Elliptic marching methods and domain decomposition:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
1995
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| Series: | Symbolic and numeric computation series
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 190 S. graph. Darst. |
| ISBN: | 0849373786 |
Staff View
MARC
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| 245 | 1 | 0 | |a Elliptic marching methods and domain decomposition |c Patrick J. Roache |
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
Preface v
Chapter 1. BASIC MARCHING METHODS FOR 2D ELLIPTIC PROBLEMS
1.1 Introduction 1
1.1.1 The Impact of Direct Methods 1
1.1.2 Direct Marching Methods 2
1.1.3 History of Marching Methods 2
1.2.1 The Marching Method in ID 4
1.2.2 The Reference 2D Problem 6
1.2.3 Operation Counts as an Index of Merit 8
1.2.4 Operation Counts for the Reference 2D Problem 9
1.2.5 Error Propagation Characteristics for the Reference 2D Problem 13
1.2.6 Gradient, Mixed, and Periodic Boundary Conditions 16
1.2.7 Irregular Mesh and Variable Coefficient Poisson Equations 19
1.2.8 Irregular Geometries 20
1.3 Other Second Order Elliptic Equations 20
1.3.1 Advection Diffusion Equations 20
1.3.2 Upwind Differences 22
1.3.3 Turbulence Terms 24
1.3.4 Fibonacci Scale 24
1.3.5 Helmholtz Terms 26
1.3.6 Cross Derivatives 27
1.3.7 Gradient Boundary Conditions and Cross Derivatives 29
1.3.8 Interior Flux Boundaries 31
1.4 Closing Note for Chapter 1 33
References for Chapter 1 33
Chapter 2. HIGH ORDER EQUATIONS
2.1 Introduction 37
2.2 High Order Accuracy Operators 37
2.3 Higher Order Accurate Solutions by Deferred Corrections 38
2.4 Higher Order Elliptic Equations 39
2.5 Operation Counts for Higher Order Systems 40
2.6 Finite Element Equations 43
References for Chapter 2 44
Chapter 3. EXTENDING THE MESH SIZE: DOMAIN DECOMPOSITION
3.1 Introduction 45
3.2 Mesh Doubling by Two Directional Marching 46
3.3 Multiple Marching 48
3.4 Patching 50
3.5 Influence Extending 51
3.6 Other Direct Methods for Extending the Mesh Size 54
3.7 Lower Accuracy Stencils Plus Iteration 55
3.8 Iterative Coupling for Subregions 56
3.8.1 Preconditioning 56
3.8.2 Block Iterative Relaxation 57
3.8.3 Schwarz Alternating Procedure 58
3.9 Higher Precision Arithmetic: Applications on Workstations and
Virtual Parallel Networks 60
References for Chapter 3 62
Chapter 4. BANDED APPROXIMATIONS TO INFLUENCE MATRICES
4.1 Introduction 67
4.2 Banded Approximation to C 67
4.3 Operation Count and Storage for Banded CB 69
4.4 Intrinsic Storage: Data Compression for Massively Parallel Computers 71
4.5 Banded Approximation to C 73
References for Chapter 4 74
Chapter 5. MARCHING METHODS IN 3D
5.1 Introduction 77
5.2 Simple 3D Marching 77
5.3 Error Propagation Characteristics for the 3D EVP 78
5.4 Operation Count and Storage Penalty for the 3D EVP Method 79
5.5 Banded Approximations in 3D 80
5.6 Operation Count for Banded Approximation in 3D 82
5.7 Additional Terms in the 3D Marching Method 83
5.8 3D EVP FFT Method 84
5.9 Error Propagation Characteristics for 3D EVP FFT Method 84
5.10 Operation Count and Storage Penalty for the 3D EVP FFT Method 84
5.11 Accuracy and Additional Terms in 3D EVP FFT Method 86
5.12 AT Plane Relaxation Within Multigrid and Domain Decomposition Methods . . 87
References for Chapter 5 88
Chapter 6. PERFORMANCE OF THE 2D GEM CODE
6.1 Introduction 91
6.2 Uses and Users 91
6.3 Overview of the GEM Codes 92
6.4 Problem Description in the Basic GEM Code 92
6.5 Tests of the Basic GEM Code 95
6.6 The Stabilizing Codes GEMPAT2 and GEMPAT4 96
6.7 Timing Tests of the Stabilized Codes 97
6.8 Representative Accuracy Testing 100
6.9 Conclusions 102
References for Chapter 6 103
Chapter 7. VECTORIZATION AND PARALLELIZATION
7.1 Introduction 105
7.2 Vectorizing the Tridiagonal Algorithm and the 9 Point March 105
7.3 Vectorizing the 5 Point March 106
7.4 Timing and Accuracy for the Vectorized Marches 106
7.5 Efficiencies 108
7.6 Multiprocessor Architectures 110
References for Chapter 7 Ill
Chapter 8. SEMIDIRECT METHODS FOR NONLINEAR EQUATIONS
OF FLUID DYNAMICS
8.1 Introduction: Time Dependent Calculations vs. Semidirect Methods 113
8.2 Burgers Equation by Time Accurate Methods 114
8.3 Basic Idea of Semidirect Methods 115
8.4 Burgers Equation by Picard Semidirect Iteration 115
8.5 Further Discussion of the Picard Semidirect Iteration 117
8.6 Genesis of Semidirect Methods 117
8.7 NOS Method 119
8.8 LAD Method 120
8.9 Performance of NOS and LAD on the Driven Cavity Problem 120
8.10 Relative Importance of Lagging Boundary Conditions 126
8.11 Performance of LAD and NOS on a Flow Through Problem 127
8.12 Optimum Relaxation Factor and Convergence for Large Problems 128
8.13 Choice between LAD and NOS 133
8.14 Split NOS Method 134
8.15 A Better Boundary Condition on Wall Vorticity 136
8.15.1 The Trouble with the Conventional Methods for Wall Vorticity 136
8.15.2 Israeli Dorodnicyn Method for Wall Vorticity 137
8.15.3 Analytical Prediction of Optimum g 137
8.15.4 Performance of Israeli Dorodnicyn Method 138
8.16 Dorodnicyn Meller Method 139
8.17 Viscous Flows in Alternate Variables 139
8.18 BID Method 139
8.18.1 BID Iteration 139
8.18.2 BID Boundary Conditions for the Driven Cavity Problem 141
8.183 BID Performance for the Driven Cavity 142
8.18.4 BID Performance for Flow Through Problems 144
8.19 FOD and Coupled Systems Solvers 145
8.20 Other Applications and Non Time Like Methods 146
8.21 Remarks on Soution Uniqueness 147
8.22 Remarks on Semidirect Methods within Domain Decomposition 148
References for Chapter 8 148
Chapter 9. COMPARISON TO MULTIGRID METHODS
9.1 Introduction 153
9.2 Definition of the Methods 153
9.3 Treatment of Nonlinearities 153
9.4 Speed and Accuracy 154
9.5 Grid Sensitivity and Word Length Sensitivity 155
9.6 Directionality 155
9.7 Storage Penalty 156
9.8 Dimensionality 156
9.9 Work Estimates 157
9.10 Boundary Conditions 157
9.11 General Coefficient Problems 157
9.12 Grid Transformations 157
9.13 Irregular Logical Space Geometry 157
9.14 Higher Order Systems 157
9.15 Higher Order Accuracy Equations 158
9.16 Finite Element Equations 158
9.17 Use in Time Dependent Problems 158
9.18 Cell Reynolds Number Difficulties 158
9.19 Virtual Problems 158
9.20 MLAT and other Grid Adaptation 159
9.21 Vectorization, Parallelization, and Convergence Testing 159
9.22 Simplicity, Modularity, and Robustness 160
9.23 Summary 160
References for Chapter 9 161
APPENDIX A. MARCHING SCHEMES AND ERROR PROPAGATION FOR
VARIOUS DISCRETE LAPLACIANS
A.1 Introduction 163
A.2 Standard 5 Point Laplacian 163
A.3 Uneven Mesh 164
A.4 Other Elliptic Operators 164
A.5 Other Analogs for the Laplacian 168
References for Appendix A 172
APPENDIX B. TRIDIAGONAL ALGORITHM FOR
PERIODIC BOUNDARY CONDITIONS
B.I Introduction 173
B.2 Problem Statement 173
B.3 Algorithm 4 174
B.4 The Influence Coefficient Algorithm 5 174
B.5 Completed Algorithm 4 175
B.6 Operation Counts and Other Comparisons 176
References for Appendix B 178
APPENDIX C. GAUSS ELIMINATION AS A DIRECT SOLVER
C.1 Introduction 179
C.2 Round Off Error 179
C.3 Speed 179
C.4 Storage Penalty 179
C.5 Operation Count and Storage Penalty for 2D 180
C.6 Operation Count and Storage Penalty for 3D 182
C.7 Conclusions 184
References for Appendix C 184
SUBJECT INDEX 185
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| spelling | Roache, Patrick J. Verfasser aut Elliptic marching methods and domain decomposition Patrick J. Roache Boca Raton [u.a.] CRC Press 1995 190 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Symbolic and numeric computation series Decomposition (Mathematics) Differential equations, Elliptic Numerical solutions Zerlegung Mathematik (DE-588)4190746-2 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Zerlegung Mathematik (DE-588)4190746-2 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007093093&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roache, Patrick J. Elliptic marching methods and domain decomposition Decomposition (Mathematics) Differential equations, Elliptic Numerical solutions Zerlegung Mathematik (DE-588)4190746-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| subject_GND | (DE-588)4190746-2 (DE-588)4128130-5 (DE-588)4014485-9 |
| title | Elliptic marching methods and domain decomposition |
| title_auth | Elliptic marching methods and domain decomposition |
| title_exact_search | Elliptic marching methods and domain decomposition |
| title_full | Elliptic marching methods and domain decomposition Patrick J. Roache |
| title_fullStr | Elliptic marching methods and domain decomposition Patrick J. Roache |
| title_full_unstemmed | Elliptic marching methods and domain decomposition Patrick J. Roache |
| title_short | Elliptic marching methods and domain decomposition |
| title_sort | elliptic marching methods and domain decomposition |
| topic | Decomposition (Mathematics) Differential equations, Elliptic Numerical solutions Zerlegung Mathematik (DE-588)4190746-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| topic_facet | Decomposition (Mathematics) Differential equations, Elliptic Numerical solutions Zerlegung Mathematik Numerisches Verfahren Elliptische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007093093&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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