Wavelets in numerical simulation: problem adapted construction and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Series: | Lecture notes in computational science and engineering
22 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 181 S. graph. Darst. |
| ISBN: | 3540430555 |
Staff View
MARC
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| 100 | 1 | |a Urban, Karsten |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Wavelets in numerical simulation |b problem adapted construction and applications |c Karsten Urban |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
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| 490 | 1 | |a Lecture notes in computational science and engineering |v 22 | |
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Table of Contents
Preface VII
1 Wavelet Bases 1
1.1 Wavelet Bases in L2{Q) 1
1.1.1 General Setting 2
1.1.2 Characterization of Sobolev Spaces 5
1.1.3 Riesz Basis Property in L,2{f2) 7
1.1.4 Norm Equivalences 8
1.1.5 General Setting Continued 9
1.1.6 Further Wavelet Features 10
1.1.7 A Program for Constructing Wavelets 11
1.2 Wavelets on the Real Line 12
1.2.1 Orthonormal Wavelets 13
1.2.2 Biorthogonal B Spline Wavelets 14
1.2.3 Interpolatory Wavelets 15
1.3 Wavelets on the Interval 17
1.3.1 Boundary Scaling Functions 19
1.3.2 Biorthogonal Scaling Functions 20
1.3.3 Biorthogonalization 25
1.3.4 Refinement Matrices 30
1.3.5 Biorthogonal Wavelets on (0,1) 33
1.3.6 Quantitative Aspects of the Biorthogonalization 41
1.3.7 Boundary Conditions 44
1.3.8 Other Bases 45
1.4 Tensor Product Wavelets 46
1.5 Wavelets on General Domains 47
1.5.1 Domain Decomposition and Parametric Mappings . 51
1.5.2 Multiresolution and Wavelets on the Subdomains 53
1.5.3 Multiresolution on the Global Domain Q 54
1.5.4 Wavelets on the Global Domain 55
1.5.5 Univariate Matched Wavelets and Other Functions . 56
1.5.6 Bivariate Matched Wavelets 62
1.5.7 Trivariate Matched Wavelets 73
1.5.8 Characterization of Sobolev Spaces 78
1.6 Vector Wavelets 81
XIV Table of Contents
2 Wavelet Bases for H(div) and if (curl) 83
2.1 Differentiation and Integration 84
2.1.1 Differentiation and Integration on the Real Line 84
2.1.2 Differentiation and Integration on (0,1) 85
2.1.3 Assumptions for General Domains 86
2.1.4 Norm Equivalences 89
2.2 The Spaces H(div) and ff (curl) 90
2.2.1 Stream Function Spaces 91
2.2.2 Flux Spaces 91
2.2.3 Hodge Decompositions 92
2.3 Wavelet Systems for #(curl) 92
2.3.1 Wavelets in H0(curl; O) 93
2.3.2 Curl Free Wavelet Bases 95
2.4 Wavelet Bases for #(div) 98
2.4.1 Wavelet Bases in if(div; Q) 98
2.4.2 Divergence Free Wavelet Bases 99
2.5 Helmholtz and Hodge Decompositions 100
2.5.1 A Biorthogonal Helmholtz Decomposition 100
2.5.2 Interrelations and Hodge Decompositions 101
2.6 General Domains 102
2.6.1 Tensor Product Domains 102
2.6.2 Parametric Mappings 103
2.6.3 Fictitious Domain Method 104
2.7 Examples 105
3 Applications 109
3.1 Robust and Optimal Preconditioning 109
3.1.1 Wavelet Galerkin Discretizations 109
3.1.2 The Lame Equations for Almost Incompressible
Material 112
3.1.3 The Maxwell Equations 116
3.1.4 Preconditioning in H(div; fl) 117
3.2 Analysis and Simulation of Turbulent Flows 118
3.2.1 Numerical Simulation of Turbulence 118
3.2.2 Divergence Free Wavelet Analysis of Turbulence 119
3.2.3 Proper Orthogonal Decomposition (POD) 120
3.2.4 Numerical Implementation and Validation 122
3.2.5 Numerical Results I: Data Analysis 124
3.2.6 Numerical Results II: Complexity of Turbulent Flows . 128
3.3 Hardening of an Elastoplastic Rod 138
3.3.1 The Physical Problem 138
3.3.2 Numerical Treatment 142
3.3.3 Stress Correction and Wavelet Bases 145
3.3.4 Numerical Results I: Variable Order Discretizations . 146
3.3.5 Numerical Results II: Plastic Indicators 154
Table of Contents XV
References 161
List of Figures 169
List of Tables 173
List of Symbols 175
Index 179 |
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| indexdate | 2024-07-20T07:39:04Z |
| institution | BVB |
| isbn | 3540430555 |
| language | English |
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| physical | XV, 181 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
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| series | Lecture notes in computational science and engineering |
| series2 | Lecture notes in computational science and engineering |
| spelling | Urban, Karsten Verfasser aut Wavelets in numerical simulation problem adapted construction and applications Karsten Urban Berlin [u.a.] Springer 2002 XV, 181 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in computational science and engineering 22 Mathematisches Modell Mathematical models Wavelets (Mathematics) Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s Wavelet (DE-588)4215427-3 s DE-604 Lecture notes in computational science and engineering 22 (DE-604)BV011386476 22 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009735265&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Urban, Karsten Wavelets in numerical simulation problem adapted construction and applications Lecture notes in computational science and engineering Mathematisches Modell Mathematical models Wavelets (Mathematics) Numerische Mathematik (DE-588)4042805-9 gnd Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4215427-3 |
| title | Wavelets in numerical simulation problem adapted construction and applications |
| title_auth | Wavelets in numerical simulation problem adapted construction and applications |
| title_exact_search | Wavelets in numerical simulation problem adapted construction and applications |
| title_full | Wavelets in numerical simulation problem adapted construction and applications Karsten Urban |
| title_fullStr | Wavelets in numerical simulation problem adapted construction and applications Karsten Urban |
| title_full_unstemmed | Wavelets in numerical simulation problem adapted construction and applications Karsten Urban |
| title_short | Wavelets in numerical simulation |
| title_sort | wavelets in numerical simulation problem adapted construction and applications |
| title_sub | problem adapted construction and applications |
| topic | Mathematisches Modell Mathematical models Wavelets (Mathematics) Numerische Mathematik (DE-588)4042805-9 gnd Wavelet (DE-588)4215427-3 gnd |
| topic_facet | Mathematisches Modell Mathematical models Wavelets (Mathematics) Numerische Mathematik Wavelet |
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