Numerical Solution of Partial Differential Equations on Parallel Computers

1. Front Matter

   Pages I-XII

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2. Parallel Computing

   1. Front Matter

      Pages 1-1

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   2. Parallel Programming Models Applicable to Cluster Computing and Beyond

      • Ricky A. Kendall, Masha Sosonkina, William D. Gropp, Robert W. Numrich, Thomas Sterling

      Pages 3-54

   3. Partitioning and Dynamic Load Balancing for the Numerical Solution of Partial Differential Equations

      • James D. Teresco, Karen D. Devine, Joseph E. Flaherty

      Pages 55-88

   4. Graphics Processor Units: New Prospects for Parallel Computing

      • Martin Rumpf, Robert Strzodka

      Pages 89-132

3. Parallel Algorithms

   1. Front Matter

      Pages 133-133

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   2. Domain Decomposition Techniques

      • Luca Formaggia, Marzio Sala, Fausto Saleri

      Pages 135-163

   3. Parallel Geometric Multigrid

      • Frank Hülsemann, Markus Kowarschik, Marcus Mohr, Ulrich Rüde

      Pages 165-208

   4. Parallel Algebraic Multigrid Methods — High Performance Preconditioners

      • Ulrike Meier Yang

      Pages 209-236

   5. Parallel Mesh Generation

      • Nikos Chrisochoides

      Pages 237-264

4. Parallel Software Tools

   1. Front Matter

      Pages 265-265

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   2. The Design and Implementation of hypre, a Library of Parallel High Performance Preconditioners

      • Robert D. Falgout, Jim E. Jones, Ulrike Meier Yang

      Pages 267-294

   3. Parallelizing PDE Solvers Using the Python Programming Language

      • Xing Cai, Hans Petter Langtangen

      Pages 295-325

   4. Parallel PDE-Based Simulations Using the Common Component Architecture

      • 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

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   2. Full-Scale Simulation of Cardiac Electrophysiology on Parallel Computers

      • Xing Cai, Glenn Terje Lines

      Pages 385-411

   3. Developing a Geodynamics Simulator with PETSc

      • Matthew G. Knepley, Richard F. Katz, Barry Smith

      Pages 413-438

   4. Parallel Lattice Boltzmann Methods for CFD Applications

      • Carolin Körner, Thomas Pohl, Ulrich Rüde, Nils Thürey, Thomas Zeiser

      Pages 439-466

6. Back Matter

   Pages 467-487

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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.

• 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

• Simula Research Laboratory, Lysaker, Fornebu, Norway

  Are Magnus Bruaset, Aslak Tveito

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