Table of contents for Numerical solution of partial differential equations on parallel computers / Are Magnus Bruaset, Aslak Tveito (eds.).


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Part I Parallel Computing
1 Parallel Programming Models Applicable to Cluster Computing
and Beyond
Ricky A. Kendall, Masha Sosonkina, William D. Gropp, Robert W Numrich,
Thomas Sterling .................................................   3
1.1 Introduction ...............................................  3
1.2  Message-Passing Interface ...................................  7
1.3  Shared-Memory Programming with OpenMP ................... 20
1.4  Distributed Shared-Memory Programming Models ................ 36
1.5  Future Programming Models ...............................  42
1.6  Final Thoughts ........... ... . .................. ......... .  49
References ........... ...........   . ............. ..  ............ .  50
2 Partitioning and Dynamic Load Balancing for the Numerical Solution
of Partial Differential Equations
James D. Teresco, Karen D. Devine, Joseph E. Flaherty .................. 55
2.1 The Partitioning and Dynamic Load Balancing Problems .......... 56
2.2  Partitioning and Dynamic Load Balancing Taxonomy ............ 60
2.3  Algorithm Comparisons ..................................... 69
2.4  Software  ................................................. .  71
2.5  Current Challenges .........................................  74
References  .....................................................  81
3 Graphics Processor Units: New Prospects for Parallel Computing
Martin Rumpf Robert Strzodka ...................................... 89
3.1 Introduction ............................................... 89
3.2  Theory  .............. .................................   97
3.3  Practice  ....................................................  103
3.4  Prospects  ..................................................  118
3.5  Appendix: Graphics Processor Units (GPUs) In-Depth ............ 121
References .................................................... .  131
Part II Parallel Algorithms
4 Domain Decomposition Techniques
Luca Formaggia, Marzio Sala, Fausto Saleri............................ 35
4.1  Introduction  ................ .......................... .  35
4.2  The Schur Complement System ............  .. ....... ......  38
4.3  The Schur Complement System Used as a Preconditioner .......... 46
4.4  The Schwarz Preconditioner ................................ 47
4.5  Applications ..............................................  52
4.6  Conclusions  .......................... ... .................  59
References ................................................... .  162
5 Parallel Geometric Multigrid
Frank Hiilsemann, Markus Kowarschik, Marcus Mohr, Ulrich Ride ......... 65
5.1  Overview  ................................................  165
5.2 Introduction to Multigrid .................................... 166
5.3  Elementary Parallel Multigrid .................................. 177
5.4  Parallel Multigrid for Unstructured Grid Applications ........... 189
5.5  Single-Node Performance ............................... . 193
5.6  Advanced Parallel Multigrid  .................................. 95
5.7  Conclusions  ...... ........................................ 4
References  ................................................... .
6 Parallel Algebraic Multigrid Methods - High
Performance Preconditioners
Ulrike M eier  Yang  .......................................... .. 2  9
6.1  Introduction  ............. . .......................... ...2  9
6.2  Algebraic Multigrid - Concept and Description ................... 210
6.3  Coarse Grid Selection ...................................... 212
6.4 Interpolation .............................................. 2 0
6.5  Smoothing ............................................   2 3
6.6  Numerical Results ........................................ 2 5
6.7  Software Packages............................. .......   2 0
6.8  Conclusions and Future Work  ......... ..................  2  2
R eferences  ...................... ........... ..................  2  3
7 Parallel Mesh Generation
Nikos Chrisochoides ............. . ............................. .27
7.1  Introduction  .............................................  237
7.2  Domain Decomposition Approaches ........................ .238
7.3  Parallel Mesh Generation Methods ............................. 2 0
7.4  Taxonomy  ............................................... 2 5
7.5  Implementation  ............................................  2  5
7.6  Future Directions. ............ .  ......................... 258
References ................. ...................  ................ .  259
Part III Parallel Software Tools
8 The Design and Implementation of hypre, a Library of Parallel High
Performance Preconditioners
Robert D. Falgout, Jim E. Jones, Ulrike Meier Yang ................... 267
8.1  Introduction  ............ .................... .... ..........  267
8.2  Conceptual Interfaces ....................................... 268
8.3  Object Model ................................. ............. .  270
8.4  The Structured-Grid Interface (Struct) ...................... 272
8.5  The Semi-Structured-Grid Interface (semiStruct) .............. 274
8.6  The Finite Element Interface (FEI) ............................ 280
8.7  The Linear-Algebraic Interface (IJ)........................... 281
8.8 Implementation ........................................... 282
8.9  Preconditioners and Solvers ................................ 289
8.10  Additional Information  .....................................  291
8.11 Conclusions and Future Work ................................ 291
References ................................................... .  292
9 Parallelizing PDE Solvers Using the Python Programming Language
Xing Cai, Hans Petter Langtangen ................................ 295
9.1  Introduction  ............................................... 295
9.2  High-Performance Serial Computing in Python ................. 296
9.3  Parallelizing Serial PDE Solvers ............................. 299
9.4  Python Software for Parallelization .............. .......... 307
9.5  Test Cases and Numerical Experiments ......................... 313
9.6  Summary ..........................................     . 323
References ....................................................  324
10 Parallel PDE-Based Simulations Using the Common
Component Architecture
Lois Curfinan Mclnnes, Benjamin A. Allan, Robert Armstrong, Steven J.
Benson, David E. Bernholdt, Tamara L. Dahlgren, Lori Freitag Diachin,
Manojkumar Krishnan, James A. Kohl, J. Walter Larson, Sophia Lefantzi,
Jarek Nieplocha, Boyana Norris, Steven G. Parker, Jaideep Ray, Shujia Zhou  327
10.1  Introduction  ............................................... 328
10.2 Motivating Parallel PDE-Based Simulations ................... 330
10.3 High-Performance Components................................ 334
10.4 Reusable Scientific Components .......... .............  344
10.5 Componentization Strategies .................................. 355
10.6 Case Studies: Tying Everything Together .................... 359
10.7 Conclusions and Future Work ................................ 371
References  ......................................................  373
Part IV Parallel Applications
11 Full-Scale Simulation of Cardiac Electrophysiology
on Parallel Computers
Xing Cai, Glenn Terje Lines ........................................ 385
11.1 Introduction ............................................. . 385
11.2 The Mathematical Model .................................... 390
11.3 The Numerical Strategy ..................................... 392
11.4 A Parallel Electro-Cardiac Simulator .......................... 399
11.5 Some Techniques for Overhead Reduction ...................... 403
11.6 Numerical Experiments ..................................... 405
11.7 Concluding Remarks........................................ . 408
References ................................................... . 409
12 Developing a Geodynamics Simulator with PETSc
Matthew G. Knepley, Richard E Katz, Barry Smith ..................... 413
12.1 Geodynamics of Subduction Zones............................ 413
12.2 Integrating PETSc ........................................  415
12.3 Data Distribution and Linear Algebra .......................... 418
12.4  Solvers  ..................................................  428
12.5  Extensions  ...............................................  431
12.6 Simulation Results ........................................ 435
References ................................................ . 437
13 Parallel Lattice Boltzmann Methods for CFD Applications
Carolin Kbrner, Thomas Pohl, Ulrich Riide, Nils Thiirey, Thomas Zeiser ..... 439
13.1  Introduction  ................................................ 439
13.2 Basics of the Lattice Boltzmann Method ........................ 440
13.3 General Implementation Aspects and Optimization of the Single
CPU Performance .......................................... 445
13.4 Parallelization of a Simple Full-Grid LBM Code ................. 452
13.5 Free Surfaces .............................................. 454
13.6 Summary and Outlook .................................... 462
References  .................................... . ... .......... ... .  463
Color Figures ................. ............................... . 467



Library of Congress subject headings for this publication: Differential equations, Partial Numerical solutions Data processing, Parallel processing (Electronic computers)