Concurrent scientific computing:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY ; Berlin [u.a.]
Springer
1994
|
| Series: | Texts in applied mathematics
16 |
| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 311 - 317 |
| Physical Description: | XIX, 328 S. graph. Darst. |
| ISBN: | 3540941959 0387941959 |
Staff View
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| 245 | 1 | 0 | |a Concurrent scientific computing |c Eric F. Van De Velde |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Series Preface v
Preface vii
Acknowledgments ix
List of Figures xvii
List of Tables xxi
1 The Basics 1
1.1 Notation 2
1.2 Multicomputers 4
1.3 Data Distribution 6
1.4 Program Development 8
1.5 Communication 11
1.6 Performance Analysis 14
1.6.1 Computations and Execution Times 15
1.6.2 Speed up: Theory 16
1.6.3 Speed up: Practice 19
1.6.4 Performance Modeling 21
1.6.5 Vector Operations 22
1.7 The Recursive Doubling Algorithm 26
1.7.1 Specification 26
xii Contents
1.7.2 Implementation 26
1.7.3 Performance Analysis 30
1.7.4 Numerical Aspects 32
1.8 Notes and References 33
1.8.1 Communicating Sequential Processes 33
1.8.2 UNITY 33
1.8.3 Stepwise Refinement 34
1.8.4 Speed up and Efficiency 34
1.8.5 Other Performance Measures 36
Exercises 38
2 Vector and Matrix Operations 39
2.1 Matrix Vector Product 39
2.1.1 Specification 39
2.1.2 Implementation 40
2.1.3 Performance Analysis 44
2.1.4 Sparse Matrices 47
2.2 Vectors and Matrices 49
2.2.1 Vector Conversion 50
2.2.2 Inner Product 52
2.3 Practical Data Distributions 53
2.4 Vector Shift 55
2.4.1 Definition and Specification 55
2.4.2 Implementation 57
2.5 The Diagonal Form of Matrices 58
2.5.1 Definition 58
2.5.2 Matrix Vector Product 60
2.5.3 Matrix Transpose 61
2.5.4 Vector Matrix Product 62
2.5.5 Matrix Matrix Product 62
2.5.6 Diagonal Form and Column Distribution 63
2.6 Notes and References 64
Exercises 65
3 Iterative Methods 67
3.1 The Power Method 68
3.1.1 Numerics 68
3.1.2 Program 70
3.2 Relaxation Methods 73
3.3 The Conjugate Gradient Method 76
3.3.1 Subspace Minimization 76
3.3.2 The Steepest Descent Method 78
3.3.3 Krylov Subspace Minimization 79
3.3.4 The Program 80
3.3.5 Preconditioning 83
Contents xiii
3.3.6 Termination and Convergence 85
3.4 The Quasi Minimal Residual Method 86
3.4.1 Krylov Space Bases 86
3.4.2 Quasi Minimization in a Subspace 88
3.4.3 Updating 89
3.4.4 The Program 92
3.5 Notes and References 93
Exercises 95
4 LU Decomposition 97
4.1 LU Decomposition Without Pivoting 97
4.1.1 Specification 97
4.1.2 Implementation 99
4.1.3 Performance Analysis 101
4.2 LU Decomposition With Pivoting 103
4.2.1 Specification 103
4.2.2 Implementation 106
4.2.3 Pivot Strategies 107
4.3 Triangular Systems Ill
4.3.1 Specification 112
4.3.2 Implementation 113
4.3.3 Performance Analysis 117
4.4 Linear System Solver 118
4.5 Sparse Systems 121
4.6 Notes and References 122
Exercises 123
5 QR Decomposition 125
5.1 Introduction 125
5.1.1 Orthogonal Matrices 125
5.1.2 Gram Schmidt Orthogonalization 126
5.1.3 QR Decomposition 126
5.1.4 QR Decomposition and Linear Systems 127
5.2 Householder QR Decomposition 128
5.2.1 Householder Reflections 128
5.2.2 QR Decomposition 130
5.3 Givens QR Decomposition 131
5.3.1 Givens Rotations 131
5.3.2 QR Decomposition 132
5.4 Multicomputer QR Decomposition 133
5.5 Notes and References 140
Exercises 140
xiv Contents
6 Tridiagonal Solvers 141
6.1 Full Recursive Doubling 141
6.1.1 Specification 142
6.1.2 Implementation 144
6.1.3 Performance Analysis 145
6.2 Rational Recursion 146
6.3 Tridiagonal LU Decomposition 147
6.3.1 Specification 147
6.3.2 Implementation 148
6.3.3 Performance Analysis 151
6.4 An Iterative Tridiagonal Solver 152
6.5 Notes and References 153
Exercises 154
7 The Fast Fourier Transform 155
7.1 Fourier Analysis 155
7.1.1 Fourier Series 155
7.1.2 The Discrete Fourier Transform 156
7.1.3 Aliasing 158
7.2 Divide and Conquer 159
7.3 The Fast Fourier Transform Algorithm 161
7.4 Multicomputer Implementation 167
7.5 Generalizations 172
7.5.1 Bit Reversal Maps 172
7.5.2 General Dimensions 172
7.5.3 The Discrete Real Fourier Transform 173
7.5.4 The Discrete Fourier Sine Transform 174
7.5.5 The Discrete Fourier Cosine Transform 176
7.5.6 Multivariate Discrete Fourier Transforms 177
7.6 Notes and References 181
Exercises 181
8 Poisson Solvers 183
8.1 The Poisson Problem 183
8.2 Jacobi Relaxation 187
8.2.1 Specification 187
8.2.2 Implementation 188
8.2.3 Performance Analysis 195
8.3 Gauss Seidel Relaxation 197
8.3.1 Specification 197
8.3.2 Implementation 198
8.3.3 Performance Analysis 199
8.3.4 Gauss Seidel Variants 200
8.4 Line Relaxation 202
8.4.1 Specification 202
Contents xv
8.4.2 Implementation 204
8.5 Domain Decomposed Relaxations 207
8.6 The Conjugate Gradient Method 208
8.7 FFT Based Fast Poisson Solvers 210
8.7.1 The Poisson Problem in Fourier Space 210
8.7.2 Fast Poisson Solvers 212
8.7.3 Variants 213
8.8 Three Dimensional Problems 214
8.9 Notes and References 215
Exercises 215
9 Multigrid Methods 217
9.1 Relaxation Methods 218
9.1.1 Model Problem 218
9.1.2 Model Problem Analysis 219
9.1.3 Convergence Factor 220
9.1.4 Smoothing Factor 220
9.1.5 Smoothing vs. Convergence 221
9.2 Two Grid Methods 222
9.2.1 Intuitive Development 222
9.2.2 Model Problem Analysis 224
9.3 Multigrid Methods 227
9.3.1 Elementary Multigrid 227
9.3.2 Performance Analysis 229
9.3.3 Full Multigrid 231
9.4 Multicomputer Multigrid 232
9.4.1 Specification Programs 232
9.4.2 Multicomputer Relaxation 235
9.4.3 Multicomputer Restriction 236
9.4.4 Multicomputer Interpolation 237
9.4.5 Multicomputer Multigrid 239
9.5 Notes and References 239
Exercises 240
10 Domain Decomposition 241
10.1 Composite Domains 242
10.1.1 The Capacitance System 242
10.1.2 Capacitance System Solvers 244
10.2 Domain Decomposition for Concurrency 246
10.2.1 Domain Decomposition 247
10.2.2 Data Distribution 249
10.2.3 Vector Operations 251
10.2.4 Sequential Poisson Solver 254
10.2.5 Matrix Operations 254
10.2.6 The Domain Decomposition Program 257
xvi Contents
10.3 Performance Analysis 260
10.4 Notes and References 263
Exercises 263
11 Particle Methods 265
11.1 The Astrophysical iV Body Problem 266
11.2 The N2 Algorithm 267
11.3 Fast Particle Methods 270
11.4 Concurrent Fast Particle Methods 275
11.5 Notes and References 280
Exercises 281
12 Computer Dependency 283
12.1 Pipelined Processors 284
12.2 Hierarchical Memories 286
12.3 Communication Networks 290
12.3.1 Hypercubes and Meshes 291
12.3.2 Process Placement 292
12.3.3 A Transpose Algorithm 295
12.3.4 Communication Hiding 298
12.4 Multiprocessors 301
12.5 Synchronous Arrays of Processors 304
12.6 Benchmarking 306
12.7 Notes and References 308
Exercises 308
Bibliography 311
Index 319
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| spelling | Van de Velde, Eric F. Verfasser aut Concurrent scientific computing Eric F. Van De Velde New York, NY ; Berlin [u.a.] Springer 1994 XIX, 328 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 16 Literaturverz. S. 311 - 317 Parallelle verwerking gtt Parallel processing (Electronic computers) Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Parallelverarbeitung (DE-588)4075860-6 gnd rswk-swf Paralleler Algorithmus (DE-588)4193615-2 gnd rswk-swf Parallelverarbeitung (DE-588)4075860-6 s DE-604 Paralleler Algorithmus (DE-588)4193615-2 s Numerische Mathematik (DE-588)4042805-9 s Texts in applied mathematics 16 (DE-604)BV002476038 16 text/html http://catdir.loc.gov/catdir/enhancements/fy0815/93043289-d.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005913158&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Van de Velde, Eric F. Concurrent scientific computing Texts in applied mathematics Parallelle verwerking gtt Parallel processing (Electronic computers) Numerische Mathematik (DE-588)4042805-9 gnd Parallelverarbeitung (DE-588)4075860-6 gnd Paralleler Algorithmus (DE-588)4193615-2 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4075860-6 (DE-588)4193615-2 |
| title | Concurrent scientific computing |
| title_auth | Concurrent scientific computing |
| title_exact_search | Concurrent scientific computing |
| title_full | Concurrent scientific computing Eric F. Van De Velde |
| title_fullStr | Concurrent scientific computing Eric F. Van De Velde |
| title_full_unstemmed | Concurrent scientific computing Eric F. Van De Velde |
| title_short | Concurrent scientific computing |
| title_sort | concurrent scientific computing |
| topic | Parallelle verwerking gtt Parallel processing (Electronic computers) Numerische Mathematik (DE-588)4042805-9 gnd Parallelverarbeitung (DE-588)4075860-6 gnd Paralleler Algorithmus (DE-588)4193615-2 gnd |
| topic_facet | Parallelle verwerking Parallel processing (Electronic computers) Numerische Mathematik Parallelverarbeitung Paralleler Algorithmus |
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