Iterative solvers for stochastic Galerkin discretizations of stokes flow with random data:
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| Main Author: | |
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| Format: | Thesis Book |
| Language: | English |
| Published: |
München
Verlag Dr. Hut
2018
|
| Edition: | 1. Auflage |
| Subjects: | |
| Online Access: | Inhaltstext http://www.dr.hut-verlag.de/978-3-8439-3832-7.html Inhaltsverzeichnis |
| Physical Description: | x, 154 Seiten Illustrationen |
| ISBN: | 9783843938327 3843938326 |
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| 245 | 1 | 0 | |a Iterative solvers for stochastic Galerkin discretizations of stokes flow with random data |c von Christopher Müller |
| 250 | |a 1. Auflage | ||
| 264 | 1 | |a München |b Verlag Dr. Hut |c 2018 | |
| 300 | |a x, 154 Seiten |b Illustrationen | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |b Dissertation |c Technische Universität Darmstadt |d 2018 | ||
| 653 | |a Uncertainty Quantification | ||
| 653 | |a Iterative Solvers | ||
| 653 | |a Stochastic Galerkin | ||
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Record in the Search Index
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| adam_text | Contents
1 Introduction 1
1 1 The stochastic Galerkin method in uncertainty quantification 1
1 2 Outline 4
1 3 Main contributions 5
2 Stokes flow with uncertain data 7
2 1 Strong formulation 7
211 Stokes flow 8
212 Uncertainty quantification 9
213 Model equations 10
2 2 Input modeling 10
221 Affine representation 10
222 Lognormal representation 14
2 3 Variational formulations 17
231 The D-weak-H-strong formulations 18
232 The D-weak-S-weak formulations 23
3 Stochastic Galerkin finite elements 35
3 1 Discretization 35
311 Finite element approximation 36
312 Generalized polynomial chaos approximation 37
313 Stochastic Galerkin finite element discretization 45
3 2 Structural properties 55
321 Uniform parametrization 57
322 Gaussian parametrization 60
IX
4 Iterative solvers and preconditioning 63
4 1 Preconditioning 64
411 Preconditioners for the finite element matrices 66
412 Preconditioners for the stochastic Galerkin matrices 69
4 2 Analysis of the preconditioned matrices 70
421 The preconditioned Laplacian 72
422 The modified divergence matrix 76
423 The preconditioned Schur complement 78
424 The block diagonal preconditioned system matrix 81
425 The block triangular precond system matrix 83
4 3 Iterative solvers 89
431 Preconditioned MINRES methods 89
432 Bramble-Pasciak conjugate gradient methods 92
5 Numerical experiments 99
5 1 Preliminary considerations 100
511 Geometry 100
512 Viscosity modeling 101
513 Numerical tools 103
5 2 Uniform parametrization 104
521 Problem description 104
522 Numerical results 108
5 3 Gaussian parametrization 117
531 Problem description 117
532 Numerical results 117
6 Summary and outlook 125
A Auxiliary results 131
A l Functional analysis 131
A 2 Linear algebra 134
A21 Properties of the Kronecker product 134
A22 Matrix analysis 135
B Additional methods and concepts 139
B l The entries of A 139
B 2 The Kronecker product preconditioner 141
Bibliography 145
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| any_adam_object | 1 |
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| bvnumber | BV045374186 |
| ctrlnum | (OCoLC)1066748503 (DE-599)DNB1171559852 |
| discipline | Mathematik |
| edition | 1. Auflage |
| format | Thesis Book |
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| indexdate | 2024-07-10T08:16:24Z |
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| spelling | Müller, Christopher Verfasser (DE-588)1028776853 aut Iterative solvers for stochastic Galerkin discretizations of stokes flow with random data von Christopher Müller 1. Auflage München Verlag Dr. Hut 2018 x, 154 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Dissertation Technische Universität Darmstadt 2018 Uncertainty Quantification Iterative Solvers Stochastic Galerkin (DE-588)4113937-9 Hochschulschrift gnd-content Verlag Dr. Hut (München) (DE-588)10174118-2 pbl X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=e11c6eb49b79468495fee4a6a51eae6e&prov=M&dok_var=1&dok_ext=htm Inhaltstext X:MVB http://www.dr.hut-verlag.de/978-3-8439-3832-7.html HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030760610&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Müller, Christopher Iterative solvers for stochastic Galerkin discretizations of stokes flow with random data |
| subject_GND | (DE-588)4113937-9 |
| title | Iterative solvers for stochastic Galerkin discretizations of stokes flow with random data |
| title_auth | Iterative solvers for stochastic Galerkin discretizations of stokes flow with random data |
| title_exact_search | Iterative solvers for stochastic Galerkin discretizations of stokes flow with random data |
| title_full | Iterative solvers for stochastic Galerkin discretizations of stokes flow with random data von Christopher Müller |
| title_fullStr | Iterative solvers for stochastic Galerkin discretizations of stokes flow with random data von Christopher Müller |
| title_full_unstemmed | Iterative solvers for stochastic Galerkin discretizations of stokes flow with random data von Christopher Müller |
| title_short | Iterative solvers for stochastic Galerkin discretizations of stokes flow with random data |
| title_sort | iterative solvers for stochastic galerkin discretizations of stokes flow with random data |
| topic_facet | Hochschulschrift |
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