A tutorial on elliptic PDE solvers and their parallelization:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia
Society for Industrial and Applied Mathematics
2003
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| Series: | Software, environments, tools
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XVIII, 135 S. graph. Darst. |
| ISBN: | 0898715415 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804129819691057152 |
|---|---|
| adam_text | CRAIG C DOUGLAS UNIVERSITY OF KENTUCKY LEXINGTON, KENTUCKY AND YALE
UNIVERSITY NEW HAVEN, CONNECTICUT GUNDOLF HAASE JOHANNES KEPLER
UNIVERSITY LINZ, AUSTRIA ULRICH HANGER JOHANNES KEPLER UNIVERSITY LINZ,
AUSTRIA A TUTORIAL ON ELLIPTIC PDE SOLVERS AND THEIR PARALLELIZATION
SIAM. SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS PHILADELPHIA
CONTENTS LIST OF FIGURES IX LIST OF ALGORITHMS XI ABBREVIATIONS AND
NOTATION XIII PREFACE XVII 1 INTRODUCTION 1 2 A SIMPLE EXAMPLE 5 2. 1
THE POISSON EQUATION AND ITS FINITE DIFFERENCE DISCRETIZATION 5 2.2
SEQUENTIAL SOLVING 8 2.2.1 DIRECT METHODS 8 2.2.2 ITERATIVE METHODS 9
2.3 PARALLEL SOLVING BY MEANS OF DD 11 2.4 SOME OTHER DISCRETIZATION
METHODS 13 3 INTRODUCTION TO PARALLELISM 15 3.1 CLASSIFICATIONS OF
PARALLEL COMPUTERS 15 3.1.1 CLASSIFICATION BY FLYNN 15 3.1.2
CLASSIFICATION BY MEMORY ACCESS 17 3.1.3 COMMUNICATION TOPOLOGIES 19 3.2
SPECIALTIES OF PARALLEL ALGORITHMS 20 3.2.1 SYNCHRONIZATION 20 3.2.2
MESSAGE PASSING 21 3.2.3 DEADLOCK 22 3.2.4 DATA COHERENCY 23 3.2.5
PARALLEL EXTENSIONS OF OPERATING SYSTEMS AND PROGRAM- MING LANGUAGES 23
3.3 BASIC GLOBAL OPERATIONS 24 3.3.1 SEND AND RECV 24 3.3.2 EXCHANGE 25
3.3.3 GATHER-SCATTER OPERATIONS 25 3.3.4 BROADCAST 26 VI CONTENTS 3.3.5
REDUCE AND REDUCE-ALL OPERATIONS 27 3.3.6 SYNCHRONIZATION BY BARRIERS 27
3.3.7 SOME REMARKS ON PORTABILITY 27 3.4 PERFORMANCE EVALUATION OF
PARALLEL ALGORITHMS 28 3.4.1 SPEEDUP AND SCALEUP 28 3.4.2 EFFICIENCY 31
3.4.3 COMMUNICATION EXPENDITURE 33 EXERCISES 33 4 GALERKIN FINITE
ELEMENT DISCRETIZATION OF ELLIPTIC PARTIAL DIFFERENTIAL EQUA- TIONS 35
4.1 VARIATIONAL FORMULATION OF ELLIPTIC BVPS 35 4.2 GALERKIN FINITE
ELEMENT DISCRETIZATION 40 4.2.1 THE GALERKIN METHOD 41 4.2.2 THE
SIMPLEST FINITE ELEMENT SCHEMES 42 4.2.3 ANALYSIS OF THE GALERKIN FEM 62
4.2.4 ITERATIVE SOLUTION OF THE GALERKIN SYSTEM 64 EXERCISES 68 5 BASIC
NUMERICAL ROUTINES IN PARALLEL 71 5.1 STORAGE OF SPARSE MATRICES 71 5.2
DD BY NONOVERLAPPING ELEMENTS 72 5.3 VECTOR-VECTOR OPERATIONS 75 5.4
MATRIX-VECTOR OPERATIONS 76 EXERCISES 79 6 CLASSICAL SOLVERS 8 3 6.1
DIRECT METHODS 84 6.1.1 LU FACTORIZATION 84 6.1.2 ILU FACTORIZATION 85
6.2 SMOOTHERS 90 6.2.1 6.2.2 GAUSS-SEIDEL ITERATION 93 6.2.3 ADI METHODS
97 6.3 ROUGHERS 103 6.3.1 CG METHOD 103 6.3.2 GMRES SOLVER 105 6.3.3
BICGSTAB SOLVER 107 6.4 PRECONDITIONERS 108 EXERCISES 108 7 MULTIGRID
METHODS 111 7.1 MULTIGRID METHODS ILL 7.2 THE MULTIGRID ALGORITHM 112
7.2.1 SEQUENTIAL ALGORITHM 112 7.2.2 PARALLEL COMPONENTS OF MULTIGRID
113 CONTENTS VII 7.2.3 PARALLEL ALGORITHM 116 EXERCISES 117 8 PROBLEMS
NOT ADDRESSED IN THIS BOOK 119 APPENDIX INTERNET ADDRESSES 121
BIBLIOGRAPHY 125 INDEX 133
|
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| indexdate | 2024-07-09T19:11:12Z |
| institution | BVB |
| isbn | 0898715415 |
| language | English |
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| physical | XVIII, 135 S. graph. Darst. |
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| spelling | Douglas, Craig C. Verfasser aut A tutorial on elliptic PDE solvers and their parallelization Craig C. Douglas, Gundolf Haase, Ulrich Langer Philadelphia Society for Industrial and Applied Mathematics 2003 XVIII, 135 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Software, environments, tools Includes bibliographical references and index Métodos computacionais (análise numérica) larpcal Datenverarbeitung Differential equations, Elliptic Numerical solutions Data processing Parallel algorithms Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Paralleler Algorithmus (DE-588)4193615-2 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 Paralleler Algorithmus (DE-588)4193615-2 s 1\p DE-604 Haase, Gundolf 1963- Sonstige (DE-588)121477754 oth Langer, Ulrich Sonstige oth HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010197335&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Douglas, Craig C. A tutorial on elliptic PDE solvers and their parallelization Métodos computacionais (análise numérica) larpcal Datenverarbeitung Differential equations, Elliptic Numerical solutions Data processing Parallel algorithms Numerisches Verfahren (DE-588)4128130-5 gnd Paralleler Algorithmus (DE-588)4193615-2 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4193615-2 (DE-588)4014485-9 |
| title | A tutorial on elliptic PDE solvers and their parallelization |
| title_auth | A tutorial on elliptic PDE solvers and their parallelization |
| title_exact_search | A tutorial on elliptic PDE solvers and their parallelization |
| title_full | A tutorial on elliptic PDE solvers and their parallelization Craig C. Douglas, Gundolf Haase, Ulrich Langer |
| title_fullStr | A tutorial on elliptic PDE solvers and their parallelization Craig C. Douglas, Gundolf Haase, Ulrich Langer |
| title_full_unstemmed | A tutorial on elliptic PDE solvers and their parallelization Craig C. Douglas, Gundolf Haase, Ulrich Langer |
| title_short | A tutorial on elliptic PDE solvers and their parallelization |
| title_sort | a tutorial on elliptic pde solvers and their parallelization |
| topic | Métodos computacionais (análise numérica) larpcal Datenverarbeitung Differential equations, Elliptic Numerical solutions Data processing Parallel algorithms Numerisches Verfahren (DE-588)4128130-5 gnd Paralleler Algorithmus (DE-588)4193615-2 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| topic_facet | Métodos computacionais (análise numérica) Datenverarbeitung Differential equations, Elliptic Numerical solutions Data processing Parallel algorithms Numerisches Verfahren Paralleler Algorithmus Elliptische Differentialgleichung |
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