Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2005
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Numerical mathematics and scientific computation
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 400 S. graph. Darst. |
| ISBN: | 0198528671 019852868X 9780198528678 9780198528685 |
Internformat
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Datensatz im Suchindex
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| adam_text | FINITE ELEMENTS AND FAST ITERATIVE SOLVERS: WITH APPLICATIONS IN
INCOMPRESSIBLE FLUID DYNAMICS HOWARD C. ELMAN DAVID J. SILVESTER ANDREW
J. WATHEN OXFORD UNIVEE.S1TY PRESS CONTENTS 0 MODELS OF INCOMPRESSIBLE
FLUID FLOW 1 1 THE POISSON EQUATION 10 1.1 REFERCNCC PROBLEMS 11 1.2
WEAK FORMULATION 14 1.3 THE GALERKIN FMITE ELEMENT METHOD 17 1.3.1
TRIANGULAER FMITE CLEMENTS (R 2 ) 20 1.3.2 QUADRILATERAL CLEMENTS (R 2 )
22 1.3.3 TETRAHEDRAL CLEMENTS (R 3 ) 25 1.3.4 BRICK CLEMENTS (M 3 ) 26
1.4 IMPLEMENTATION ASPECTS 27 1.4.1 TRIANGULAER DEMENT MATRICES 28 1.4.2
QUADRILATERAL ELEMENT MATRICES 31 1.4.3 ASSEMBLY OF THE GALERKIN SYSTEM
33 1.5 THEORY OF ERRORS 36 1.5.1 A PRIORI ERROR BOUNDS 38 1.5.2 A
POSTERIORI ERROR BOUNDS 48 1.6 MATRIX PROPERTIES 56 PROBLEMS 61
COMPUTATIONAL EXERCISES 66 2 SOLUTION OF DISCRETE POISSON PROBLEMS 68
2.1 THE EONJUGATC GRADIENT METHOD 69 2.1.1 CONVCRGENCE ANALYSIS 73 2.1.2
STOPPING CRITERIA 75 2.2 PRECONDITIONING 78 2.3 SINGULAR SYSTEMS ARE NOT
A PROBLEM 83 2.4 TIIE LANCZOS AND MINIMUM RESIDUAL METHODS 84 2.5
MULTIGRID 88 2.5.1 TWO-GRID CONVERGENCE THEORY 95 2.5.2 EXTENDING
TWO-GRID TO MULTIGRID 101 PROBLEMS 107 COMPUTATIONAL EXERCISES 110 3 THE
CONVECTION-DIFFUSION EQUATION 113 3.1 REFERENCE PROBLEMS 115 3.2 WEAK
FORMULATION AND THE CONVECTION TERM 120 3.3 APPROXIMATION BY FMITE
ELEMCNTS 123 3.3.1 THE GALERKIN FINITE DEMENT METHOD 123 3.3.2 THE
STREAMLINC DIFFUSION METHOD 126 XI XII CONTENTS 3.4 THEORY OF ERRORS 134
3.4.1 A PRIORI ERROR BOUNDS 134 3.4.2 A POSTERIORI ERROR BOUNDS 142 3.5
MATRIX PROPERTIES 148 3.5.1 COMPUTATIONAL MOLECULES AND FOURICR ANALYSIS
152 3.5.2 ANALYSIS OF DIFFERENCE EQUATIONS 156 DISCUSSION AND
BIBLIOGRAPHICAL NOTES 161 PROBLEMS 163 COMPUTATIONAL EXERCISES 164 4
SOLUTION OF DISCRETE CONVECTION*DIFFUSION PROBLEMS 166 4.1 KRYLOV
SUBSPACE MET.HODS 166 4. IT GMRES 167 4.1.2 BIORTHOGONALIZATION METHODS
172 4.2 PRECONDITIONING METHODS AND SPLITTING OPERATORS 176 4.2.1
SPLITTING OPERATORS FOR CONVECTION-DIFFUSION SYSTEMS 178 4.2.2 MATRIX
ANALYSIS OF CONVERGENCE 181 4.2.3 ASYMPTOTIC ANALYSIS OF CONVERGENCE 185
4.2.4 PRACTICAL CONSIDERATIONS 190 4.3 MULTIGRID 194 4.3.1 PRACTICAL
ISSUES 195 4.3.2 TOOLS OF ANALYSIS: SMOOTLIING AND APPROXIINATION
PROPERTIES 200 4.3.3 SMOOTHING 202 4.3.4 ANALYSIS 205 DISCUSSION AND
BIBLIOGRAPHICAL NOTES 208 PROBLEMS 211 COMPUTATIONAL EXERCISES 212 5 THE
STOKES EQUATIONS 214 5.1 REFERENCC PROBLEMS 217 5.2 WEAK FORMULATION 222
5.3 APPROXIMATION USING MIXED FINITE CLEMENTS 224 5.3.1 STABLE
RECTANGULAR ELEMENTS (Q 2 QU Q2 P- , Q2-P0) 229 5.3.2 STABILIZED
RECTANGULAR ELEMENTS (QI-P 0 , QI Q ) 235 5.3.3 TRIANGULAER ELEMENTS 245
5.3.4 BRIEK AND TETRAHEDRAL ELEMENTS 248 5.4 THEORY OF ERRORS 249 5.4.1
A PRIORI ERROR BOUNDS 250 5.4.2 A POSTERIORI ERROR BOUNDS 262 5.5 MATRIX
PROPERTIES 268 5.5.1 STABLE MIXED APPROXIMATION 270 5.5.2 STABILIZCD
MIXED APPROXIMATION 273 DISCUSSION AND BIBLIOGRAPHICAL NOTES 277
PROBLEMS 280 COMPUTATIONAL EXERCISES 283 CONTENTS XUEI 6 SOLUTION OF
DISCRETE STOKES PROBLEMS 285 6.1 THE PRCCONDITIONED MINRES METHOD 286
6.2 PRCCONDITIONING 289 6.2.1 GENERAL STRATEGIEN FOR PRCCONDITIONING 291
6.2.2 EIGENVALUC BOUNDS 296 6.2.3 EQUIVALCNT NORMS FOR MINRES 303 6.2.4
MINRES CONVERGENCC ANALYSIS 306 DISCUSSION AND BIBLIOGRAPHICAL NOTES 308
PROBLEMS 309 COMPNTATIONAL EXERCISES 310 7 THE NAVIER-STOKES EQUATIONS
313 7.1 REFERERICE PROBLEMS 315 7.2 WEAK FORMULATION AND LINEARIZATION
318 7.2.1 STABILITY THEORY AND BIFURCATION ANALYSIS 320 7.2.2 NONLINCAR
ITERATION 324 7.3 MIXED FIUITE ELEMENT APPROXIMATION 327 7.4 THEORY OF
ERRORS 330 7.4.1 A PRIORI ERROR BOUNDS 331 7.4.2 A POSTERIORI ERROR
BOUNDS 333 DISCUSSION AND BIBLIOGRAPHICAL NOT ES 337 PROBLEMS 339
COMPUTATIONAL EXERCISES 339 8 SOLUTION OF DISCRETE NAVIER-STOKES
PROBLEMS 341 8.1 GENERAL STRATEGIES FOR PRECONDITIONING 342 8.2
APPROXIMATIONS TO THE SCHUR COMPLEMEIIT OPERATOR 346 8.2.1 THE PRESSURE
CONVECTION-DIFFUSION PRECONDITIONER 347 8.2.2 THE LEAST-SQUARES
COMMUTATOR PRECONDITIONER 353 8.3 PERFORMANCE AND ANALYSIS 354 8.3.1
IDEAL VERSIONS OF THE PRECONDITIONERS 355 8.3.2 USE OF ITERATIVE METHODS
FOR SUBPROBLEMS 359 8.3.3 CONVERGEIICE ANALYSIS 364 8.3.4 ENCLOSCD FLOW:
SINGULAR SYSTEMS ARE NOT A PROBLEM 365 8.3.5 RELATION TO SIMPLE
ITERATION 368 8.4 NONLINEAR ITERATION 370 DISCUSSION AND BIBLIOGRAPHICAL
NOTES 375 PROBLEMS 378 COMPUTATIONAL EXERCISES 379 BIBLIOGRAPHY 382
INDEX 397
|
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| author | Elman, Howard C. Silvester, David J. Wathen, Andrew J. |
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| id | DE-604.BV019817848 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:06:49Z |
| institution | BVB |
| isbn | 0198528671 019852868X 9780198528678 9780198528685 |
| language | English |
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| physical | XIII, 400 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series2 | Numerical mathematics and scientific computation |
| spelling | Elman, Howard C. Verfasser (DE-588)141967862 aut Finite elements and fast iterative solvers with applications in incompressible fluid dynamics Howard C. Elman ; David J. Silvester ; Andrew J. Wathen 1. publ. Oxford [u.a.] Oxford Univ. Press 2005 XIII, 400 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Numerical mathematics and scientific computation Equações diferenciais parciais larpcal Fluides, Dynamique des - Informatique Mecânica dos fluídos computacional larpcal Método dos elementos finitos larpcal Éléments finis, Méthode des Équations aux dérivées partielles Datenverarbeitung Differential equations, Partial Finite element method Fluid dynamics Data processing Inkompressible Strömung (DE-588)4129759-3 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s Partielle Differentialgleichung (DE-588)4044779-0 s Inkompressible Strömung (DE-588)4129759-3 s DE-604 Silvester, David J. Verfasser (DE-588)11391220X aut Wathen, Andrew J. Verfasser (DE-588)113912196 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013143158&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Elman, Howard C. Silvester, David J. Wathen, Andrew J. Finite elements and fast iterative solvers with applications in incompressible fluid dynamics Equações diferenciais parciais larpcal Fluides, Dynamique des - Informatique Mecânica dos fluídos computacional larpcal Método dos elementos finitos larpcal Éléments finis, Méthode des Équations aux dérivées partielles Datenverarbeitung Differential equations, Partial Finite element method Fluid dynamics Data processing Inkompressible Strömung (DE-588)4129759-3 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4129759-3 (DE-588)4044779-0 (DE-588)4017233-8 |
| title | Finite elements and fast iterative solvers with applications in incompressible fluid dynamics |
| title_auth | Finite elements and fast iterative solvers with applications in incompressible fluid dynamics |
| title_exact_search | Finite elements and fast iterative solvers with applications in incompressible fluid dynamics |
| title_full | Finite elements and fast iterative solvers with applications in incompressible fluid dynamics Howard C. Elman ; David J. Silvester ; Andrew J. Wathen |
| title_fullStr | Finite elements and fast iterative solvers with applications in incompressible fluid dynamics Howard C. Elman ; David J. Silvester ; Andrew J. Wathen |
| title_full_unstemmed | Finite elements and fast iterative solvers with applications in incompressible fluid dynamics Howard C. Elman ; David J. Silvester ; Andrew J. Wathen |
| title_short | Finite elements and fast iterative solvers |
| title_sort | finite elements and fast iterative solvers with applications in incompressible fluid dynamics |
| title_sub | with applications in incompressible fluid dynamics |
| topic | Equações diferenciais parciais larpcal Fluides, Dynamique des - Informatique Mecânica dos fluídos computacional larpcal Método dos elementos finitos larpcal Éléments finis, Méthode des Équations aux dérivées partielles Datenverarbeitung Differential equations, Partial Finite element method Fluid dynamics Data processing Inkompressible Strömung (DE-588)4129759-3 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Equações diferenciais parciais Fluides, Dynamique des - Informatique Mecânica dos fluídos computacional Método dos elementos finitos Éléments finis, Méthode des Équations aux dérivées partielles Datenverarbeitung Differential equations, Partial Finite element method Fluid dynamics Data processing Inkompressible Strömung Partielle Differentialgleichung Finite-Elemente-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013143158&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT elmanhowardc finiteelementsandfastiterativesolverswithapplicationsinincompressiblefluiddynamics AT silvesterdavidj finiteelementsandfastiterativesolverswithapplicationsinincompressiblefluiddynamics AT wathenandrewj finiteelementsandfastiterativesolverswithapplicationsinincompressiblefluiddynamics |