Discretization methods and iterative solvers based on domain decomposition: with 25 tables
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2001
|
| Series: | Lecture notes in computational science and engineering
17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 197 S. graph. Darst. |
| ISBN: | 354041083X |
Staff View
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| 245 | 1 | 0 | |a Discretization methods and iterative solvers based on domain decomposition |b with 25 tables |c Barbara I. Wohlmuth |
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Record in the Search Index
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| adam_text | Contents
Preface V
1. Discretization Techniques Based on Domain Decomposition 1
1.1 Introduction to Mortar Finite Element Methods 3
1.2 Mortar Methods with Alternative Lagrange Multiplier Spaces .. 11
1.2.1 An Approximation Property 15
1.2.2 The Consistency Error 19
1.2.3 Discrete Inf sup Conditions 24
1.2.4 Examples of Lagrange Multiplier Spaces 27
1.2.4.1 The First Order Case in 2D 29
1.2.4.2 The First Order Case in 3D 33
1.2.4.3 The Second Order Case in 2D 36
1.3 Discretization Techniques Based on the Product Space 37
1.3.1 A Dirichlet Neumann Formulation 40
1.3.2 Variational Formulations 43
1.3.3 Algebraic Formulations 47
1.4 Examples for Special Mortar Finite Element Discretizations ... 50
1.4.1 The Coupling of Primal and Dual Finite Elements 51
1.4.2 An Equivalent Nonconforming Formulation 54
1.4.3 Crouzeix Raviart Finite Elements 58
1.5 Numerical Results 61
1.5.1 Influence of the Lagrange Multiplier Spaces 64
1.5.2 A Non optimal Mortar Method 71
1.5.3 Influence of the Choice of the Mortar Side 74
1.5.4 Influence of the Jump of the Coefficients 83
2. Iterative Solvers Based on Domain Decomposition 85
2.1 Abstract Schwarz Theory 87
2.1.1 Additive Schwarz Methods 88
2.1.2 Multiplicative Schwarz Methods 95
2.1.3 Multigrid Methods 97
2.2 Vector Field Discretizations 99
2.2.1 Raviart Thomas Finite Elements 101
2.2.2 An Iterative Substructuring Method 103
X Contents
2.2.2.1 An Interpolation Operator onto ~Vu 105
2.2.2.2 An Extension Operator onto Vp 107
2.2.2.3 Quasi optimal Bounds 113
2.2.3 A Hierarchical Basis Method 114
2.2.3.1 Horizontal Decomposition 115
2.2.3.2 Vertical Decomposition 118
2.2.4 Numerical Results 121
2.2.4.1 The 2D Case 122
2.2.4.2 The 3D Case 123
2.3 A Multigrid Method for the Mortar Product Space Formulation 125
2.3.1 Bilinear Forms 126
2.3.2 An Approximation Property 129
2.3.3 Smoothing and Stability Properties 131
2.3.4 Implementation of the Smoothing Step 136
2.3.5 Numerical Results in 2D and 3D 137
2.3.6 Extensions to Linear Elasticity 142
2.3.6.1 Uniform Ellipticity 145
2.3.6.2 Numerical Results 149
2.3.6.3 A Weaker Interface Condition 151
2.4 A Dirichlet Neumann Type Method 155
2.4.1 The Algorithm 155
2.4.2 Numerical Results 158
2.5 A Multigrid Method for the Mortar Saddle Point Formulation . 162
2.5.1 An Approximation Property 164
2.5.2 Smoothing and Stability Properties 167
2.5.2.1 A Block Diagonal Smoother 168
2.5.2.2 An Indefinite Smoother 171
2.5.3 Numerical Results 174
Bibliography 177
List of Figures 187
List of Tables 189
Notations 191
Index 195
|
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| discipline | Mathematik |
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| id | DE-604.BV013585955 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:48:27Z |
| institution | BVB |
| isbn | 354041083X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009279259 |
| oclc_num | 614619658 |
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| physical | X, 197 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in computational science and engineering |
| series2 | Lecture notes in computational science and engineering |
| spelling | Wohlmuth, Barbara 1967- Verfasser (DE-588)11316520X aut Discretization methods and iterative solvers based on domain decomposition with 25 tables Barbara I. Wohlmuth Berlin [u.a.] Springer 2001 X, 197 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in computational science and engineering 17 Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Gebietszerlegungsmethode (DE-588)4309232-9 gnd rswk-swf Diskretisierung (DE-588)4012469-1 gnd rswk-swf Iteration (DE-588)4123457-1 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Randwertproblem (DE-588)4048395-2 s Diskretisierung (DE-588)4012469-1 s Iteration (DE-588)4123457-1 s Gebietszerlegungsmethode (DE-588)4309232-9 s DE-604 Lecture notes in computational science and engineering 17 (DE-604)BV011386476 17 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009279259&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wohlmuth, Barbara 1967- Discretization methods and iterative solvers based on domain decomposition with 25 tables Lecture notes in computational science and engineering Partielle Differentialgleichung (DE-588)4044779-0 gnd Gebietszerlegungsmethode (DE-588)4309232-9 gnd Diskretisierung (DE-588)4012469-1 gnd Iteration (DE-588)4123457-1 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4309232-9 (DE-588)4012469-1 (DE-588)4123457-1 (DE-588)4048395-2 |
| title | Discretization methods and iterative solvers based on domain decomposition with 25 tables |
| title_auth | Discretization methods and iterative solvers based on domain decomposition with 25 tables |
| title_exact_search | Discretization methods and iterative solvers based on domain decomposition with 25 tables |
| title_full | Discretization methods and iterative solvers based on domain decomposition with 25 tables Barbara I. Wohlmuth |
| title_fullStr | Discretization methods and iterative solvers based on domain decomposition with 25 tables Barbara I. Wohlmuth |
| title_full_unstemmed | Discretization methods and iterative solvers based on domain decomposition with 25 tables Barbara I. Wohlmuth |
| title_short | Discretization methods and iterative solvers based on domain decomposition |
| title_sort | discretization methods and iterative solvers based on domain decomposition with 25 tables |
| title_sub | with 25 tables |
| topic | Partielle Differentialgleichung (DE-588)4044779-0 gnd Gebietszerlegungsmethode (DE-588)4309232-9 gnd Diskretisierung (DE-588)4012469-1 gnd Iteration (DE-588)4123457-1 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Partielle Differentialgleichung Gebietszerlegungsmethode Diskretisierung Iteration Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009279259&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011386476 |
| work_keys_str_mv | AT wohlmuthbarbara discretizationmethodsanditerativesolversbasedondomaindecompositionwith25tables |