Domain decomposition: parallel multilevel methods for elliptic partial differential equations
An easy-to-read discussion of domain decomposition algorithms, their implementation and analysis.
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2004
|
| Edition: | 1. paperback ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Summary: | An easy-to-read discussion of domain decomposition algorithms, their implementation and analysis. |
| Physical Description: | XII, 224 S. graph. Darst. |
| ISBN: | 0521602866 9780521602860 |
Staff View
MARC
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| 100 | 1 | |a Smith, Barry F. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Domain decomposition |b parallel multilevel methods for elliptic partial differential equations |c Barry F. Smith ; Petter E. Bjørstad ; William D. Gropp |
| 250 | |a 1. paperback ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2004 | |
| 300 | |a XII, 224 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 520 | 3 | |a An easy-to-read discussion of domain decomposition algorithms, their implementation and analysis. | |
| 650 | 4 | |a Ayrıştırma metodu - Bilgi işlem | |
| 650 | 4 | |a Diferensiyel denklemler, Eliptik - Sayısal çözümler - Bilgi işlem | |
| 650 | 4 | |a Paralel işlem (Elektronik bilgisayarlar) | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Decomposition method |x Data processing | |
| 650 | 4 | |a Differential equations, Elliptic |x Numerical solutions |x Data processing | |
| 650 | 4 | |a Parallel processing (Electronic computers) | |
| 650 | 0 | 7 | |a Gebietszerlegungsmethode |0 (DE-588)4309232-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Gebietszerlegungsmethode |0 (DE-588)4309232-9 |D s |
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| 700 | 1 | |a Bjørstad, Petter E. |e Verfasser |4 aut | |
| 700 | 1 | |a Gropp, William |d 1955- |e Verfasser |0 (DE-588)133539989 |4 aut | |
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Record in the Search Index
| _version_ | 1804136203022237696 |
|---|---|
| adam_text | Contents
Introduction page
ix
Chapter
1
One Level Algorithms
1
1.1
Classical Alternating
Schwarz
Method
1
1.2
Approximate Solvers
18
1.3
Many
Subdomains
19
1.4
Convergence Behavior
24
1.5
Implementation Issues
30
1.6
Variational Formulation
34
Chapter
2
Two Level Algorithms
41
2.1
Subdomain
Solves Are Not Sufficient
41
2.2
A Simple Two Level Method
43
2.3
General Two Level Methods
45
2.4
Coarse Grid Corrections
48
2.5
Convergence Behavior
49
2.6
Implementation Issues
53
2.7
Fourier Analysis of Two Level Methods
57
2.8
Variational Formulation
61
Chapter
3
Multilevel Algorithms
67
3.1
Additive Multilevel
Schwarz
Methods
67
3.2
Multiplicative Multilevel
Schwarz
Methods
76
3.3
Full Multigrid
85
3.4
Practical Multilevel Methods
87
3.5
Multilevel Methods as Classical Jacobi and Gauss-Seidel
89
3.6
Complexity Issues
91
3.7
Implementation Issues
98
3.8
Variational Formulation
99
Chapter
4
Substructuring Methods
101
4.1
Direct Substructuring Methods
101
4.2
The Two
Subdomain
Case
110
4.3
Many
Subdomains
124
4.4
Inexact
Subdomain
Solvers
141
CONTENTS
4.5 Implementation
Issues
144
4.6 Variational
Formulation
144
Chapter
5
A Convergence Theory
149
5.1 Schwarz
Framework
149
5.2
Abstract Convergence Analysis
153
5.3
Analysis of Standard Methods
161
5.4
Indefinite and Nonsymmetric Problems
185
Appendixes
1
Preconditioners and Accelerators
195
A
1.1
Simple Preconditioners
195
Al
.2
Accelerators:
Krylov
Subspace Methods
197
2
Software for Numerical Parallel Computing
201
A2.1 Abstraction in Programming
201
A2.2 Abstract Data Types
204
A2.3 Our Standard Model for Parallel Computing
207
References
209
Index
223
viii
|
| adam_txt |
Contents
Introduction page
ix
Chapter
1
One Level Algorithms
1
1.1
Classical Alternating
Schwarz
Method
1
1.2
Approximate Solvers
18
1.3
Many
Subdomains
19
1.4
Convergence Behavior
24
1.5
Implementation Issues
30
1.6
Variational Formulation
34
Chapter
2
Two Level Algorithms
41
2.1
Subdomain
Solves Are Not Sufficient
41
2.2
A Simple Two Level Method
43
2.3
General Two Level Methods
45
2.4
Coarse Grid Corrections
48
2.5
Convergence Behavior
49
2.6
Implementation Issues
53
2.7
Fourier Analysis of Two Level Methods
57
2.8
Variational Formulation
61
Chapter
3
Multilevel Algorithms
67
3.1
Additive Multilevel
Schwarz
Methods
67
3.2
Multiplicative Multilevel
Schwarz
Methods
76
3.3
Full Multigrid
85
3.4
Practical Multilevel Methods
87
3.5
Multilevel Methods as Classical Jacobi and Gauss-Seidel
89
3.6
Complexity Issues
91
3.7
Implementation Issues
98
3.8
Variational Formulation
99
Chapter
4
Substructuring Methods
101
4.1
Direct Substructuring Methods
101
4.2
The Two
Subdomain
Case
110
4.3
Many
Subdomains
124
4.4
Inexact
Subdomain
Solvers
141
CONTENTS
4.5 Implementation
Issues
144
4.6 Variational
Formulation
144
Chapter
5
A Convergence Theory
149
5.1 Schwarz
Framework
149
5.2
Abstract Convergence Analysis
153
5.3
Analysis of Standard Methods
161
5.4
Indefinite and Nonsymmetric Problems
185
Appendixes
1
Preconditioners and Accelerators
195
A
1.1
Simple Preconditioners
195
Al
.2
Accelerators:
Krylov
Subspace Methods
197
2
Software for Numerical Parallel Computing
201
A2.1 Abstraction in Programming
201
A2.2 Abstract Data Types
204
A2.3 Our Standard Model for Parallel Computing
207
References
209
Index
223
viii |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV022219982 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:28:52Z |
| indexdate | 2024-07-09T20:52:40Z |
| institution | BVB |
| isbn | 0521602866 9780521602860 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015431213 |
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| physical | XII, 224 S. graph. Darst. |
| publishDate | 2004 |
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| publisher | Cambridge Univ. Press |
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| spelling | Smith, Barry F. Verfasser aut Domain decomposition parallel multilevel methods for elliptic partial differential equations Barry F. Smith ; Petter E. Bjørstad ; William D. Gropp 1. paperback ed. Cambridge [u.a.] Cambridge Univ. Press 2004 XII, 224 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier An easy-to-read discussion of domain decomposition algorithms, their implementation and analysis. Ayrıştırma metodu - Bilgi işlem Diferensiyel denklemler, Eliptik - Sayısal çözümler - Bilgi işlem Paralel işlem (Elektronik bilgisayarlar) Datenverarbeitung Decomposition method Data processing Differential equations, Elliptic Numerical solutions Data processing Parallel processing (Electronic computers) Gebietszerlegungsmethode (DE-588)4309232-9 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Gebietszerlegungsmethode (DE-588)4309232-9 s Elliptische Differentialgleichung (DE-588)4014485-9 s DE-604 Bjørstad, Petter E. Verfasser aut Gropp, William 1955- Verfasser (DE-588)133539989 aut http://www.loc.gov/catdir/toc/cam023/95042362.html Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015431213&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Smith, Barry F. Bjørstad, Petter E. Gropp, William 1955- Domain decomposition parallel multilevel methods for elliptic partial differential equations Ayrıştırma metodu - Bilgi işlem Diferensiyel denklemler, Eliptik - Sayısal çözümler - Bilgi işlem Paralel işlem (Elektronik bilgisayarlar) Datenverarbeitung Decomposition method Data processing Differential equations, Elliptic Numerical solutions Data processing Parallel processing (Electronic computers) Gebietszerlegungsmethode (DE-588)4309232-9 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| subject_GND | (DE-588)4309232-9 (DE-588)4014485-9 |
| title | Domain decomposition parallel multilevel methods for elliptic partial differential equations |
| title_auth | Domain decomposition parallel multilevel methods for elliptic partial differential equations |
| title_exact_search | Domain decomposition parallel multilevel methods for elliptic partial differential equations |
| title_exact_search_txtP | Domain decomposition parallel multilevel methods for elliptic partial differential equations |
| title_full | Domain decomposition parallel multilevel methods for elliptic partial differential equations Barry F. Smith ; Petter E. Bjørstad ; William D. Gropp |
| title_fullStr | Domain decomposition parallel multilevel methods for elliptic partial differential equations Barry F. Smith ; Petter E. Bjørstad ; William D. Gropp |
| title_full_unstemmed | Domain decomposition parallel multilevel methods for elliptic partial differential equations Barry F. Smith ; Petter E. Bjørstad ; William D. Gropp |
| title_short | Domain decomposition |
| title_sort | domain decomposition parallel multilevel methods for elliptic partial differential equations |
| title_sub | parallel multilevel methods for elliptic partial differential equations |
| topic | Ayrıştırma metodu - Bilgi işlem Diferensiyel denklemler, Eliptik - Sayısal çözümler - Bilgi işlem Paralel işlem (Elektronik bilgisayarlar) Datenverarbeitung Decomposition method Data processing Differential equations, Elliptic Numerical solutions Data processing Parallel processing (Electronic computers) Gebietszerlegungsmethode (DE-588)4309232-9 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| topic_facet | Ayrıştırma metodu - Bilgi işlem Diferensiyel denklemler, Eliptik - Sayısal çözümler - Bilgi işlem Paralel işlem (Elektronik bilgisayarlar) Datenverarbeitung Decomposition method Data processing Differential equations, Elliptic Numerical solutions Data processing Parallel processing (Electronic computers) Gebietszerlegungsmethode Elliptische Differentialgleichung |
| url | http://www.loc.gov/catdir/toc/cam023/95042362.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015431213&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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