DOCSLIB.ORG

2Nd Annual Meeting of SIAM Central States Section Meeting Program

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

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. 10:10 a.m. - 10:40 a.m. Irene Gamba Plenary Speaker 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
Recommended publications
  • Conservative High Order Semi-Lagrangian Finite Difference WENO Methods for Advection in Incompressible Flow Jing-Mei Qiu1 and Ch

    Conservative High Order Semi-Lagrangian Finite Difference WENO Methods for Advection in Incompressible Flow Jing-Mei Qiu1 and Ch

    Conservative high order semi-Lagrangian finite difference WENO methods for advection in incompressible flow Jing-Mei Qiu1 and Chi-Wang Shu 2 Abstract In this paper, we propose a semi-Lagrangian finite difference formulation for approximat- ing conservative form of advection equations with general variable coefficients. Compared with the traditional semi-Lagrangian finite difference schemes [4, 21], which approximate the advective form of the equation via direct characteristics tracing, the scheme proposed in this paper approximates the conservative form of the equation. This essential difference makes the proposed scheme naturally conservative for equations with general variable coef- ficients. The proposed conservative semi-Lagrangian finite difference framework is coupled with high order essentially non-oscillatory (ENO) or weighted ENO (WENO) reconstructions to achieve high order accuracy in smooth parts of the solution and to capture sharp inter- faces without introducing spurious oscillations. The scheme is extended to high dimensional problems by Strang splitting. The performance of the proposed schemes is demonstrated by linear advection, rigid body rotation and swirling deformation. As the information is propa- gating along characteristics, the proposed scheme does not have CFL time step restriction of the Eulerian method, allowing for a more efficient numerical realization for many application problems. Keywords: advection in incompressible flow; conservative scheme; semi-Lagrangian meth- ods; WENO reconstruction. 1Department of Mathematical and Computer Science, Colorado School of Mines, Golden, 80401. E-mail: [email protected]. Research supported by NSF grant number 0914852 and Air Force Office of Scientific Research grant number FA9550-09-1-0344. 2Division of Applied Mathematics, Brown University, Providence, 02912.
  • Finite Difference and Discontinuous Galerkin Methods for Wave Equations

    Finite Difference and Discontinuous Galerkin Methods for Wave Equations

    Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1522 Finite Difference and Discontinuous Galerkin Methods for Wave Equations SIYANG WANG ACTA UNIVERSITATIS UPSALIENSIS ISSN 1651-6214 ISBN 978-91-554-9927-3 UPPSALA urn:nbn:se:uu:diva-320614 2017 Dissertation presented at Uppsala University to be publicly examined in Room 2446, Polacksbacken, Lägerhyddsvägen 2, Uppsala, Tuesday, 13 June 2017 at 10:15 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Professor Thomas Hagstrom (Department of Mathematics, Southern Methodist University). Abstract Wang, S. 2017. Finite Difference and Discontinuous Galerkin Methods for Wave Equations. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1522. 53 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-9927-3. Wave propagation problems can be modeled by partial differential equations. In this thesis, we study wave propagation in fluids and in solids, modeled by the acoustic wave equation and the elastic wave equation, respectively. In real-world applications, waves often propagate in heterogeneous media with complex geometries, which makes it impossible to derive exact solutions to the governing equations. Alternatively, we seek approximated solutions by constructing numerical methods and implementing on modern computers. An efficient numerical method produces accurate approximations at low computational cost. There are many choices of numerical methods for solving partial differential equations. Which method is more efficient than the others depends on the particular problem we consider. In this thesis, we study two numerical methods: the finite difference method and the discontinuous Galerkin method.
  • PROGRAM and ABSTRACTS

    PROGRAM and ABSTRACTS

    LASERENANUM E´ R I C A II Octavo Encuentro de Analisis´ Numerico´ de Ecuaciones Diferenciales Parciales Departamento de Matem´aticas,Universidad de La Serena La Serena, Chile, Enero 14 - 16, 2015 PROGRAM and ABSTRACTS Contents 1 Introduction 2 2 Wednesday, January 14 3 3 Thursday, January 15 4 4 Friday, January 16 5 5 Abstracts 6 1 1 Introduction The Octavo Encuentro de An´alisisNum´ericode Ecuaciones Diferenciales Parciales has been organized in sequential talks of 45 and 30 minutes length (40 and 25 minutes of presentation, respectively, and 5 minutes for questions and comments). All the talks will be given at Salon´ Multiuso, CETECFI (3th floor), Facultad de Ingenier´ıa, Universi- dad de la Serena. In the following pages we describe the corresponding program. In case of a multi-authored contribution, the speaker is underlined. The organizers acknowledge financial support by: • CONICYT-Chile through Project Anillo ACT 1118 ANANUM, • Departamento de Matem´aticas, Universidad de La Serena, • Centro de Modelamiento Matem´atico(CMM), Universidad de Chile, and • Centro de Investigaci´onen Ingenier´ıaMatem´atica(CI2MA), Universidad de Concepci´on. In addition, we express our recognition and gratitude to all speakers for making La Serena Num´ericaII possible. Organizing Committee Raimund B¨urger Gabriel N. Gatica Ricardo Oyarz´ua H´ectorTorres La Serena, January 2015 2 2 Wednesday, January 14 8.30-9.15 REGISTRATION 9.15-9.30 WELCOME SPEECH [Chairman: N. HEUER] 9.30-10.15 Alexandre Ern, Martin Vohral´ık: Polynomial-degree-robust a posteri- ori estimates in a unified setting. 10.15-10.45 Dante Kalise: High-order semi-Lagrangian schemes for static Hamilton- Jacobi-Bellman equations.
  • AN13 and CT13 Abstracts

    AN13 and CT13 Abstracts

    AN13 and CT13 Abstracts Abstracts are printed as submitted by the authors. Society for Industrial and Applied Mathematics 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Telephone: +1-215-382-9800 Fax: +1-215-386-7999 Conference E-mail: [email protected] Conference web: www.siam.org/meetings/ Membership and Customer Service: 800-447-7426 (US & Canada) or +1-215-382-9800 (worldwide) 2 2013 SIAM Annual Meeting • SIAM Conference on Control & Its Applications Table of Contents Annual Meeting (AN13) Abstracts ...............................................3 Control & Its Applications (CT13) .............................................127 SIAM Presents Since 2008, SIAM has recorded many Invited Lectures, Prize Lectures, and selected Minisymposia from various conferences. These are available by visiting SIAM Presents (http://www.siam.org/meetings/presents.php). 2013 SIAM Annual Meeting • SIAM Conference on Control & Its Applications 3 AN13 Abstracts 4 AN13 Abstracts IC1 system including cars, buses, pedestrians, ants and molecu- Social Networks as Information Filters lar motors, which are considered as ”self-driven particles”. We recently call this interdisciplinary research on jamming Social networks, especially online social networks, are of self-driven particles as ”jamology”. This is based on driven by information sharing. But just how much informa- mathematical physics, and and includes engineering appli- tion sharing is influenced by social networks? A large-scale cations as well. In the talk, starting from the backgroud experiment measured the effect of the social network on the of this research, simple mathematical models, such as the quantity and diversity of information being shared within asymmetric simple exclusion process and the Burgers equa- Facebook. While strong ties were found to be individu- tion, are introduced as basis of all kinds of traffic flow.
  • AN17-CT17-GD17 Abstracts

    AN17-CT17-GD17 Abstracts

    AN17-CT17-GD17 Abstracts Abstracts are printed as submitted by the authors. SIAM 2017 Events Mobile App Scan the QR code with any QR reader and download the TripBuilder EventMobile™ app to your iPhone, iPad, iTouch or Android mobile device. You can also visit www.tripbuildermedia.com/apps/siamevents Society for Industrial and Applied Mathematics 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Telephone: +1-215-382-9800 Fax: +1-215-386-7999 Conference E-mail: [email protected] Conference Web: www.siam.org/meetings/ Membership and Customer Service: (800) 447-7426 (USA & Canada) or +1-215-382-9800 (worldwide) www.siam.org/meetings/ 2 2017 SIAM Annual Meeting Table of Contents AN17 Annual Meeting Abstracts ................................................3 CT17 Abstracts .........................................................................130 GD17 Abstracts .........................................................................183 SIAM Presents Since 2008, SIAM has recorded many Invited Lectures, Prize Lectures, and selected Minisymposia from various conferences. These are available by visiting SIAM Presents (http://www.siam.org/meetings/presents.php). 2017 SIAM Annual Meeting AN17 Abstracts 4 AN17 Abstracts IP1 for mapping services this is obtained from mobile phones, Genetic Consequences of Range Expansion Under while for ambulance fleets it is obtained from automatic ve- Climate Change hicle location devices. We demonstrate greatly improved accuracy relative to a system used in Bing Maps, and show Range expansion is a crucial population response to cli- the impact of our methods for improving ambulance fleet mate change. Genetic consequences are coupled to ecolog- management decisions. ical dynamics that, in turn, are driven by shifting climate conditions. We model a population with a reactiondiffu- Dawn Woodard sion system, coupled to a heterogeneous environment that Uber, USA shifts with time due to climate change.
  • 4 AN10 Abstracts

    4 AN10 Abstracts

    4 AN10 Abstracts IC1 IC4 On Dispersive Equations and Their Importance in Kinematics and Numerical Algebraic Geometry Mathematics Kinematics underlies applications ranging from the design Dispersive equations, like the Schr¨odinger equation for ex- and control of mechanical devices, especially robots, to the ample, have been used to model several wave phenom- biomechanical modelling of human motion. The major- ena with the distinct property that if no boundary con- ity of kinematic problems can be formulated as systems ditions are imposed then in time the wave spreads out of polynomial equations to be solved and so fall within spatially. In the last fifteen years this field has seen an the domain of algebraic geometry. While symbolic meth- incredible amount of new and sophisticated results proved ods from computer algebra have a role to play, numerical with the aid of mathematics coming from different fields: methods such as polynomial continuation that make strong Fourier analysis, differential and symplectic geometry, an- use of algebraic-geometric properties offer advantages in alytic number theory, and now also probability and a bit of efficiency and parallelizability. Although these methods, dynamical systems. In this talk it is my intention to present collectively called Numerical Algebraic Geometry, are ap- few simple, but still representative examples in which one plicable wherever polynomials arise, e.g., chemistry, biol- can see how these different kinds of mathematics are used ogy, statistics, and economics, this talk will concentrate on in this context. applications in mechanical engineering. A brief review of the main algorithms of the field will indicate their broad Gigliola Staffilani applicability.
  • High Order ADER Schemes and GLM Curl Cleaning for a First Order Hyperbolic Formulation of Compressible Flow with Surface Tension

    High Order ADER Schemes and GLM Curl Cleaning for a First Order Hyperbolic Formulation of Compressible Flow with Surface Tension

    High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension Simone Chiocchetti∗a, Ilya Peshkova, Sergey Gavrilyukb, Michael Dumbsera aLaboratory of Applied Mathematics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento, Italy bIUSTI UMR 7343-CNRS, D´epartement de M´ecanique, Aix-Marseille Universit´e,5 rue Enrico Fermi, 13453 Marseille, France Abstract In this work, we introduce two novel reformulations of the weakly hyperbolic model for two-phase flow with surface tension, recently forwarded by Schmidmayer et al. In the model, the tracking of phase boundaries is achieved by using a vector interface field, rather than a scalar tracer, so that the surface-force stress tensor can be expressed directly as an algebraic function of the state variables, without requiring the computation of gradients of the scalar tracer. An interesting and important feature of the model is that this interface field obeys a curl involution constraint, that is, the vector field is required to be curl-free at all times. The proposed modifications are intended to restore the strong hyperbolicity of the model, and are closely related to divergence-preserving numerical approaches developed in the field of numerical magnetohydrody- namics (MHD). The first strategy is based on the theory of Symmetric Hyperbolic and Thermodynamically Compatible (SHTC) systems forwarded by Godunov in the 60s and 70s and yields a modified system of governing equations which includes some symmetrisation terms, in analogy to the approach adopted later by Powell et al in the 90s for the ideal MHD equations.
  • Final Program

    Final Program

    Final Program The SIAM Conference on the Life Sciences is sponsored by the SIAM Activity Group on Life Sciences (SIAG/LS) The SIAM Activity Group on the Life Sciences was established to foster the application of mathematics to the life sciences and research in mathematics that leads to new methods and techniques useful in the life sciences. The life sciences have become quantitative as new technologies facilitate collection and analysis of vast amounts of data ranging from complete genomic sequences of organisms to satellite imagery of forest landscapes on continental scales. Computers enable the study of complex models of biological processes. The activity group brings together researchers who seek to develop and apply mathematical and computational methods in all areas of the life sciences. It provides a forum that cuts across disciplines to catalyze mathematical research relevant to the life sciences and rapid diffusion of advances in mathematical and computational methods. AN16/LS16 Mobile App Scan the QR code with any QR reader and download the TripBulder EventMobileTM app to your iPhone, iPad, iTouch, or Android devices. You can also visit www.tripbuildermedia.com/apps/siam2016events Society for Industrial and Applied Mathematics 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Telephone: +1-215-382-9800 Fax: +1-215- 386-7999 Conference E-mail: [email protected] Conference Web: www.siam.org/meetings/ Membership and Customer Service: (800) 447-7426 (US & Canada) or +1-215-382-9800 (worldwide) www.siam.org/meetings 2 2016 SIAM Annual Meeting General Information Table of Contents C. David Levermore SIAM Registration Desk University of Maryland, College Park, USA General Information ...............................2 The SIAM registration desk is located on Rachel Levy Exhibitor and Sponsor Information .6 the Concourse Level of the Westin Boston Harvey Mudd College, USA Waterfront.
  • Metric Analysis Solvers April 2018

    Metric Analysis Solvers April 2018

    Eingereicht von Dipl.-Ing. Christoph Hofer, BSc. Angefertigt am Doktoratskolleg “Computational Mathematics” Betreuer und Erstbeurteiler O. Univ.-Prof. Dipl.-Ing. Dr. Ulrich Langer Fast Multipatch Isogeo- Zweitbeurteiler Prof. Dr. Giancarlo Sangalli metric Analysis Solvers April 2018 Dissertation zur Erlangung des akademischen Grades Doktor der technischen Wissenschaften im Doktoratsstudium Technische Wissenschaften JOHANNES KEPLER UNIVERSITAT¨ LINZ Altenbergerstraße 69 4040 Linz, Osterreich¨ www.jku.at DVR 0093696 2 Abstract This thesis is devoted to the generalization of the Dual-Primal Finite Element Tearing and Interconnecting (FETI-DP) method to linear algebraic systems arising from the Isogemetric Analysis (IgA) of linear elliptic boundary value problems, like stationary diffusion or heat conduction problems. This IgA version of the FETI-DP method is called Dual-Primal Isogeometric Tearing and Interconnect (IETI-DP) method. The FETI-DP method is well established as parallel solver for large-scale systems of finite element equations, especially, in the case of heterogeneous coefficients having jumps across subdomain interfaces. These methods belong to the class of non-overlapping domain decomposition methods. In practise, a complicated domain can often not be represented by a single patch, instead a collection of patches is used to represent the computational domain, called multi-patch domains. Regarding the solver, it is a natural idea to use this already available decomposition into patches directly for the construction of a robust and parallel solver. We investigate the cases where the IgA spaces are continuous or even discontinuous across the patch interfaces, but smooth within the patches. In the latter case, a stable formulation is obtained by means of discontinuous Galerkin (dG) techniques.
  • Numerical Investigation of Parallel-In-Time Methods for Dominantly Hyperbolic Equations

    Numerical Investigation of Parallel-In-Time Methods for Dominantly Hyperbolic Equations

    Numerical Investigation of Parallel-in-Time Methods for Dominantly Hyperbolic Equations Vom Fachbereich Maschinenbau an der Technischen Universität Darmstadt zur Erlangung des akademischen Grades eines Doktor-Ingenieurs (Dr.-Ing.) genehmigte Dissertation vorgelegt von Andreas Schmitt, M.Sc. aus Düsseldorf Berichterstatter: Prof. Dr. rer. nat. Michael Schäfer Mitberichterstatter: Prof. Dr. rer. nat. Sebastian Schöps Tag der Einreichung: 23.07.2018 Tag der mündlichen Prüfung: 10.10.2018 Darmstadt 2019 D 17 Schmitt, Andreas Numerical Investigation of Parallel-in-Time Methods for Dominantly Hyperbolic Equations Technische Universität Darmstadt Tag der mündlichen Prüfung: 10.10.2018 Jahr der Veröffentlichung auf TUprints: 2019 URN: urn:nbn:de:tuda-tuprints-83286 Veröffentlicht unter CC BY-NC-ND 4.0 International https://creativecommons.org/licences/by-nc-nd/4.0/ Vorwort Die vorliegende Arbeit “Numerical Investigation of Parallel-in-Time Methods for Dominantly Hyperbolic Equations” ist mein Beitrag zum Forschungsgebiet der zeitparallelen Methoden. Diese Dissertation wurde als Abschlussarbeit meines Promotionsvorhabens an der Technischen Universität Darmstadt am Fachgebiet für Numerische Berechnungsverfahren im Maschinenbau und der Graduiertenschule Computational Engineering verfasst. Mit den Inhalten der Dissertation habe ich mich von Mai 2015 bis Juli 2018 beschäftigt. Ich möchte mich bei Prof. Michael Schäfer für die Möglichkeit zur Pro- motion, den Vorschlag des spannenden Themengebietes und die Betreuung bedanken. Insbesondere danke ich Ihm auch für die gegebenen Freiheiten, so dass ich das Thema nach meinen Interessen erforschen konnte. Des Weiteren danke ich Prof. Sebastian Schöps für die Übernahme der Mitberichterstatter- schaft und die konstruktiven Gespräche. Für viele konstruktive Gespräche möchte ich mich auch bei den Mitentwick- lern von SWEET bedanken.
  • Computers and Mathematics with Applications the Method of Lines For

    Computers and Mathematics with Applications the Method of Lines For

    Computers and Mathematics with Applications 56 (2008) 2175–2188 Contents lists available at ScienceDirect Computers and Mathematics with Applications journal homepage: www.elsevier.com/locate/camwa The method of lines for solution of the one-dimensional wave equation subject to an integral conservation condition Fatemeh Shakeri, Mehdi Dehghan ∗ Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran 15914, Iran article info a b s t r a c t Article history: Hyperbolic partial differential equations with an integral condition serve as models in Received 14 November 2007 many branches of physics and technology. Recently, much attention has been expended Received in revised form 22 March 2008 in studying these equations and there has been a considerable mathematical interest in Accepted 25 March 2008 them. In this work, the solution of the one-dimensional nonlocal hyperbolic equation is presented by the method of lines. The method of lines (MOL) is a general way of viewing Keywords: a partial differential equation as a system of ordinary differential equations. The partial Hyperbolic partial differential equation derivatives with respect to the space variables are discretized to obtain a system of ODEs Non-classic boundary condition Method of lines in the time variable and then a proper initial value software can be used to solve this ODE System of ordinary differential equations system. We propose two forms of MOL for solving the described problem. Several numerical Integral conservation condition examples and also some comparisons with finite difference methods will be investigated to confirm the efficiency of this procedure.
  • The Method of Lines for Solution of the Two- Dimensional Elliptic Equation

    The Method of Lines for Solution of the Two- Dimensional Elliptic Equation

    ANNALS of Faculty Engineering Hunedoara – International Journal of Engineering Tome XIV [2016] – Fascicule 1 [February] ISSN: 1584-2665 [print; online] ISSN: 1584-2673 [CD-Rom; online] a free-access multidisciplinary publication of the Faculty of Engineering Hunedoara 1. G.V. PATEL, 2. K.B. PATEL THE METHOD OF LINES FOR SOLUTION OF THE TWO- DIMENSIONAL ELLIPTIC EQUATION 1-2. Department of Mathematics, Veer Narmad South Gujarat University, Surat, Gujarat, INDIA ABSTACT: The solution of the two-dimensional elliptic equation is presented by the method of lines. The method of lines (MOL) is a general way of viewing a partial differential equation as a system of ordinary differential equations. The partial derivatives with respect to the one dimension spatial variable is discretized to obtain a system of ODEs in the second dimension spatial variable and then using analytic method with eigenvalues and eigenvectors to solve this ODEs system. Keywords: Elliptic equation, Method of lines, Eigenvalues and Eigenvectors 1. INTRODUCTION Over the last few years, it has become increasingly apparent that many physical phenomena can be described in terms of elliptic partial differential equations with the classical boundary condition [3,13,14].Growing attention is being paid to the development, analysis and implementation of numerical methods for the solution of these problems[1,2,3].Elliptic boundary value problems in two dimensions that have been studied by several authors [5 - 10].This equation have been solved directly by various numerical methods such as Adomain decomposition method, Finite volume method, Finite difference method, Finite element method and etc. In this research, we consider the following problem of this family of equations ∂ 2 u ∂ 2 u + = 0, ∂x 2 ∂y2 (1) u = u(x, y),0 ≤ x ≤ a,0 ≤ y ≤ b with Direchlet boundary conditions u(0, y) = f1(y) (2) u(a, y) = f2 (y) (3) u(x,0) = g1(x) (4) u(x,b) = g2 (x) (5) where f1(y),f2 (y),g1(x) and g2 (x)are known functions.