Adaptive wavelet frame domain decomposition methods for elliptic operator equations:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin
Logos-Verl.
2009
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 219 S. graph. Darst. 24 cm |
| ISBN: | 3832522867 9783832522865 |
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MARC
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| 100 | 1 | |a Werner, Manuel |e Verfasser |0 (DE-588)1059104873 |4 aut | |
| 245 | 1 | 0 | |a Adaptive wavelet frame domain decomposition methods for elliptic operator equations |c vorgelegt von Manuel Werner |
| 264 | 1 | |a Berlin |b Logos-Verl. |c 2009 | |
| 300 | |a XVIII, 219 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a Zugl.: Marburg, Univ., Diss., 2009 | ||
| 546 | |a Zsfassung in dt. Sprache | ||
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| 650 | 0 | |a Elliptischer Differentialoperator / swd | |
| 650 | 0 | |a Mehrskalenanalyse / swd | |
| 650 | 0 | |a Gebietszerlegungsmethode / swd | |
| 650 | 0 | |a Wavelet / swd | |
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Record in the Search Index
| _version_ | 1804141063250640896 |
|---|---|
| adam_text | XV CONTENTS INTRODUCTION 1 1 ELLIPTIC OPERATOR EQUATIONS 13 1.1 ELLIPTIC
BOUNDARY VALUE PROBLEMS 13 1.2 SOBOLEV SPACES 14 1.3 WEAK FORMULATION 17
1.4 INHOMOGENEOUS BOUNDARY CONDITIONS 19 1.5 THE GALERKIN APPROACH 20
1.6 BOUNDARY INTEGRAL EQUATIONS 22 2 WAVELET FRAMES ON BOUNDED DOMAINS
23 2.1 BASIC FRAME THEORY 23 2.1.1 FRAMES FOR HUBERT SPACES 23 2.1.2
RIESZ BASES 27 2.1.3 BANACH FRAMES 28 2.1.4 HUBERT FRAMES REVISITED 28
2.2 CLASSICAL WAVELET BASES 29 2.2.1 COMMON CONSTRUCTION PRINCIPLES 29
2.2.2 NORM EQUIVALENCES 34 2.2.3 CANCELLATION PROPERTIES 36 2.2.4 SPLINE
WAVELET BASES ON THE INTERVAL 36 2.2.5 WAVELET BASES ON THE UNIT CUBE 38
2.3 CONSTRUCTION OF WAVELET FRAMES 39 2.3.1 AGGREGATED FRAMES AND STABLE
SPACE SPLITTINGS 39 2.3.2 AGGREGATED WAVELET FRAMES 43 2.3.3 GELFAND
FRAMES 45 2.4 SUMMARY OF FUNDAMENTAL WAVELET PROPERTIES 50 2.5
DISCRETIZATION OF OPERATOR EQUATIONS 51 2.6 HOW TO SELECT THE DOMAIN
DECOMPOSITION 53 2.7 PARTITIONS OF UNITY 54 3 NONLINEAR APPROXIMATION
WITH AGGREGATED WAVELET FRAMES 61 3.1 FUNCTION SPACES 62 3.2
INTERPOLATION AND APPROXIMATION SPACES 64 3.2.1 INTERPOLATION SPACES 64
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/99721984X DIGITALISIERT
DURCH CONTENTS 3.2.2 APPROXIMATION CLASSES 65 3.3 THE CLASSICAL WAVELET
BASIS SETTING 66 3.3.1 LINEAR APPROXIMATION WITH WAVELETS IN /I*(F2) 66
3.3.2 TV-TERM WAVELET APPROXIMATION IN //*($!) 66 3.3.3 N-TERM
APPROXIMATION IN 2 69 3.3.4 SPLINE WAVELETS AND BOUNDARY CONDITIONS 71
3.4 AGGREGATED WAVELET FRAMES 72 3.4.1 BASIC ASSUMPTIONS 73 3.4.2
COVERINGS PERMITTING A SMOOTH PARTITION OF UNITY 73 3.4.3 THE L-SHAPED
DOMAIN 73 AN ADAPTIVE STEEPEST DESCENT WAVELET FRAME ALGORITHM 85 4.1
OPTIMALITY OF ADAPTIVE ALGORITHMS 86 4.2 THE EXACT STEEPEST DESCENT
SCHEME 87 4.3 DEVELOPMENT OF THE ADAPTIVE SOLVER 89 4.3.1 THE ADAPTIVE
MATRIX-VECTOR PRODUCT 91 4.3.2 COARSENING 93 4.3.3 ADAPTIVE
APPROXIMATION OF THE RIGHT-HAND SIDE 94 4.3.4 COMPUTATION OF AN
APPROXIMATE RESIDUAL 94 4.3.5 THE ADAPTIVE STEEPEST DESCENT METHOD 97
4.3.6 ASSUMPTION 4.2 AND WAYS TO CIRCUMVENT IT 101 4.4 NUMERICAL
EXAMPLES 104 4.4.1 THE POISSON EQUATION IN AN INTERVAL 105 4.4.2 THE
POISSON EQUATION IN AN L-SHAPED DOMAIN ILL 4.4.3 CONCLUSION AND
MOTIVATION FOR FURTHER IMPROVEMENT. . . . . . . 113 COMPUTATION OF
DIFFERENTIAL OPERATORS IN FRAME COORDINATES 119 5.1 COMPRESSIBILITY 119
5.2 COMPUTABILITY 123 5.2.1 THE QUADRATURE PARADIGM 123 5.2. CONTENTS
6.1.6 SMOOTHNESS OF THE LIMITS ON THE SUBDOMAINS: PROOF OF THEO- REM 6.2
(B) 158 6.2 AN ADDITIVE SCHWARZ ADAPTIVE WAVELET FRAME METHOD 161 6.2.1
THE EXACT ADDITIVE SCHWARZ METHOD 161 6.2.2 THE ADAPTIVE METHOD AND ITS
CONVERGENCE 164 6.2.3 OPTIMALITY 168 6.2.4 IMPLEMENTATION OF THE
PROJECTOR P 172 6.2.5 CONCLUDING REMARKS 174 7 NUMERICAL TESTS 175 7.1
THE ADAPTIVE MULTIPLICATIVE SCHWARZ METHOD 175 7.1.1 THE POISSON
EQUATION IN THE UNIT INTERVAL 175 7.1.2 THE POISSON EQUATION IN THE
L-SHAPED DOMAIN 180 7.1.3 COMPARISON WITH AN ADAPTIVE FINITE ELEMENT
CODE 189 7.1.4 THE BIHARMONIC EQUATION IN THE L-SHAPED DOMAIN 191 7.2
THE ADAPTIVE ADDITIVE SCHWARZ METHOD 194 7.2.1 PARALLELIZATION STRATEGY
194 7.2.2 THE L-SHAPED DOMAIN 195 7.2.3 A RING-SHAPED DOMAIN 198
CONCLUSION AND OUTLOOK 201 LIST OF FIGURES 205 LIST OF TABLES 209
BIBLIOGRAPHY 211 XVII
|
| any_adam_object | 1 |
| author | Werner, Manuel |
| author_GND | (DE-588)1059104873 |
| author_facet | Werner, Manuel |
| author_role | aut |
| author_sort | Werner, Manuel |
| author_variant | m w mw |
| building | Verbundindex |
| bvnumber | BV036036812 |
| ctrlnum | (OCoLC)488691535 (DE-599)GBV616804288 |
| dewey-full | 518.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.64 |
| dewey-search | 518.64 |
| dewey-sort | 3518.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| id | DE-604.BV036036812 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:09:55Z |
| institution | BVB |
| isbn | 3832522867 9783832522865 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018928774 |
| oclc_num | 488691535 |
| open_access_boolean | |
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| owner_facet | DE-634 |
| physical | XVIII, 219 S. graph. Darst. 24 cm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Logos-Verl. |
| record_format | marc |
| spelling | Werner, Manuel Verfasser (DE-588)1059104873 aut Adaptive wavelet frame domain decomposition methods for elliptic operator equations vorgelegt von Manuel Werner Berlin Logos-Verl. 2009 XVIII, 219 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Zugl.: Marburg, Univ., Diss., 2009 Zsfassung in dt. Sprache Operatorgleichung / swd Elliptischer Differentialoperator / swd Mehrskalenanalyse / swd Gebietszerlegungsmethode / swd Wavelet / swd (DE-588)4113937-9 Hochschulschrift gnd-content DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018928774&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Werner, Manuel Adaptive wavelet frame domain decomposition methods for elliptic operator equations Operatorgleichung / swd Elliptischer Differentialoperator / swd Mehrskalenanalyse / swd Gebietszerlegungsmethode / swd Wavelet / swd |
| subject_GND | (DE-588)4113937-9 |
| title | Adaptive wavelet frame domain decomposition methods for elliptic operator equations |
| title_auth | Adaptive wavelet frame domain decomposition methods for elliptic operator equations |
| title_exact_search | Adaptive wavelet frame domain decomposition methods for elliptic operator equations |
| title_full | Adaptive wavelet frame domain decomposition methods for elliptic operator equations vorgelegt von Manuel Werner |
| title_fullStr | Adaptive wavelet frame domain decomposition methods for elliptic operator equations vorgelegt von Manuel Werner |
| title_full_unstemmed | Adaptive wavelet frame domain decomposition methods for elliptic operator equations vorgelegt von Manuel Werner |
| title_short | Adaptive wavelet frame domain decomposition methods for elliptic operator equations |
| title_sort | adaptive wavelet frame domain decomposition methods for elliptic operator equations |
| topic | Operatorgleichung / swd Elliptischer Differentialoperator / swd Mehrskalenanalyse / swd Gebietszerlegungsmethode / swd Wavelet / swd |
| topic_facet | Operatorgleichung / swd Elliptischer Differentialoperator / swd Mehrskalenanalyse / swd Gebietszerlegungsmethode / swd Wavelet / swd Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018928774&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wernermanuel adaptivewaveletframedomaindecompositionmethodsforellipticoperatorequations |