZZ A Posterior Error 2034 - An Added-Mass/Added- general framework acting as a postprocessing step accommodating many point-based or cell Estimation For Diffusion Problem Damping Partitioned Algorithm average-based discretizations. The method is Cuiyu He, Purdue University proven to preserve the bounds of the numerical For Rigid Bodies And Incompressible For diffusion problems with intersecting solution while conserving a prescribed quantity Flows interface, a reasonably good approximation designated as a weighted average of values Qi Tang, Rensselaer Polytechnic Institute requires very small mesh size around the from all points. The technique is demonstrated intersecting interface points. As a popular A stable added-mass/added-damping to work well with a spectral method, high order alternative, we use AMR to get a optimal partitioned algorithm is developed for fluid- finite difference and finite volume methods for locally refined mesh. In order to obtain a structure interaction (FSI) problems involving scalar conservation laws and incompressible robust A Posteriori error estimation in the
33 Society for Industrial and Applied Mathematics
Session Abstracts | Sunday, October 2, 2016 | 8:30 a.m. - 10:10 a.m. sense that constants are independent of the has comparable accuracy to the scheme of As well, the RPT model follows the analytic jump of diffusion coefficients which could Maire and collaborators, while being more (well-mixed) PDE solution (with slope t^−1) be very large, we introduce the improved ZZ accurate in resolving rarefaction waves. before transitioning to the imperfectly mixed conforming flux recovery for the confirming regime (slope t^{−d/4}, in d dimensions). In this FEM. The A Posteriori error estimator and direction, we will describe the algorithm and indicators are then defined as the energy norm 2041 - A Moving Mesh Method For present some preliminary simulation results. of the difference between the recovered flux The Numerical Simulation Of Fracture and the numerical one. This procedure shares Propagation 2043 - Numerical Methods For Solving the advantage with ZZ of very cheap cost, on Fei Zhang, China University of Petroleum (Beijing) the other hand, it overcomes the inefficiency of The Fractional Schrodinger Equation ZZ. Numerical results are presented at last. In this talk, we present a moving mesh method Siwei Duo, Missouri University of for the numerical simulation of two dimensional Science and Technology 2039 - A New Functional For fracture propagation in elastic media using The fractional Schrodinger equation is a non- the phase field method. A continuous phase local partial differential equation which can Variational Mesh Generation And field variable is introduced to describe the describe new phenomena that are absent from Adaption Based On Equidistribution “unbroken” or “broken” status of the material, the standard Schrodinger equation. However, which can model fractures without explicitly the nonlocality introduces considerable And Alignment Conditions tracking discontinuous displacement fields. The Avary Kolasinski, The University of Kansas challenges in solving this equation both behavior of the fracture is then determined by a analytically and numerically. In this talk, we We will introduce a new meshing functional coupled system of partial differential equations. will present several mass and/or energy for variational mesh generation with minimal To avoid the requirement of fine meshes conservative methods for solving the fractional parameters based on the equidistribution and throughout the domain, we apply a variational- Schrodinger equation. The accuracy and alignment conditions. We will discuss the type moving mesh method that relocates the the dispersion relation of these methods are theoretical properties of this function including mesh nodes automatically to capture the studied analytically. Also, we numerically study coercivity, nonsingularity, and the existence of fracture propagation. The numerical results for the plane wave and soliton dynamics, the limiting mesh. We will present a comparative 2D crack propagation under quasi-static loads performance of these methods are compared numerical study of this new functional with one are presented, and the effectiveness of the and discussed. well known functional, which is also based on moving mesh method together with phase-field the equidistribution and alignment conditions. model for fracture simulation is demonstrated. 2044 - Spatial Adaptivity For Numerical PDEs In The Presence 2040 - A Four-Rarefaction Approximate EIT 224: Partial Differential Of Parametric Uncertainty Riemann Solver With Elastic Wave Hans-Werner van Wyk, Auburn University Equations: Analysis, And Von Mises’ Yielding Condition For Localized descriptions of random fields, such Two-Dimension Elastic-Plastic Flows Computation, Modeling, as Markov random fields, provide a means Junbo Cheng, Beijing Institute of Computational and Applications of coupling their spatial and stochastic Mathematics and Applied Physics Organizers: John Singler, Weiwei Hu variations. In this talk, we leverage this feature to develop an algorithm for achieving spatial For the equations of two-dimensional elastic- Speakers: Michael Schmidt, Siwei Duo, Hans-Wer- adaptivity in the stochastic setting, through plastic flows with the hypo-elastic constitutive ner van Wyk, Yangwen Zhang the use of localized, statistical a posteriori model and von-Mises’ yielding condition, it error estimators. We illustrate our method with is difficult to build an approximate Riemann numerical examples. solver because of non-conservative hypo- 2042 - Novel Lagrangian Methods elastic constitutive model and von-Mises’ for Imperfectly Mixed Chemical yielding condition. Up to now, there is no good Reactions 2045 - Group Finite Element Method approximate Riemann solver for this problem. In Michael Schmidt, Colorado School of Mines For 2D And 3D Navier-Stokes And this paper, we first analyse the wave structure of the Riemann problem in the normal direction Most traditional models for simulating Boussinesq Equations Yangwen Zhang, Missouri University of and develop, accordingly, a four-rarefaction chemical reactions are based on the principle Science and Technology Riemann solver with elastic waves (FRRSE). of perfect mixing, which seldom occurs in Because of elastic limit and complex EOS, in natural settings. For example, Eulerian methods The standard finite element method for the constructing FRRSE, one need consider four allow for non-homogeneity across grid points Navier-Stokes and Boussinesq equations cases and use a iteration method to solve the but still require perfect mixing within each can be very time consuming since the large- problem of FRRSE. Moreover, in order to reduce grid element. In this talk, we present a novel scale global matrix must be updated at each CPU time of iteration, we use two nested Lagrangian method known as reactive particle nonlinear iteration. We show how group finite small iterations of two variables to replace tracking (RPT) that is able to simulate transport elements can be used to treat the nonlinear one iteration of four variables. Based on and reaction dynamics without the well-mixed term; this method is based on interpolation FRRSE, we propose a 2nd-order cell-centered assumption needed for other methods. One and does not require an update to the global Lagrangian scheme. The numerical results major advantage of RPT is that it allows for matrix at each iteration. We present 2D and show that the present scheme achieves the the formation of inhomogeneous “islands” of 3D numerical experiments demonstrating (1) desired 2nd-order accuracy in space and time. reactant anywhere in the domain, without the the group method has the same accuracy Moreover, a number of numerical experiments necessity of small-scale discretization. For this as the standard method, and (2) the group show that our scheme is stable, essentially reason, RPT is able to model the experimentally method leads to much faster simulation times, non-oscillatory and appears to be convergent. observed transition of a well-mixed system into especially for 3D simulations. Moreover, for shock waves the present scheme one with imperfect mixing and the subsequent slowdown in reaction speed that follows.
34 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Session Abstracts | Sunday, October 2, 2016 | 8:30 a.m. - 10:10 a.m.
EIT 318: Methods Of Applied 2048 - A Fast Fourier Recursive of the phase field free-energy functional to Relation Method To Evaluate Singular its sharp-interface limit. We also define the And Numerical Complex dielectric boundary force for any phase field as Integrals In A Complex Plane the negative first variation of the free-energy Analysis Aditi Ghosh, University Of Idaho, Moscow Organizers: Anna Zemlyanova, Thomas DeLillo functional, and prove the convergence of such Speakers: Anna Zemlyanova, Yuri Antipov, Aditi A FFTRR based sequential algorithm for solving force to the corresponding sharp-interface Ghosh the Poisson or the biharmonic problem in a unit limit. disk in the complex plane needs evaluation of 2046 - Two-Dimensional Fluid Flows some singular integrals. We present recursive 2051 - Theoretical And Numerical relations in Fourier space together with fast Analysis Of Singularly Perturbed Around Multiple Cylinders In The Fourier transform (FFTRR) which lead to a Presence Of Vortices fast and accurate evaluations of the singular Problems Anna Zemlyanova, Kansas State University integrals. The complexity of this method to Youngjoon Hong, University of Illinois, Chicago evaluate the singular integrals are $\mathcal{O} The talk is dedicated to a two-dimensional In this talk, we consider various singularly (\log_2 N)$ per point compared to $\mathcal{O} steady irrotational flow of ideal fluid around perturbed problems. The main focus has been (N^2)$ per degree of freedom as in the case of multiple cylinders with impenetrable walls in the use of a correction function usually called direct evaluation using quadrature method. the presence of vortices. Fluid flows in the the “corrector” (proposed by J. L. Lions), which multiply-connected domains are notoriously resolves the discrepancy between the zero difficult to study, and currently very few boundary conditions and those of the outer analytic solutions are available. In this solutions, in order to analyze boundary layers. talk, I will describe a simple procedure of EIT 319: Nonlinear Analysis Introducing the corrector function, the specific Organizer: Matt Insall building a complex potential of such a flow convergence rate is explored in certain spaces. Speakers: Giles Auchmuty, Shibin Dai, Youngjoon using method of images and Schottky group. In addition, some new semi-analytic methods Hong, Ning Ju, Matt Insall Numerical computations will be presented. have been proposed and successfully applied The convergence of numerical method is very under the names of enriched spaces. The main fast for well-separated cylinders. Study of 2049 - Nonlinear Boundary Value ingredient of the enriched method is to add a global basis function, and supplement the two-dimensional flows with vortex structures Problems for Harmonic Functions presents an important problem of fluid discrete space with the corrector functions. In Giles Auchmuty, University of Houston mechanics and has applications to ocean flows our treatment, we implement the modified finite with eddies. This talk will outline results about the existence element method using a quasi-uniform mesh and representation of $H^1$-solutions of which remains unchanged as time evolves. 2047 - A Crack Induced By A Thin Laplace’s equation subject to nonlinear Robin, or Neumann, boundary conditions of the form 2052 - Solution Regularity for Rigid Inclusion Partly Debonded From $D_v u + bu = g(u)$ on bounded regions $\ the Primitive Equations The Matrix Omega\in R^N$. Since the space H of $H^1$- Ning Ju, Oklahoma State University Yuri Antipov, Louisiana State University harmonic functions on is a proper closed subspace of $H^1(\Omega)$, it is sufficient to Some new results recently obtained by the The interaction of a thin rigid inclusion with study this problem on this subspace. Some speaker about the Primitive Equations for large a finite crack is studied. The upper side of general existence criteria for solvability will be scale oceanic flows will be presented and the inclusion is completely debonded from described. An orthonormal basis of $H$ is given discussed. the matrix, and the crack penetrates into by a class of harmonic Steklov eigenfunctions the medium. It is shown that the problem on $\Omega$. This enables the construction is governed by a certain singular integral 2053 - Advances in the Mathematical of an integral kernel and a boundary integral equation. Its closed-form solution is found by Analysis of the Complete Iterative equation for solutions that enables other solving an associated vector Riemann-Hilbert conditions for existence to be obtained. Further Inversion Method problem with the Chebotarev-Khrapkov matrix properties of the solutions are deduced from Matt Insall, Missouri S&T coefficient. A feature of the method proposed this formulation. is that the vector Riemann-Hilbert problem We expand on the Complete Iterative Inversion is set on a finite segment, while the original Method (CIIM) used in physical chemistry to Khrapkov method of matrix factorization is 2050 - Phase-Field Free Energy generate an energy potential of a gas system. developed for a closed contour. In the case, and Boundary Force for Molecular While originally designed to be used with Lennard-Jones potentials, we explore, among when the crack and inclusion lengths are the Solvation same, the solution is derived from the general other things, the application of the CIIM to step Shibin Dai, New Mexico State University case by passing to the limit. It is demonstrated functions which approximate Lennard-Jones that the limiting case is unstable, and when the We discuss a phase-filed variational model for potentials. This is joint work with Abdulrahman crack length is less than that of the inclusion the solvation of charged molecules with implicit S. Alharbi, David E. Grow, and Brittany M. and the crack tips approach the inclusion solvent. The solvation free-energy functional of Cuchta ends, the crack tends to accelerate in order to all phase fields consists of the surface energy, penetrate into the matrix. solute excluded volume and solute-solvent van der Waals dispersion energy, and electrostatic free energy. The last part is defined through the electrostatic potential governed by the Poisson-Boltzmann equation in which the dielectric coefficient is defined through a phase field. We prove Gamma- convergence
35 Society for Industrial and Applied Mathematics
Session Abstracts | Sunday, October 2, 2016 | 8:30 a.m. - 10:10 a.m.
EIT 321: Modeling and infectious disease. Particularly, we discuss the arrays of nanodots. It is necessary to be able impacts of spatial heterogeneity and seasonal to measure the degree of order present in Computations for General and variation on the transmission dynamics of a pattern to identify not only variation in the Chaotic Biological Systems cholera, using both mathematical analysis and pattern, but also defects. With D. Pearson, M. Organizers: Majid Bani-Yaghoub, Naveen K. Vaidya, numerical simulation. Based on a deterministic Bradley, F. Motta, and P. Shipman, we purpose Xianping Li, Noah Rhee modeling framework that involves systems a topological method relying on persistent Speakers: Majid Bani-Yaghoub, James Moore, of ODEs and PDEs, we establish results of homology to measure the degree of order Jin Wang, Joe Tien disease extinction and persistence for each present in a pattern. There are several standard model, and compare the threshold dynamics in methods of measuring order using Fourier homogeneous and heterogeneous settings. methods, the autocorrelation function, and a 2054 - Optimal Control Policies nearest-neighbor measure. We will compare For Reducing Johne’s Disease 2057 - Modeling The Trade-Off these methods with our topological method for various lattice patterns. In Dairy Farms Between Transmission And Contact Majid Bani-Yaghoub, University of Missouri-Kansas City In Disease Dynamics 2059 - The Soft Mode Plays A Role Joe Tien, The Ohio State University Johne’s disease is a chronic contagious In Defect Persistence In Pattern- infection, caused by Mycobaterium Symptom severity affects disease transmission both by impacting contact rates, as well as by Forming Systems paratuberculosis. Each year, the U.S. dairy Patrick Shipman, Colorado State University industry loses over 200 million dollars due to influencing the probability of transmission given the infection. Using the cattle movement data contact. This involves a trade-off between When the surface of a nominally flat binary of six dairy farms and the Johne’s disease these two factors, as increased symptom material is bombarded with a broad, normally data, a mathematical model is developed to severity will tend to decrease contact rates, but incident ion beam, disordered hexagonal determine control policies that can minimize increase the probability of transmission given arrays of nanodots can form. Defects, such as the prevalence of infection in a dairy farm. contact (as pathogen shedding rates increase dislocations in ripple patterns or penta-hepta The model incorporates progression of the with symptom severity). Here we explore this pairs in hexagonal arrays, limit the utility of infection within each pen and the cattle trade-off between contact and transmission patterns produced by ion bombardment. We movements between the pens. Using the basic given contact, using a simple compartmental show that a neutrally stable soft mode can and target reproduction numbers, the infection susceptible-infected-recovered type model. contribute to the persistence over time of risk in each pen is calculated. It is shown Under mild assumptions on how contact and defects that form in the early stages of pattern that the overall infection risk is substantially transmission probability vary with symptom formation. Topological measures of order reduced when the average residence time severity, we give sufficient, biologically intuitive provide a method for determining if a defect is and the population size in high risk pens are criteria for when the basic reproduction removed as the pattern evolves. minimized. Using numerical simulations, spread number varies non-monotonically with symptom of epidemic waves in dairy farms and impacts severity. Multiple critical points are possible. 2060 - Computational topology and We give a complete characterization of the of control measures are numerically explored. computational electromagnetism This is a joint work with Malinee Konboon. region in parameter space where multiple critical points are located in the special case Pawel Dlotko, Inria Saclay where contact decreases exponentially with 2055 - Modeling the Acceleration It is not well recognized in the topology and symptom severity. We consider a multi-strain physics community that from the very early and Delay of Type 1 Diabetes by version of the model with complete cross- years of their existence unified theory of Viral Infection immunity and no super-infection. In this model, electricity and magnetism and algebraic James Moore, Emory University we prove that the strain with highest basic topology are closely related. Concepts reproduction number drives the other strains which have clear physical interpretation It has been suggested that lack of childhood to extinction. This has both evolutionary and are well defined objects in homology and infection may predispose individuals to epidemiological implications, including the cohomology theory. Recent advantages in autoimmune diseases such as type 1 diabetes. possibility of an intervention paradoxically computational topology makes this relation Experimental infections of laboratory mice resulting in increased disease prevalence. This even more interesting since now we have suggest that the age of exposure to certain is joint work with Chiu-Ju Lin and Kristen Deger. efficient algorithms and their implementations viral infections is a key determinant of diabetes at our disposal, and we can use them in susceptibility. Mice infected at an earlier age computational electromagnetism. tend to be protected while mice infected at During this presentation we will describe a later age become more prone to diabetes. EIT 323: Applied and my long and ongoing cooperation with Biologists have suggested several hypotheses Ruben Specogna on the problems between to explain this pattern such as immune Computational Topology Organizers: Henry Adams, Patrick Shipman computational electromagnetism and algebraic regulation, immune competition and infection topology. We will focus on the eddy current induced inflammation. In this talk, I will present Speakers: Rachel Neville, Patrick Shipman, Pawel Dlotko, David Letscher approximation to Maxwell’s equations. We will a mathematical model of type 1 diabetes show how one can build discrete counterparts and viral infection and use it to evaluate the of Maxwell’s equations on a finite polyhedral plausibility of each hypothesis. 2058 - Topological Measure mesh, and how concepts from homology and of Order on Lattice Patterns cohomology are essential to make the whole 2056 - Modeling Cholera In Rachel Neville, Colorado State University theory work. Later we will summarize our quest for efficient and easy to use algorithm Heterogeneous Environments Pattern-forming systems can give rise to to compute topological invariant needed to Jin Wang, University of Tennessee at Chattanooga perfect or near-perfect lattice patterns. For solve Maxwell’s equations. We will show instance, bombarding a binary surface with We present some recent work in mathematical how the two theories can benefit from each modeling of cholera, a severe water-borne a broad ion beam can lead to hexagonal 36 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Session Abstracts | Sunday, October 2, 2016 | 8:30 a.m. - 10:10 a.m. other in a matter of knowledge and efficient cut. Let Г(a,b) be the family of walks originating ETAS 229: Recent Developments computational methods. In particular, we will at a and terminating at b.We have shown that present an topology based idea we discovered the reciprocal of min cut, Mod_1(Г(a,b))^{-1} is of High Order Numerical which is currently used in commercial solvers also a metric and more generally, d_p(a,b):= Methods of Maxwell’s equations. Mod_p(Г(a,b))^{-1/p} is a metric for all 1≤ p < ∞. Organizer: Ying Wang When p tends to infinity d_p recovers shortest- Speaker order: Songting Luo, Lin Mu, Jin-song Pei, 2061 - Persistent Homotopy: path, but when p=2, d_p is the square-root of Ran Zhang effective resistance and effective resistance An Overview itself is a metric. Therefore, it is natural to ask Davi Letscher, Saint Louis University what is the optimal function ψ(d_p ) that yields 2066 - High-Order Methods For We provide a overview of the use of homotopy a metric for each p. We wish to investigate the Traveltime And Amplitude In Fast groups to study topological persistence. In optimal exponent α(p):=sup{t: d_p^t is a metric}. Huygens Sweeping Method For High particular, we will focus on 3-dimensions We produced sets of 50 Erdȍs-Renyi graphs on Frequency Helmholtz Equation where we can utilize normal surface 10 nodes with average degree 6 and found that Songting Luo, Iowa State University theory to construct theoretical algorithms. α(p)=p works for 1≤ p ≤2. For p>2, α(p) seems to These algorithms can be used to calculate be a decreasing function that converges to 1. We present efficient methods to compute persistent homotopy groups, construct We also found examples for p>2 where d_p^p high order accurate traveltime and amplitude. persistence diagrams and perform topological = Modp(Г(a,b))^{-1} is not a metric. However, we Efficient factorization approaches are simplification. conjecture that Modp(Г(a,b))^{-1} serves as a presented to resolve the source singularities metric for 1≤ p ≤ 2 and so far this is confirmed such that high-order methods can be designed numerically. and applied effectively to obtain high-order accurate traveltimes and amplitudes. With EIT 325: Interactions Among 2065 - Quasisymmetric Embeddings Of high accurate traveltimes and amplitudes, we present an efficient method, namely the Analysis, Optimization And Metric Spaces fast Huygens sweeping method, to solve the Hrant Hakobyan, Kansas State University Network Science Helmholtz equation in the high frequency A mapping between metric spaces is called regime. Numerical examples verify the (8:05 a.m. - 10:10 a.m.) quasisymmetric if it distorts relative distances effectiveness of the methods. Organizers: Pietro Poggi-Corradini, Nathan Albin and sizes of sets by a bounded amount. One of Speakers: Jason Clemens, Jim Gill, Thiwanka the most important questions in the theory is Fernando, Hrant Hakobyan 2067 - Weak Galerkin Finite Element the problem of quasisymmetrically embedding a metric space into a Euclidean space. In this Methods and Implementations 2062 - Blocker Duality for Modulus talk we will define a class of spaces called Lin Mu, Oak Ridge National Laboratory Jason Clemens, Missouri Valley College slit carpets and will completely characterize The Weak Galerkin method is a new those slit carpets which can be embedded discontinuous version of finite element methods Using the formulation given by Fulkerson, quasisymetrically into the plane. The main tools for solving partial differential equations. The we explore the idea of blocking duality as it are classical and transboundary modulus of key is to replace the classical derivatives pertains to the modulus of families of objects families of curves. weakly defined derivatives on functions on finite undirected graphs. In particular, we with discontinuity. The WG methods have generalize the concept of conjugate family in the flexibility in handling complex geometry complex analysis and obtain a relation between 2065A - A Hamilton Type Gradient and low regularity solutions, the simplicity in the p-modulus of family of objects and a Estimate For Solutions To The formulation. In this talk, we will talk about the related p’-modulus for its blocker family. Heat Equation On Graphs numerical formulations and implementations of As an example, we discuss the family of all Paul Horn, University of Denver the weak Galerkin framework. spanning trees and show that the Fulkerson blocker is different from the combinatorial In this talk we will describe how to derive a blocker (the family of all cuts) in this case. gradient estimate for positive solutions to the 2068 - A Brief Introduction to heat equation on graphs satisfying a curvature lower bound. The gradient estimate derived, “Mem-Models” in Engineering 2063 - Modulus and Spaces unlike the classical Li-Yau inequality, controls Mechanics Applications Without Walks how the solution changes in space alone and is Jin-Song Pei, The University of Oklahoma James Gill, Saint Louis University. originally due to Hamilton in the manifold case. We discuss spaces without enough paths to A significant event happened for electrical Our curvature type is a variant of the curvature engineering in 2008, when researchers at HP make modulus an available tool. What can still dimension inequalities $CD (n, K)$ of Bakry be said? Labs announced that they had found “the and Emery, known as $CDE(n, K)$, which was missing memristor”, a fourth basic circuit introduced in work of the speaker and others element that was postulated nearly four 2064 - An Investigation Of Node-Based in deriving a version of the Li-Yau inequality decades earlier by Dr. Leon Chua who also for graphs. One nice feature of the estimate is Metrics On Networks Arising From developed the theory of memristive systems. that, unlike the Li-Yau inequality, it is dimension One consequence of this announcement P-Modulus independent and applies to some graphs which has been revitalized research in all areas Thiwanka Fernando, Kansas State University are known to satisfy $CDE(\infty, 0)$ but do of brain-imitating computer technologies, not satisfy $CDE(n, 0) for any finite $n$. Some primarily because memristors mimic synapses. p-Modulus of families of walks on graphs applications will be briefly discussed as well. generalizes and interpolates among three Moreover, the theory involving memristor important quantities in graph theory: shortest devices and memristive systems was extended path, effective resistance and max-flow/min- to include memcapacitors and meminductors, thereby introducing an entire class of “mem-
37 Society for Industrial and Applied Mathematics
Session Abstracts | Sunday, October 2, 2016 | 8:30 a.m. - 10:10 a.m. models”. This model class is the foundation generation of soliton waves and head on weakly soluble salt. For this reaction diffusion of the present study. By applying well-known collisions of solitary waves. system we use a Continuous Galerkin finite mechanical-electrical system analogies, element scheme to analyse the system in the mathematics of mem-models may be 2071 - Multisymplectic HDG methods both one dimension and two dimensions. With transferred to the setting of engineering Ari Stern, Washington University in St. Louis our simulations we try to match amplitude mechanics, resulting in mechanical and frequency data of the reaction from counterparts of memristors, memcapacitors, For Hamiltonian ODEs, symplectic numerical experiments. etc. We identify some recent examples of methods exhibit superior numerical “mem-dashpots” and “mem-springs”. In performance. For Hamiltonian PDEs, a suitable addition to a “zero-crossing” condition, we numerical method should be “multisymplectic” highlight the role played by discontinuities -- but what does this mean? We answer this ETAS 480: Some Advances in in the model and/or the excitation, the question using the “unified framework” of combination of which enables mem-models to Cockburn et al. for hybridizable discontinuous Finite Element Methods Organizers: Yuchuan Chu, Feng Shi produce numerous hysteresis patterns. We also Galerkin (HDG) methods, which turns out to Speaker order: Fatma Songul Ozesenli Tetikoglu, consider some new properties and modeling be particularly well-suited to this problem. Lulu Quan, Fatih Sabahattin Tetikoglu, Yingwei techniques that call for further improvement so Specifically, we give necessary and Wang that these new types of mechanical models can sufficient conditions for an HDG method to be become more usable for analyzing real-world multisymplectic, and examine these criteria for data. several popular methods. 2074 - Numerical Solution of an (Joint work with Robert McLachlan, Massey University, New Zealand.) Elliptic-Hyperbolic Equation with an 2069 - Maximum Principles For P1- Unknown Parameter P0 Weak Galerkin Finite Element 2072 - High-order DG-FEM for Micro- Fatma Songul Ozesenli Tetikoglu, Fatih University Approximations Of Quasi-Linear Macro Partitioned Kinetic Models In the present study, the boundary value Second Order Elliptic Equations James Rossmanith, Iowa State University problem for the elliptic-hyperbolic differential Ran Zhang, Jilin University equation with an unknown parameter in a The dynamics of gases can be simulated using Hilbert space with self adjoint definite operator This talk will introduce maximum principles kinetic or fluid models. Kinetic models are is investigated. The well-posedness of this for the weak Galerkin method dealing with valid over most of the spatial and temporal problem is established. The stability inequalities the second order elliptic equation. Under the scales that are of physical relevance in many for the solution of source identification problem h-acute assumption for the mesh partition, two application problems; however, they are for elliptic-hyperbolic equations are obtained. maximum principles with respect to midpoints computationally expensive due to the high The first and second order of accuracy are proved. The theoretical analysis is based on dimensionality of phase space. Fluid models difference schemes approximately solving the the variational form and De Giorgi technique. have a more limited range of validity, but are boundary value problem are presented. The Some numerical results are also presented. generally computationally more tractable than stability estimates for the solutions of these kinetic models. One critical aspect of fluid difference schemes are established. models is the question of what assumptions to make in order to close the fluid model. In this ETAS 230: Recent Developments work we develop a high-order discontinuous 2075 - Time-domain Immersed in Discontinuous Galerkin Galerkin finite element method (DG-FEM) Finite Element Methods for for a so-called micro-macro decomposition Methods for Partial Differential Electromagnetic Scattering and approximation of the kinetic equations. The Radiation in Composite Material Equations micro-macro decomposition approach allows us to obtain accurate solutions of the fluid Lulu Quan, Harbin Institue of Technology Organizer: Mahboub Baccouch Shenzhen Graduate School Speakers: Joshua Buli, Ari Stern, James Ross- model, but instead of forcing a particular manith, Bahaudin Hashmi moment-closure approximation, which would This paper solves the wave equation interface typically only have a limited range of validity, problem with immersed finite element this approach directly solves a version of the (IFE) method. This problem arises from 2070 - A Local Discontinuous Galerkin kinetic equations and uses this solution to electromagnetic scattering and radiation Method for the Coupled BBM-BBM provide a closure for the fluid equations. The simulation in composite materials. The meshes System proposed approach in this work makes use of used in these IFE methods can be independent Joshua Buli, University of California, Riverside an efficient semi-Lagrangian DG method for of the interface geometry and position; solving the kinetic portion of the update. The therefore, if desired, a structured mesh such as The well known Euler equations for fluid flow resulting numerical method is validated on a Cartesian mesh can be used in an IFE method can be approximated using the four-parameter several standard test cases. to simulate 2-D scattering and radiation in a class of equations known as the “abcd” domain with non-trivial interfaces separating Boussinesq equations. With a specific choice 2073 - Modeling of Important different materials. Numerical examples are of these parameters, one obtains the coupled provided to demonstrate that the accuracies BBM-BBM system which approximates the 2D Vapor-to-Particle Reactions of these IFE methods are comparable to Bahaudin Hashmi, Colorado State University propagation of surface waves in a channel. We the standard finite element method with present a local discontinuous Galerkin method In this talk we discuss the threshold kinetics unstructured body-fit mesh. to solve the coupled BBM-BBM system. The that govern the formation of Liesegang high order Runge-Kutta methods, and midpoint rings in the ammonia and hydrogen chloride rule are utilized for the time discretization. reaction. Liesegang ring formation is a special Numerical examples are shown to establish type of chemical pattern in which a spatial accuracy and stability of the method, including order is formed by density fluctuations of a
38 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Session Abstracts | Sunday, October 2, 2016 | 10:40 a.m. - 12:20 p.m.
2076 - The positivity of the difference waves with discontinuous vorticity. Further- parameters of the model using the method of operator with periodic conditions and more, we utilize a modified moving planes least squares that he invented for this purpose. method to show that such solitary waves This aspect of estimating the parameters of the its application possess even symmetry. model has come to be known as data assim- Fatih Sabahattin Tetikoglu, Fatih University ilation. Using the assimilated model we then In this study, the second order of approximation 2079 - An Introductory Course in generate the forecast much like Gauss was able to predict the time and bearings for the of the difference operator is presented. The Partial Differential Equations Using positivity of this operator in a Banach space reappearance of Ceres. is established. In application, theorems on Mathematica well-posedness for difference schemes of the Dennis Brewer, University of Arkansas, Fayetteville 2082 - The Transmission Problem approximate solution of the boundary value An upper-level undergraduate course in partial for Elliptic Equations with Wentzel problem for elliptic differential equations are differential equations is offered each semes- presented. ter at the University of Arkansas. The course Boundary Condition Hung Le, University of Missouri-Columbia stresses applications and analytic methods for 2077 - Muntz-Galerkin Methods And solving the heat equation, wave equation, and The talk presents some results about the exis- Applications To Mixed Dirichlet- Laplace equation with particular emphasis on tence and uniqueness of weak and classical series solutions of orthogonal functions. This solutions for elliptic equations with transmis- Neumann Boundary Value Problems talks discusses a supplementary text written sion problem and Wentzel boundary condition. Yingwei Wang, Purdue University in the form of a Mathematica notebook. This Applications to steady water waves in the interactive format allows students to explore presence of wind will be discussed. Solutions for many problems of interest exhibit larger classes of orthogonal functions and singular behaviors at domain corners or points consider the nature of the convergence of where boundary condition changes type, series solutions, including Gibbs Phenomenon. Sunday, October 2, 2016 which adversely a ects the accuracy and Animations in Mathematica also facilitate dy- 10:40 a.m. - 12:20 p.m. convergence of standard numerical methods. namic visualization of time-dependent solutions We developed a Muntz-Galerkin method of partial differential equations in one or two ______which is based on specially tuned Muntz space variables. polynomials to deal with the singular behaviors EIT 219: No scheduled talks of the underlying problems. By exploring the relations between Jacobi polynomials and 2080 - A Squared Correlation Muntz polynomials, we developed efficient Coefficient of the Correlation Matrix EIT 224: No scheduled talks implementation procedures for the Muntz- Rong Fan, Southern Illinois University Galerkin method and provide optimal error Multivariate linear correlation analysis estimates. As examples of applications, we is important in statistical analysis and EIT 318: Methods Of Applied considered the Poisson equation with mixed applications. This paper defines a one Dirichlet-Neumann boundary conditions, whose number summary gamma^2 of the population And Numerical Complex solution behaves like $O(r^{1/2})$ near the correlation matrix that behaves like a squared Analysis singular point, and demonstrate that the Muntz- correlation. The squared Pearson’s correlation Organizers: Anna Zemlyanova, Thomas DeLillo Galerkin method greatly improves the rates of coefficient is a special case of gamma^2 Speakers: Tom DeLillo, Justin Mears, Mehran convergence of the usual spectral method. for two variables. Unlike the coefficient of Mehrabi multiple determination, also known as the ETAS 483: Contributed multiple correlation coefficient, gamma^2 does 2083 - A Comparison of Some not depend on the choice of the dependent presentations variable. Numerical Conformal Mapping Speakers: Adelaide Akers, Dennis Brewer, Rong Fan, Methods for Simply and Multiply S. Lakshmivarahan, Hung Le 2081 - Data Ming, Data Assimilation Connected Domains Thomas DeLillo, Wichita State University 2078 - Existence and Symmetry of and Prediction - Parts of a Continuum S. Lakshmivarahan, University of Oklahoma We compare some methods for computing Small-amplitude Solitary Water conformal maps from simply and multiply Waves with Discontinuous Vorticity Data mining relates to the process of solving a class of inverse problems - of building the connected domains bounded by circles to Adelaide Akers, University of models from data much like Kepler discovered target domains bounded by smooth curves Missouri-Columbia his famous four laws from the analysis of the and curves with corners. We discuss the We consider the classical water wave problem astronomical observations and the way we use of explicit preliminary maps, including comprised of a two-dimensional body of water build models for times series today. Models the osculation method of Grassmann, to first with constant density which lies below a vacu- come in various shapes and forms- (a) static/ conformally map the target domain to a more um. The ocean bed is assumed to be impene- dynamic (b) deterministic/stochastic and (c) nearly circular domain. The Fourier series trable, while the boundary which separates the causality based or empirical. Independent of its method due to Fornberg and its generalizations fluid and the vacuum is assumed to be a free type, models have unknown parameters and/ to multiply connected domains are then applied boundary. Following the work of M.D. Groves or initial conditions. These unknowns are esti- to compute the maps to the nearly circular and E. Wahlen (2008), we use the Hamiltonian mated using the very same data that lead to the domains. The final map is represented as a structure of the system coupled with center model in the first place. Recall that Gauss fitted composition of the Fourier/Laurent series with manifold reduction techniques to establish the a model for the for the path of Ceres, using the inverted explicit preliminary maps. A novel existence of small-amplitude solitary water the past observations and then estimated the method for systematically removing corners
39 Society for Industrial and Applied Mathematics
Session Abstracts | Sunday, October 2, 2016 | 10:40 a.m. - 12:20 p.m. with power maps is also implemented and EIT 319: Contributed talks 2089 - Bootstrapping Analogs of the composed with the Fornberg maps (which Speakers: Lasanthi Pelawa Watagoda, Liangya Pi, Two Sample Hotelling’s T^2 Test} require smooth boundaries) and the level Changxin Qiu, Hasthika Rupasinghe Arachchige Don Hasthika Rupasinghe Arachchige Don, of error that can be expected when using Southern Illinois University; Lasanthi Pelawa Fourier series to treat domains with corners Watagoda is illustrated. This is joint work with Mohamed 2086 - Inference After Variable Badreddine. Selection Suppose there are two independent random Lasanthi Pelawa Watagoda, Southern Illinois Univer- samples from two populations or groups. 2084 - Computation of Stokes Waves sity; Dr. David Olive A common multivariate two sample test of hypotheses is H_0: mu_1 = mu_2 versus Using Conformal Mapping This work presents inference for the multiple H_1: mu_1 not equal to mu_2 where mu_i Justin Mears, Wichita State University linear regression model Y = beta_1x_1 + ... is a population location measure of the Stokes waves for water of infinite and + beta_px_p + e after variable selection, ith population for i = 1, 2. The two sample finite depth are computed using numerical including prediction intervals for a future Hotelling’s T^2 test is the classical method, methods for conformal mapping of simply and value of the response variable Y_f given a and is a special case of the one way MANOVA doubly connected domains, resp. These two p x 1 vector of predictors x_f , and testing model if the two populations are assumed to dimensional, time dependent waves satisfy hypotheses with the bootstrap. If n is the have the same population covariance matrix. dynamic and kinematic conditions on the free sample size, most results are for n >> p, but This paper suggests using the Olive (2016ab) surface of the fluid. The periodic waves at each prediction intervals are developed that increase bootstrap technique to develop analogs of time step are mapped to bounded domains and in average length slowly as p increases for Hotelling’s T^2 test. The new tests can have modifications of Fornberg’s method for simply fixed n, if the model is sparse: k predictors have considerable outlier resistance, and the tests and doubly connect domains are used to map nonzero coefficients beta_i where n >> k do not need the population covariance matrices the unit disk or an annulus to the simply and to be equal. doubly connected domains. The transplanted 2087 - An Investigation on the Data boundary value problems for the velocity Assimilation with Kalman Filter and potential are solved by Fourier series in the disk Finite Elements for Subsurface Flows or annulus and the velocity potential and free EIT 321: Modeling and surface are advanced in time. This is joint work Liangya Pi, Missouri University of Science and with Thomas DeLillo. Technology Computations for General and Kalman filter has been showed to be a very Chaotic Biological Systems 2085 - Analytical Analysis of Gas efficient tool for data assimilation. Based on the Organizers: Majid Bani-Yaghoub, Naveen K. Vaidya, Diffusion into Noncircular Pores of state equation and observation equation arising Xianping Li, Noah Rhee from the finite element discretization in space, Speakers: Xianping Li, Weijiu Liu, Gayla Shale Organic Matter we utilize the Kalman filter to investigate the Olbricht, Yi Sun Mehran Mehrabi, The University of Texas at Austin effect of the data noise, low solution regularity, Total gas in shale gas reservoirs sourced and the number and locations of observation 2090 - Mathematical Modeling and from free, adsorbed and dissolved/diffused wells for subsurface flow problems. gas. The mechanisms of production of free Computation of Spatio-temporal and adsorbed gas have been studied by 2088 - A Multi-Physics Domain Dynamics of Dengue Epidemics numerous researchers. In contrast, evolution Decomposition Method for Navier- Xianping Li, University of Missouri-Kansas City of the dissolved gas and its contribution Stokes-Darcy Model In recent years, growing spatial spread of to the total gas production is not well dengue, a mosquito-borne disease, has been understood. In this study we model the effect Changxin Qiu, Missouri University of Science and Technology a major international public health concern. of pore microstructure in organic matter Many epidemiological parameters, including (OM) on the rate of gas production in shale In a karst aquifer, free flow and porous media those related to mosquito entomology, highly reservoirs. In this regard, first, we solve the flow are tightly coupled together, for which the depend on temperature, indicating that the gas-in-solid diffusion equation over a general Navier-Stokes-Darcy model has higher fidelity spatial variation of temperature may have doubly-connected spatial domain with an than either the Darcy or Navier-Stokes systems important effects on the spatial spread external Neumann and internal Dirichlet on their own. The Stokes-Darcy type model of dengue. In this talk, we will present a boundary conditions. The obtained solution has attracted significant attention in the past mathematical model to describe spatio- is applied systematically to multi-pore porous ten years. However, coupling the two constit- temporal transmission dynamics of dengue. OM domains and then, the effect of pore uent models leads to a very complex system. Using our model, we evaluate how variation morphology on the rate of gas production is This presentation discusses a multi-physics of temperature across space can affect the studied. Our model results show that pore domain decomposition method for solving the spatial expansion of dengue epidemics. Our geometry has slight effect on gas diffusion Navier-Stokes-Darcy system. Computational results may provide useful information for process, while total organic content (TOC), results are presented to illustrate the features effective deployment of spatially targeted and OM porosity, pore size distribution, and of the proposed method and the convergence interventions. specific surface area are dominant parameters. analysis is demonstrated. Abundance of very small pores in OM tremendously increase diffuse gas contribution in total gas reserve and production.
40 Central States Section Meeting | Sept 30 - Oct. 2, 2016
Session Abstracts | Sunday, October 2, 2016 | 10:40 a.m. - 12:20 p.m.
2091 - Asymptotic Tracking and 2093 - Kinetic Monte Carlo talk about persistent homology over integer Disturbance Rejection of the Blood Simulations of coefficients! Glucose Regulation System Multicellular Aggregate Self- Weijiu Liu, University of Central Arkansas 2095 - Persistent Homology on Assembly in Biofabrication Grassmann Manifolds for Analysis of Type 1 diabetes patients need external insulin Yi Sun, University of South Carolina to maintain blood glucose within a narrow Hyperspectral Movies We present a three-dimensional lattice Lori Ziegelmeier, Macalester College range from 65 to 108 mg/dl (3.6 to 6.0 mmol/L). model to study self-assembly and fusion of A mathematical model for the blood glucose multicellular aggregate systems by using We present an application of persistent regulation is required for integrating a glucose kinetic Monte Carlo (KMC) simulations. This homology to the detection of chemical plumes monitoring system into insulin pump technology model is developed to describe and predict the in hyperspectral movies of Long-Wavelength to form a closed-loop insulin delivery system on time evolution of postprinting morphological Infrared data which capture the release of the feedback of the blood glucose level, the so- structure formation during tissue or organ a quantity of chemical into the air. Regions called “artificial pancreas.” We present such a maturation in a novel biofabrication process (or of interest within the hyperspectral data model by treating the exogenous glucose from technology) known as bioprinting. In this new cubes are used to produce points on the real food as a glucose disturbance and developing a technology, live multicellular aggregates as bio- Grassmann manifold $G(k, n)$ (whose points closed-loop feedback and feedforward control ink are used to make tissue or organ constructs parameterize the k-dimensional subspaces system. We show that the glucose disturbance via the layer-by-layer deposition technique in of $\mathbb{R}^n)$, contrasting our approach can be generated by an exogenous periodic biocompatible hydrogels; the printed bio- with the more standard framework in Euclidean system and the center manifold theory can constructs embedded in the hydrogels are space. An advantage of this approach is be used to establish blood glucose regulator then placed in bioreactors to undergo the that it allows a sequence of time slices in equations, and then the required feedback self-assembly process to form the desired a hyperspectral movie to be collapsed to a and feedforward controllers to reject the functional tissue or organ products. Here we sequence of points in such a way that some disturbance and asymptotically track the implement our model with an efficient KMC of the key structure within and between glucose reference can be synthesized by.using algorithm to simulate the making of a set of the slices is encoded by the points on the the solutions of the regulator equations. tissues/organs in several designer’s geometries Grassmann manifold. This motivates the search like a ring, a sheet and a tube, which can for topological structure, associated with the 2092 - Modeling Sleep Patterns In involve a large number of cells and various evolution of the frames of a hyperspectral The Fruit Fly To Investigate The Link other support materials like agarose constructs movie, within the corresponding points on the etc. We also study the process of cell sorting/ Grassmann manifold. The proposed framework Between Sleep And Alzheimer’s migration within the cellular aggregates affords the processing of large data sets while Disease formed by multiple types of cells with different retaining valuable discriminative information. Gayla Olbricht, Missouri University of Science and adhesivities. In this paper, we discuss how embedding our Technology data in the Grassmann manifold, together with topological data analysis, captures dynamical Sleep is a critical, restorative process that is events that occur as the chemical plume is imperative to human health, yet links between released and evolves. sleep and many health outcomes are not EIT 323: Applied and well understood. Sleep is often disrupted in patients with Alzheimer’s Disease (AD) and Computational Topology 2096 - Studying Knots Via Heat Maps Organizers: Henry Adams, Patrick Shipman the brains of sleep deprived people may not Isabel Darcy, University of Iowa Speakers: Amit Patel, Lori Ziegelmeier, Isabel Darcy, clear aggregating proteins appropriately, Iuliana Oprea Heat maps have been used to visualize pseudo potentially leading to AD. We utilize the fruit 2-dimensional persistence when one wishes fly, Drosophila melanogaster, as a model to visualize changes in homology using more system to better understand how an individual’s 2094 - Semicontinuity of Persistence than one parameter. Given points taken sleep pattern may predict the susceptibility or Diagrams uniformly from a knot, we create a simplicial severity of disease progression. Using genetic Amit Patel, Colorado State University complex for a fixed epsilon by forming the techniques, different degrees of disease Rips complex obtained from connecting The persistence diagram is very different in severity of an Alzheimer’s like condition can be points with edges if the distance between philosophy from the barcode. Suppose we induced in the fly. The sleep-wake status of the points is less than epsilon. We create the have a constructible persistence module individual flies is monitored over the fly lifespan 1-dimensional persistence homology barcode of vector spaces. Its barcode is its list of and used to create descriptive variables, such for the filtration formed from increasing indecomposables. Its persistence diagram is as transition probabilities of staying asleep or epsilon. One can create a 1-dimensional an encoding of all persistent vector spaces. awake from one minute to the next (a measure heatmap from this barcode by encoding In the setting of vector spaces, we know that of sleep or wake consolidation). When the betti number at each fixed epsilon via a these two notions are equivalent. However, calculated on a daily basis, it is informative to heatmap color. In other words, we can color we quickly run into problems if we try to study how these variables change over time. the interval [0, M) by assignment a color to generalize the barcode beyond the setting of We employ methods based on first differences each epsilon in this interval based on the betti vector spaces. In this talk, I will generalize and functional principal component analysis to number of the Rips complex formed at time the persistence diagram to the setting of summarize trajectories over time. Through this epsilon. One dimensional heat maps can be constructible persistence modules valued work, we examine sleep patterns differences stacked together to form a 2-dimensional heat in any symmetric monoidal category. For between flies with and without Alzheimer’s and map in order to visualize simplicial complex example, the category of sets, the category use sleep variables as predictors of longevity formation involving a second parameter. For of vector spaces, and the category of abelian and an individual’s potential AD susceptibility. knots our second parameter involves looking at groups are symmetric monoidal categories. superlevel sets based on local curvature. We As an immediate consequence, we can finally
41 Society for Industrial and Applied Mathematics
Session Abstracts | Sunday, October 2, 2016 | 10:40 a.m. - 12:20 p.m.
apply this technique to Lissajous knots. This is of the research is, in particular, motivated by joint work with Katie Betancourt, V. Gerardi, G. the current demands for analysis on topological Heo, R. Neville, M. Pietrosanu, and M. Tsuruga manifolds, fractals, graphs, and on Carnot- and was supported by WinCompTop. Caratheodory spaces. In this talk I would like to discuss several analogues for function spaces 2097 - Topological Measures of Snow of fractional smoothness, Besov spaces and Triebel-Lizorkin spaces, in the setting of a Surface Roughness metric space with a doubling measure. Iuliana Oprea, Colorado State University Understanding the spatiotemporal changes in snow surface - the interface between the 3000 - Analyzing Loop Structures atmosphere and the Earth - can improve In Networks knowledge of hydrologic processes within Heman Shakeri, Kansas State University the snowpack and their impact on melt We study the structure of loops in a network dynamics and, further, on the climatology using the notion of modulus of loop families. of the environment. In this talk topological We introduce a new measure of network data analysis and roughness measures are clustering by quantifying the richness of certain proposed for the study of the characteristics families of loops. Modulus tries to minimize the of anisotropic patterns observed in the snow expected overlap among loops by spreading surface and the estimate of the snow surface the expected link-usage optimally. We propose roughness. weighting networks using these expected link-usages to improve classical community detection algorithms. We show that the proposed method enhances the performance EIT 325: Interactions Among of algorithms, such as spectral partitioning and modularity maximization, on standard Analysis, Optimization And benchmarks. Network Science Organizers: Pietro Poggi-Corradini, Nathan Albin 3001 - Metric Spaces of Small Cotype Speakers: Dominique Zosso, Lizaveta Ihnatsyeva, Kevin Wildrick, Montana State University Heman Shakeri, Kevin Wildrick Embedding an abstract metric space into a space with more structure while distorting 2098 - Primal-Dual Methods for the notion of distance in a controlled way is a p-Modulus on Graphs useful tool in situations ranging from classical Dominique Zosso, Department of Mathematical Riemannian geometry to data science. We will Sciences, Montana State University discuss a few results about such embeddings and focus on an obstruction to embedding, Recently the notion of p-Modulus has been Metric Co-type, introduced by Mendel and extended to families of walks on graphs by Naor. We examine the metric cotype of tree- Albin, Poggi-Coradini, et al. Here we propose to like metric spaces. This is joint work with Ellen employ a primal-dual hybrid gradients scheme Veomett. (Chambolle and Pock) to the greedy algorithm for p-Modulus computation. All optimization steps are simple first order. In the particular case of 2-modulus, the proposed scheme ETAS 229: No scheduled talks simplifies into a boosted dual problem. We compare against existing methods. ETAS 230: No scheduled talks 2099 - Functions Of Fractional Smoothness On Metric ETAS 480: No scheduled talks Measure Spaces Lizaveta Ihnatsyeva, Kansas State University ETAS 483: No scheduled talks Function spaces with fractional order of smoothness are actively applied in partial differential equations, calculus of variations and optimization. Recently there has been an increasing interest in extending the scope of classical analytic and geometric theories from the Euclidean space to more general metric spaces equipped with a measure. This direction
42 Central States Section Meeting | Sept 30 - Oct. 2, 2016
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