Solving partial differential equations on parallel computers:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1994
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 259 S. graph. Darst. |
| ISBN: | 9810215789 |
Staff View
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| 245 | 1 | 0 | |a Solving partial differential equations on parallel computers |c Jianping Zhu |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1994 | |
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Record in the Search Index
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| adam_text | Contents
1 Introduction 1
1.1 Exploiting Parallelism 1
1.2 Parallel Computers 2
1.2.1 Shared Memory and Distributed Memory 3
1.2.1.1 Shared Memory Parallel Computers 3
1.2.1.2 Distributed Memory Parallel Computers 4
1.2.2 SIMD and MIMD 6
1.2.2.1 SIMD Parallel Computers 6
1.2.2.2 MIMD Parallel Computers 8
1.2.3 Shared Address Space and Distributed Physical Memory ... 8
1.3 Performance Evaluations 12
1.3.1 Speedup 12
1.3.2 Efficiency 14
1.3.3 Amdahl s Law 15
1.3.4 Gustafson s Model 16
2 Parallel Algorithms for Solving PDE 19
2.1 Discretization by Finite Difference Method 22
2.2 Parallel Relaxation Algorithms 27
2.2.1 Jacobi Algorithm 27
2.2.2 Gauss Seidel and SOR Algorithms 28
2.2.2.1 Gauss Seidel Algorithm 28
2.2.2.2 SOR Algorithm (Successive Over Relaxation Algorithm) 29
2.2.3 Parallel Relaxation Algorithms 30
2.2.3.1 Parallel Jacobi Algorithm 30
2.2.3.2 Parallel Gauss Seidel Algorithm and Red Black Or¬
dering 33
2.3 Parallel ADI Algorithm 41
2.3.1 ADI Algorithm 41
xi
2.3.2 ADI Algorithm on a Ring of Parallel Processors 45
2.3.3 ADI Algorithm on a 2 D Grid of Parallel Processors 49
2.3.4 Further Improvement on Parallel ADI Algorithm 52
2.3.5 Three Dimensionai Problems 55
2.4 Parallel Multigrid Method 55
2.4.1 Multigrid Method 55
2.4.2 Parallelization by Grid Splitting 63
2.4.3 Agglomeration 65
2.4.4 Filtering Algorithm 65
2.4.5 Concurrent Relaxations on Multiple Grids 68
2.5 Parallel Conjugate Gradient Algorithm 73
2.5.1 Conjugate Gradient Method 73
2.5.2 Parallel Conjugate Gradient Algorithm 75
2.5.3 Preconditioned Conjugate Gradient Method (PCG) 78
2.5.3.1 Truncated Series and Polynomial Preconditioning . . 81
2.5.3.2 Incomplete Factorization Preconditioning 84
2.5.3.3 Domain Decomposition Preconditioning 88
3 Implementations 95
3.1 Intel iPSC/860 Hypercubes 95
3.2 Inter processor Communications on iPSC/860 98
3.2.1 Connection Topology 98
3.2.2 Inter processor Communications 104
3.3 Communication Analysis for Domain Decomposition Method .... 107
3.3.1 Two Dimensional Domains 108
3.3.2 Three Dimensional Domains 113
3.4 Bandwidth Improvement using Forced Message Type 117
3.4.1 Message Passing Using Forced Message Type 118
3.4.2 Application: One Dimensional Domain Decomposition .... 119
3.4.3 Application: Two Dimensional Domain Decomposition .... 122
3.5 KSR 1 Parallel Computers 124
3.6 Automatic, Semi automatic and Manual Parallelization 126
3.6.1 Automatic Parallelization 127
3.6.2 Semi automatic and Manual Parallelization 129
3.6.2.1 Where to Parallelize 130
3.6.2.2 How to Parallelize 133
xii
4 Applications 139
4.1 Numerical Solution of Poisson s Equation 139
4.2 Numerical Simulations of Multi phase Plow 145
4.3 Discretization and Parallelization 149
4.4 Numerical Experiments 155
4.4.1 Results on iPSC/860 Hypercubes 155
4.4.2 Results on KSR 1 Parallel Computers 164
5 Parallel Time Stepping Algorithms 173
5.1 A New Dimension for Parallelization 173
5.2 Waveform Relaxation 176
5.2.1 Waveform Relaxation for Time Dependent PDEs 178
5.2.2 Multigrid Waveform Relaxation 181
5.2.3 Parallel Implementation of the Multigrid Waveform Relaxations 183
5.3 Pipeline Iteration 186
5.4 Window Relaxation 195
5.5 Parabolic Multigrid Method 202
5.6 General Form of Parallel Time Stepping Algorithms 203
5.7 Complexity Analysis 209
6 Future Development 217
6.1 More on Performance Evaluations 217
6.2 Programming Language 223
6.3 Automatic Parallelization Tools 224
6.4 Distributed Computing Network 229
6.4.1 Homogeneous Computing Network 229
6.4.2 Heterogeneous Computing Network 230
6.4.3 Software Tools 232
6.5 Metacenters and Metacomputers 235
Bibliography 239
Index 257
xiii
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| isbn | 9810215789 |
| language | English |
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| physical | XIII, 259 S. graph. Darst. |
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| publisher | World Scientific |
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| spelling | Zhu, Jianping Verfasser aut Solving partial differential equations on parallel computers Jianping Zhu Singapore [u.a.] World Scientific 1994 XIII, 259 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bilgisayar algoritmaları Diferansiyel denklemler, Kısmi - Sayısal çözümler Paralel işlem (Elektronik bilgisayarlar) Computer algorithms Differential equations, Partial Numerical solutions Parallel processing (Electronic computers) Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Parallelrechner (DE-588)4173280-7 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 s Partielle Differentialgleichung (DE-588)4044779-0 s Parallelrechner (DE-588)4173280-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007074469&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zhu, Jianping Solving partial differential equations on parallel computers Bilgisayar algoritmaları Diferansiyel denklemler, Kısmi - Sayısal çözümler Paralel işlem (Elektronik bilgisayarlar) Computer algorithms Differential equations, Partial Numerical solutions Parallel processing (Electronic computers) Partielle Differentialgleichung (DE-588)4044779-0 gnd Parallelrechner (DE-588)4173280-7 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4173280-7 (DE-588)4128130-5 |
| title | Solving partial differential equations on parallel computers |
| title_auth | Solving partial differential equations on parallel computers |
| title_exact_search | Solving partial differential equations on parallel computers |
| title_full | Solving partial differential equations on parallel computers Jianping Zhu |
| title_fullStr | Solving partial differential equations on parallel computers Jianping Zhu |
| title_full_unstemmed | Solving partial differential equations on parallel computers Jianping Zhu |
| title_short | Solving partial differential equations on parallel computers |
| title_sort | solving partial differential equations on parallel computers |
| topic | Bilgisayar algoritmaları Diferansiyel denklemler, Kısmi - Sayısal çözümler Paralel işlem (Elektronik bilgisayarlar) Computer algorithms Differential equations, Partial Numerical solutions Parallel processing (Electronic computers) Partielle Differentialgleichung (DE-588)4044779-0 gnd Parallelrechner (DE-588)4173280-7 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Bilgisayar algoritmaları Diferansiyel denklemler, Kısmi - Sayısal çözümler Paralel işlem (Elektronik bilgisayarlar) Computer algorithms Differential equations, Partial Numerical solutions Parallel processing (Electronic computers) Partielle Differentialgleichung Parallelrechner Numerisches Verfahren |
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