Algorithms for elliptic problems: efficient sequential and parallel solvers
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Czech |
| Published: |
Dordrecht u.a.
Kluwer Acad. Publ.
1993
|
| Series: | Mathematics and its applications / East European series
58 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Tschech. übers. |
| Physical Description: | XVIII, 292 S. graph. Darst. |
| ISBN: | 8022403741 |
Staff View
MARC
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| 240 | 1 | 0 | |a Moderné algoritmy na riešenie niektorých eliptických parciálnych diferenciálnych rovníc |
| 245 | 1 | 0 | |a Algorithms for elliptic problems |b efficient sequential and parallel solvers |c by Marián Vajteršic |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1993 | |
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| 500 | |a Aus dem Tschech. übers. | ||
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Record in the Search Index
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| adam_text | Contents
Series editor s preface v
INTRODUCTION xiii
1 FAST METHODS FOR SOLVING THE POISSON EQUATION 1
1.1 Introduction 1
1.2 Direct methods 5
1.2.1 Introduction 5
1.2.2 Shintani s algorithm 7
1.2.3 Fundamental marching algorithms 10
1.2.4 Mejran s modification of the matrix decomposition algorithm ... 12
1.2.5 Lorenz s variant of the marching method 14
1.3 Applications of direct methods to solving other boundary value problems 17
1.3.1 Neumann s boundary value problem 17
1.3.2 Problem with periodic boundary value conditions 23
1.4 Iterative methods 26
1.4.1 Introduction 26
1.4.2 Fundamental iterative methods 27
1.4.3 Two step and optimalization methods 29
1.4.4 Relaxation multigrid method 33
1.5 Solving the Poisson equation on non rectangular domains 35
1.5.1 Introduction 35
1.5.2 Method of embedding into a rectangle 37
1.5.3 Method of fictive unknowns 39
1.5.4 Method of decomposition 41
1.5.5 An algorithm for an octagonal domain 44
1.5.6 An algorithm for a disc 47
References 50
2 FAST SERIAL ALGORITHMS FOR SOLVING BIHARMONIC EQUATION 53
2.1 Introduction 53
2.2 Direct methods 56
2.2.1 Golub s algorithm 58
2.2.2 The Buzbee Dorr algorithm 60
2.2.3 BJ0rstad s algorithm 61
2.3 Algorithms based on splitting 63
2.3.1 The splitting method 63
x Contents
2.3.2 A fast iterative process for the splitting method and its algorithmic
and program realization 68
2.3.3 An algorithm for one iteration using an elimination procedure . . 73
2.4 Solving the eigenvalue problem for a Inharmonic operator 78
References 84
3 PARALLEL ALGORITHMS FOR SOLVING CERTAIN ELLIPTIC BOUND¬
ARY VALUE PROBLEMS 87
3.1 Introduction 87
3.2 Parallel methods for solving the Poisson equation on multiprocessors . . 90
3.2.1 Introduction 90
3.2.2 Parallel block matrix decomposition 91
3.2.3 Parallel marching algorithms 95
3.2.4 A parallel domain decomposition method 101
3.2.5 A parallel variant of the cyclic odd even reduction solver .... 105
3.2.6 An iterative parallel algorithm 108
3.3 Parallel algorithms for solving biharmonic equations on SIMD computers 111
3.3.1 Introduction Ill
3.3.2 Parallel algorithms using matrix decomposition 114
3.3.3 Application of reduction algorithms 118
3.3.4 Elimination parallel algorithm 124
3.3.5 A block explicit, iterative method 128
References 130
4 IMPLEMENTATION OF PARALLEL ALGORITHMS ON SPECIALIZED
COMPUTERS 134
4.1 Introduction 134
4.2 Implementation of parallel algorithms on matrix processors 139
4.2.1 Introduction 139
4.2.2 Algorithms for the matrix processor ICL DAP 141
4.2.3 Multicolour iteration schemes for the specialized FEM processor . 147
4.3 Parallel algorithms for pipeline computers 149
4.3.1 Introduction 149
4.3.2 Conjugate gradient algorithm for CDC STAR 100 152
4.3.3 Black white iteration scheme on the CRAY 1 computer 157
4.4 Implementation of fast parallel algorithms for solving Poisson and biharmo¬
nic equations on multiprocessor computers 161
4.4.1 Introduction 161
4.4.2 Principal characteristics of the EGPA system 164
4.4.3 Formulation of algorithms for EGPA 166
4.4.4 The results of the implementation 170
4.5 Algorithms for massively parallel computers 173
4.5.1 Introduction 173
4.5.2 An example for the Connection Machine 174
4.5.3 Matrix multiplication on the MasPar computer 179
References 198
5 PARALLEL MULTIGRID ALGORITHMS 203
5.1 Introduction 203
5.2 Parallelization principles for multigrid algorithms 207
Contents xi
5.2.1 Introduction 207
5.2.2 Parallel implementation of a multigrid cycle 207
5.2.3 SIMD implementation of the multigrid algorithm 211
5.2.4 Algorithm for a parallel computation over all grids 214
5.2.5 Complexity of multigrid algorithms for some parallel computer to¬
pologies 218
5.3 Multigrid algorithms for parallel systems with hypercube structure . . 226
5.3.1 Introduction 226
5.3.2 Hypercube and Gray code 228
5.3.3 Parallelization of multigrid algorithms by Gray codes 231
5.4 Experiments with multigrid algorithms on parallel computers 237
5.4.1 Introduction 237
5.4.2 The multigrid parallel method for the CRAY X MP 238
5.4.3 Algorithms for the DIRMU modular system 243
5.4.4 Multigrid method amenable for implementation on systems with
massive parallelism 246
References 249
6 VLSI ELLIPTIC SOLVERS 252
6.1 Introduction 252
6.2 VLSI algorithms for special band systems 253
6.2.1 Introduction 253
6.2.2 Recursive algorithm for band systems 253
6.2.3 VLSI cyclic reduction 256
6.3 VLSI Poisson solvers 258
6.3.1 Introduction 258
6.3.2 Matrix decomposition VLSI algorithm 259
6.3.3 VLSI implementation of an elimination Poisson solver 261
6.3.4 VLSI cyclic odd even designs 266
6.3.5 VLSI multigrid solver 270
6.4 VLSI Helmholtz and biharmonic solvers 272
6.4.1 Introduction 272
6.4.2 A VLSI capacitance matrix solver for the Helmholtz equation . . 273
6.4.3 A VLSI biharmonic semidirect solver with multigrid Poisson blocks 277
6.4.4 An application of direct VLSI Poisson solvers to the biharmonic
problem 283
References 286
Subject index 288
|
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| id | DE-604.BV008236247 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:16:50Z |
| institution | BVB |
| isbn | 8022403741 |
| language | English Czech |
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| physical | XVIII, 292 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series2 | Mathematics and its applications / East European series |
| spelling | Vajteršic, Marián Verfasser aut Moderné algoritmy na riešenie niektorých eliptických parciálnych diferenciálnych rovníc Algorithms for elliptic problems efficient sequential and parallel solvers by Marián Vajteršic Dordrecht u.a. Kluwer Acad. Publ. 1993 XVIII, 292 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / East European series 58 Aus dem Tschech. übers. Equations différentielles elliptiques - Solutions numériques ram Differential equations, Elliptic Numerical solutions 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 East European series Mathematics and its applications 58 (DE-604)BV000006709 58 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005437008&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vajteršic, Marián Algorithms for elliptic problems efficient sequential and parallel solvers Equations différentielles elliptiques - Solutions numériques ram Differential equations, Elliptic Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4014485-9 |
| title | Algorithms for elliptic problems efficient sequential and parallel solvers |
| title_alt | Moderné algoritmy na riešenie niektorých eliptických parciálnych diferenciálnych rovníc |
| title_auth | Algorithms for elliptic problems efficient sequential and parallel solvers |
| title_exact_search | Algorithms for elliptic problems efficient sequential and parallel solvers |
| title_full | Algorithms for elliptic problems efficient sequential and parallel solvers by Marián Vajteršic |
| title_fullStr | Algorithms for elliptic problems efficient sequential and parallel solvers by Marián Vajteršic |
| title_full_unstemmed | Algorithms for elliptic problems efficient sequential and parallel solvers by Marián Vajteršic |
| title_short | Algorithms for elliptic problems |
| title_sort | algorithms for elliptic problems efficient sequential and parallel solvers |
| title_sub | efficient sequential and parallel solvers |
| topic | Equations différentielles elliptiques - Solutions numériques ram Differential equations, Elliptic Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| topic_facet | Equations différentielles elliptiques - Solutions numériques Differential equations, Elliptic Numerical solutions Numerisches Verfahren Elliptische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005437008&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000006709 |
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