Domain decomposition methods in optimal control of partial differential equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2004
|
| Schriftenreihe: | International series of numerical mathematics
148 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 443 S. graph. Darst. |
| ISBN: | 3764321946 |
Internformat
MARC
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| 245 | 1 | 0 | |a Domain decomposition methods in optimal control of partial differential equations |c John E. Lagnese ; Günter Leugering |
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Datensatz im Suchindex
| _version_ | 1804132885034172416 |
|---|---|
| adam_text | DOMAIN DECOMPOSITION METHODS IN OPTIMAL CONTROL OF PARTIAL DIFFERENTIAL
EQUATIONS JOHN E. LAGNESE GIINTER LEUGERING BIRKHAUSER VERLAG BASEL *
BOSTON * BERLIN CONTENTS PREFACE IX 1 INTRODUCTION 1 2 BACKGROUND
MATERIAL ON DOMAIN DECOMPOSITION 2.1 INTRODUCTION 9 2.2 DOMAIN
DECOMPOSITION FOR 1-D PROBLEMS 10 2.2.1 UNBOUNDED DOMAINS 10 2.2.2
BOUNDED DOMAINS 14 2.2.3 SEMI-DISCRETIZATION 14 2.3 DOMAIN DECOMPOSITION
METHODS FOR ELLIPTIC PROBLEMS 17 2.3.1 REVIEW OF BASIC METHODS 17 2.3.2
VIRTUAL CONTROLS 27 2.3.3 THE BASIC ALGORITHM OF P.-L. LIONS 40 2.3.4 -
AN AUGMENTED LAGRANGIAN FORMULATION 46 2.3.5 GENERAL ELLIPTIC PROBLEMS
AND MORE GENERAL SPLITTINGS ... 48 2.3.6 AN A POSTERIORI ERROR ESTIMATE
54 2.3.7 INTERPRETATION AS A DAMPED RICHARDSON ITERATION . . . . . . 57
2.3.8 A SERIAL ONE-DIMENSIONAL PROBLEM 64 3 PARTIAL DIFFERENTIAL
EQUATIONS ON GRAPHS 3.1 INTRODUCTION 71 3.2 PARTIAL DIFFERENTIAL
OPERATORS ON GRAPHS ;* . 72 3.3 ELLIPTIC PROBLEMS ON GRAPHS 76 3.3.2
DOMAIN DECOMPOSITION 79 3.3.3 CONVERGENCE 82 3.3.4 INTERPRETATION AS A
RICHARDSON ITERATION 86 3.4 HYPERBOLIC PROBLEMS ON GRAPHS 91 3.4.1 THE
MODEL . 91 3.4.2 THE DOMAIN DECOMPOSITION PROCEDURE 96 CONTENTS OPTIMAL
CONTROL OF ELLIPTIC PROBLEMS 4.1 INTRODUCTION 107 4.2 DISTRIBUTED
CONTROLS 109 4.2.2 DOMAIN DECOMPOSITION ILL 4.2.3 A COMPLEX HELMHOLTZ
PROBLEM AND ITS DECOMPOSITION ... ILL 4.2.4 CONVERGENCE 113 4.2.5
METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS 116 4.2.6 AN A POSTERIORI
ERROR ESTIMATE 117 4.3 BOUNDARY CONTROLS 120 4.3.2 DOMAIN DECOMPOSITION
120 4.3.3 CONVERGENCE 121 4.3.4 AN A POSTERIORI ERROR ESTIMATE 125
CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS ON GRAPHS. 5.1 INTRODUCTION
131 5.2 ELLIPTIC PROBLEMS 131 5.2.1 THE GLOBAL OPTIMAL CONTROL PROBLEM
ON A GRAPH 131 5.2.2 DOMAIN DECOMPOSITION 133 5.2.3 DISTRIBUTED CONTROLS
135 5.2.4 BOUNDARY CONTROLS 141 5.3 HYPERBOLIC PROBLEMS 146 5.3.1 THE
GLOBAL OPTIMAL CONTROL PROBLEM ON A GRAPH 146 5.3.2 THE DOMAIN
DECOMPOSITION PROCEDURE 148 CONTROL OF DISSIPATIVE WAVE EQUATIONS 6.1
INTRODUCTION 159 6.2 OPTIMAL DISSIPATIVE BOUNDARY CONTROL 160 6.2.1
SETTING THE PROBLEM 160 6.2.2 EXISTENCE AND REGULARITY OF SOLUTIONS 162
6.2.3 THE GLOBAL OPTIMALITY SYSTEM 172 6.3 TIME DOMAIN DECOMPOSITION 173
6.3.1 DESCRIPTION OF THE ALGORITHM 173 6.3.2 CONVERGENCE OF THE ITERATES
179 6.3.3 A POSTERIORI ERROR ESTIMATES 188 6.3.4 EXTENSION TO GENERAL
DISSIPATIVE CONTROL SYSTEMS 201 6.4 DECOMPOSITION OF THE SPATIAL DOMAIN
208 6.4.1 DESCRIPTION OF THE ALGORITHM 208 6.4.2 CONVERGENCE OF THE
ITERATES 216 6.4.3 A POSTERIORI ERROR ESTIMATES 231 6.5 SPACE AND TIME
DOMAIN DECOMPOSITION 239 6.5.1 SEQUENTIAL SPACE-TIME DOMAIN
DECOMPOSITION 239 6.5.2 SEQUENTIAL TIME-SPACE DOMAIN DECOMPOSITION 250
CONTENTS VII 7 BOUNDARY CONTROL OF MAXWELL S SYSTEM 7.1 INTRODUCTION 257
7.2 OPTIMAL DISSIPATIVE BOUNDARY CONTROL 258 7.2.1 SETTING THE PROBLEM
258 7.2.2 EXISTENCE AND UNIQUENESS OF SOLUTION 260 7.2.3 THE GLOBAL
OPTIMALITY SYSTEM 265 7.3 TIME DOMAIN DECOMPOSITION 266 7.3.1
DESCRIPTION OF THE ALGORITHM 266 7.3.2 CONVERGENCE OF THE ITERATES 270
7.3.3 A POSTERIORI ERROR ESTIMATES 277 7.4 DECOMPOSITION OF THE SPATIAL
DOMAIN 289 7.4.1 DESCRIPTION OF THE ALGORITHM 289 7.4.2 CONVERGENCE OF
THE ITERATES 293 7.4.3 A POSTERIORI ERROR ESTIMATES 306 7.5 TIME AND
SPACE DOMAIN DECOMPOSITION 313 7.5.1 SEQUENTIAL SPACE-TIME DOMAIN
DECOMPOSITION 313 7.5.2 SEQUENTIAL TIME-SPACE DOMAIN DECOMPOSITION 317 8
CONTROL OF CONSERVATIVE WAVE EQUATIONS 8.1 INTRODUCTION 321 8.2 OPTIMAL
BOUNDARY CONTROL 322 8.2.1 SETTING THE PROBLEM 322 8.2.2 EXISTENCE AND
REGULARITY OF SOLUTIONS ... :. 324 8.2.3 THE GLOBAL OPTIMALITY SYSTEM
326 8.3 TIME DOMAIN DECOMPOSITION 327 8.3.1 DESCRIPTION OF THE ALGORITHM
*. . . 327 8.3.2 CONVERGENCE OF THE ITERATES : . . 329 8.3.3 A
POSTERIORI ERROR ESTIMATES 333 8.3.4 EXTENSION TO GENERAL CONSERVATIVE
CONTROL SYSTEMS . . . . 337 8.4 DECOMPOSITION OF THE SPATIAL DOMAIN 340
8.4.1 THE LOCAL OPTIMALITY SYSTEMS :. 340 8.4.2 THE DOMAIN DECOMPOSITION
ALGORITHM 342 8.4.3 CONVERGENCE OF THE ITERATES 345 8.5 THE EXACT
REACHABILITY PROBLEM 353 8.5.1 THE GLOBAL OPTIMALITY SYSTEM 353 8.5.2
THE LIMIT OF THE LOCAL OPTIMALITY SYSTEMS 355 8.5.3 APPLICATION TO
DOMAIN DECOMPOSITION 365 8.5.4 CONVERGENCE TO THE GLOBAL OPTIMALITY
SYSTEM 369 VIII CONTENTS 9 DOMAIN DECOMPOSITION FOR 2-D NETWORKS 9.1
ELLIPTIC SYSTEMS ON 2-D NETWORKS 375 9.1.2 EXAMPLES 378 9.1.3 EXISTENCE
AND UNIQUENESS OF SOLUTIONS 384 9.1.4 DOMAIN DECOMPOSITION 386 9.1.5
CONVERGENCE OF THE ALGORITHM 388 9.2 OPTIMAL CONTROL ON 2-D NETWORKS 395
9.2.1 OPTIMAL FINAL VALUE CONTROL 395 9.2.2 EXISTENCE AND REGULARITY OF
SOLUTIONS 397 9:3 DECOMPOSITION OF THE SPATIAL DOMAIN 400 9.3.2 THE
DECOMPOSITION ALGORITHM 403 9.3.3 CONVERGENCE OF THE ALGORITHM 409
BIBLIOGRAPHY * 435 INDEX 441
|
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| indexdate | 2024-07-09T19:59:55Z |
| institution | BVB |
| isbn | 3764321946 |
| language | English |
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| series2 | International series of numerical mathematics |
| spelling | Lagnese, John E. 1937- Verfasser (DE-588)112132812 aut Domain decomposition methods in optimal control of partial differential equations John E. Lagnese ; Günter Leugering Basel [u.a.] Birkhäuser 2004 XIII, 443 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series of numerical mathematics 148 Decomposition method Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Gebietszerlegungsmethode (DE-588)4309232-9 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Gebietszerlegungsmethode (DE-588)4309232-9 s Optimale Kontrolle (DE-588)4121428-6 s DE-604 Leugering, Günter 1953- Verfasser (DE-588)110610024 aut International series of numerical mathematics 148 (DE-604)BV035415862 148 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012882498&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lagnese, John E. 1937- Leugering, Günter 1953- Domain decomposition methods in optimal control of partial differential equations International series of numerical mathematics Decomposition method Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd Gebietszerlegungsmethode (DE-588)4309232-9 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4309232-9 (DE-588)4121428-6 |
| title | Domain decomposition methods in optimal control of partial differential equations |
| title_auth | Domain decomposition methods in optimal control of partial differential equations |
| title_exact_search | Domain decomposition methods in optimal control of partial differential equations |
| title_full | Domain decomposition methods in optimal control of partial differential equations John E. Lagnese ; Günter Leugering |
| title_fullStr | Domain decomposition methods in optimal control of partial differential equations John E. Lagnese ; Günter Leugering |
| title_full_unstemmed | Domain decomposition methods in optimal control of partial differential equations John E. Lagnese ; Günter Leugering |
| title_short | Domain decomposition methods in optimal control of partial differential equations |
| title_sort | domain decomposition methods in optimal control of partial differential equations |
| topic | Decomposition method Differential equations, Partial Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd Gebietszerlegungsmethode (DE-588)4309232-9 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | Decomposition method Differential equations, Partial Numerical solutions Partielle Differentialgleichung Gebietszerlegungsmethode Optimale Kontrolle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012882498&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035415862 |
| work_keys_str_mv | AT lagnesejohne domaindecompositionmethodsinoptimalcontrolofpartialdifferentialequations AT leugeringgunter domaindecompositionmethodsinoptimalcontrolofpartialdifferentialequations |