Numerical Solution of Partial Differential Equations on Parallel Computers

  • Are Magnus Bruaset
  • Aslak Tveito
Conference proceedings

DOI: 10.1007/3-540-31619-1

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 51)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Parallel Computing

    1. Front Matter
      Pages 1-1
    2. Ricky A. Kendall, Masha Sosonkina, William D. Gropp, Robert W. Numrich, Thomas Sterling
      Pages 3-54
    3. James D. Teresco, Karen D. Devine, Joseph E. Flaherty
      Pages 55-88
    4. Martin Rumpf, Robert Strzodka
      Pages 89-132
  3. Parallel Algorithms

    1. Front Matter
      Pages 133-133
    2. Luca Formaggia, Marzio Sala, Fausto Saleri
      Pages 135-163
    3. Frank Hülsemann, Markus Kowarschik, Marcus Mohr, Ulrich Rüde
      Pages 165-208
    4. Nikos Chrisochoides
      Pages 237-264
  4. Parallel Software Tools

    1. Front Matter
      Pages 265-265
    2. Robert D. Falgout, Jim E. Jones, Ulrike Meier Yang
      Pages 267-294
    3. Xing Cai, Hans Petter Langtangen
      Pages 295-325
    4. Lois Curfman McInnes, Benjamin A. Allan, Robert Armstrong, Steven J. Benson, David E. Bernholdt, Tamara L. Dahlgren et al.
      Pages 327-381
  5. Parallel Applications

    1. Front Matter
      Pages 383-383
    2. Matthew G. Knepley, Richard F. Katz, Barry Smith
      Pages 413-438
    3. Carolin Körner, Thomas Pohl, Ulrich Rüde, Nils Thürey, Thomas Zeiser
      Pages 439-466
  6. Back Matter
    Pages 467-487

About these proceedings

Introduction

Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the supercomputing power of today. When trying to replicate Nature in the computer’s silicon test tube, there is need for precise and computable process descriptions. The scienti?c ?elds of Ma- ematics and Physics provide a powerful vehicle for such descriptions in terms of Partial Differential Equations (PDEs). Formulated as such equations, physical laws can become subject to computational and analytical studies. In the computational setting, the equations can be discreti ed for ef?cient solution on a computer, leading to valuable tools for simulation of natural and man-made processes. Numerical so- tion of PDE-based mathematical models has been an important research topic over centuries, and will remain so for centuries to come. In the context of computer-based simulations, the quality of the computed results is directly connected to the model’s complexity and the number of data points used for the computations. Therefore, computational scientists tend to ?ll even the largest and most powerful computers they can get access to, either by increasing the si e of the data sets, or by introducing new model terms that make the simulations more realistic, or a combination of both. Today, many important simulation problems can not be solved by one single computer, but calls for parallel computing.

Keywords

Computer Simulation architecture computer science differential equation domain decomposition multigrid numerical analysis numerical methods parallel computing partial differential equation partial differential equations programming programming language scientific computing

Editors and affiliations

  • Are Magnus Bruaset
    • 1
  • Aslak Tveito
    • 1
  1. 1.Simula Research LaboratoryLysaker, FornebuNorway

Bibliographic information

  • Copyright Information Springer-Verlag Berlin Heidelberg 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-29076-6
  • Online ISBN 978-3-540-31619-0
  • Series Print ISSN 1439-7358