Algebraic multigrid for the multi-ion-transport and reaction model: a physics-aware approach
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin
Logos-Verl.
2012
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | IX, 214 S. graph. Darst. 24 m |
| ISBN: | 9783832532857 3832532854 |
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| 245 | 1 | 0 | |a Algebraic multigrid for the multi-ion-transport and reaction model |b a physics-aware approach |c vorgelegt von Peter Thum |
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Record in the Search Index
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IMAGE 1
CONTENTS
CONTENTS VII
1 INTRODUCTION 1
1.1 CONTEXT 1
1.2 MAIN FOCUS AND STRUCTURE 3
2 T H E MULTI-ION TRANSPORT A N D R E A C T I O N M O D E L ( M I T R E
M ) 9 2.1 ELECTROCHEMICAL BACKGROUND 11
2.2 HOMOGENEOUS REACTIONS 14
2.3 BASIC SYSTEM 15
2.4 BOUNDARY CONDITIONS 17
2.4.1 BOUNDARY CONDITIONS ON INSULATORS, INLETS AND OUTLETS 18 2.4.2
BOUNDARY CONDITIONS ON ELECTRODES 19
2.5 EXISTENCE AND UNIQUENESS OF SOLUTIONS 21
2.6 DISCRETIZATION AND LINEARIZATION 23
2.6.1 THE PECLET NUMBER 25
2.6.2 FINITE ELEMENT METHOD 27
2.6.3 RESIDUAL-DISTRIBUTION SCHEME 28
3 ALGEBRAIC MULTIGRID ( A M G ) FOR CONVECTION-DOMINATED FLOW P R O B L
E M S 29
3.1 AMG 31
3.1.1 THE AMG TECHNOLOGY 31
3.1.2 AMG VARIANTS 32
3.2 PAMG 33
3.2.1 SMOOTHING 34
3.2.2 PRIMARY MATRICES AND POINT-COARSENING 34
3.2.3 INTERPOLATION 35
VII
HTTP://D-NB.INFO/1030003874
IMAGE 2
VIII CONTENTS
3.3 AMG FOR CONVECTION-DOMINATED FLOW PROBLEMS 36
4 T H E REORDERING FRAMEWORK 3 9
4.1 TERMINOLOGY 41
4.2 STATE-OF-THE-ART REORDERING IN THE CONTEXT OF AMG 42
4.3 BASIC MATRIX 43
4.4 REDUCTION TECHNIQUES 45
4.4.1 ALGEBRAIC REDUCTION 45
4.4.2 PHYSICS-BASED REDUCTION 47
4.5 SORTING ALGORITHMS 49
4.5.1 STARTING POINT 50
4.5.2 ACYCLIC GRAPHS 50
4.5.3 CYCLIC GRAPHS 51
4.6 SCALAR EXAMPLE 55
4.7 REORDERING FRAMEWORK FOR THE MITREM 60
4.7.1 BASIC MATRIX 61
4.7.2 FLOW-BASED REDUCTION '. 63
4.7.3 PERMUTATIONS 69
5 T H E HEURISTIC P E C L E T N U M B E R 75
5.1 HEURISTIC PECLET NUMBER FOR SCALAR EQUATIONS 77
5.1.1 FULFILLED PECLET CONDITION 79
5.1.2 LOCALLY VIOLATED PECLET CONDITION 81
5.1.3 PHYSICS-AWARE COARSE-GRID CORRECTION FOR PROBLEMS WITH LOCALLY
VIOLATED PECLET CONDITION 89
5.2 HEURISTIC PECLET NUMBER FOR SYSTEMS OF PDES 97
5.2.1 SCALAR AUXILIARY PROBLEM 98
5.2.2 THE PECLET NUMBER FOR SYSTEMS OF PDES 99
6 A PHYSICS-AWARE POINT-BASED A M G APPROACH ( P A M G ) FOR T H E
MIGRATION-DIFFUSION S Y S T E M 1 0 3
6.1 THE MIGRATION-DIFFUSION SYSTEM 104
6.2 STATE-OF-THE-ART PAMG APPROACHES 107
6.2.1 APPROACHES 107
6.2.2 CONVERGENCE RESULTS 110
6.2.3 PECLET NUMBERS ON COARSE LEVELS 112
6.2.4 IGNORING CRITICAL POINTS 116
6.2.5 CONCLUSION 117
IMAGE 3
CONTENTS IX
6.3 THE PHYSICS-AWARE PRIMARY MATRIX 118
6.3.1 RESULTS FOR LINEAR SYSTEMS A-5 AND B-5 120
6.3.2 RESULTS FOR LINEAR SYSTEMS A-30 AND B-46 123
6.3.3 SUMMARY OF THE RESULTS 127
6.4 PAMG FOR A LOCALLY VIOLATED PECLET CONDITION 127
6.4.1 USING FORCED F-POINTS 128
6.4.2 USING FORCED C-POINTS 132
6.5 THE FINAL PHYSICS-AWARE PAMG APPROACH 139
6.5.1 LINEAR SYSTEMS FROM EARLY NEWTON STEPS 140
6.5.2 LINEAR SYSTEMS FROM LATE NEWTON STEPS 142
6.5.3 CONCLUSION 143
7 A PHYSICS-AWARE P A M G A P P R O A C H FOR T H E M I T R E M 145
7.1 THE MITREM SYSTEM 147
7.1.1 ION SYSTEMS . . ! ? 147
7.1.2 GEOMETRIES 148
7.1.3 THE NEWTON METHOD 151
7.2 STATE-OF-THE-ART PAMG FOR THE MITREM 151
7.2.1 LINEAR SOLVER 151
7.2.2 PERFORMANCE RESULTS 153
7.3 DERIVATION OF EFFICIENT AND ROBUST PAMG APPROACHES . . . 153 7.3.1
THE BASIC PAMG COMPONENTS 154
7.3.2 THE EFFECT OF REORDERING 160
7.3.3 INTRODUCTION OF A PHYSICS-AWARE COARSENING 170
7.4 PAMG FOR THE MITREM 184
7.4.1 THE PAMG APPROACHES CONSIDERED 184
7.4.2 CHANNEL 187
7.4.3 BACKWARD FACING-STEP 189
7.4.4 CREVICE 191
7.4.5 - SUMMARY 192
7.5 CONCLUSION 193
8 CONCLUSIONS A N D FUTURE W O R K 195
BIBLIOGRAPHY 199
LIST O F FIGURES 2 0 9
LIST O F TABLES 2 1 2 |
| any_adam_object | 1 |
| author | Thum, Peter 1983- |
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| dewey-full | 518.64 |
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| spelling | Thum, Peter 1983- Verfasser (DE-588)1030356130 aut Algebraic multigrid for the multi-ion-transport and reaction model a physics-aware approach vorgelegt von Peter Thum Berlin Logos-Verl. 2012 IX, 214 S. graph. Darst. 24 m txt rdacontent n rdamedia nc rdacarrier Zugl.: Köln, Univ., Diss., 2012 System von partiellen Differentialgleichungen (DE-588)4116672-3 gnd rswk-swf Mehrgitterverfahren (DE-588)4038376-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content System von partiellen Differentialgleichungen (DE-588)4116672-3 s Mehrgitterverfahren (DE-588)4038376-3 s DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4238927&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026035771&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Thum, Peter 1983- Algebraic multigrid for the multi-ion-transport and reaction model a physics-aware approach System von partiellen Differentialgleichungen (DE-588)4116672-3 gnd Mehrgitterverfahren (DE-588)4038376-3 gnd |
| subject_GND | (DE-588)4116672-3 (DE-588)4038376-3 (DE-588)4113937-9 |
| title | Algebraic multigrid for the multi-ion-transport and reaction model a physics-aware approach |
| title_auth | Algebraic multigrid for the multi-ion-transport and reaction model a physics-aware approach |
| title_exact_search | Algebraic multigrid for the multi-ion-transport and reaction model a physics-aware approach |
| title_full | Algebraic multigrid for the multi-ion-transport and reaction model a physics-aware approach vorgelegt von Peter Thum |
| title_fullStr | Algebraic multigrid for the multi-ion-transport and reaction model a physics-aware approach vorgelegt von Peter Thum |
| title_full_unstemmed | Algebraic multigrid for the multi-ion-transport and reaction model a physics-aware approach vorgelegt von Peter Thum |
| title_short | Algebraic multigrid for the multi-ion-transport and reaction model |
| title_sort | algebraic multigrid for the multi ion transport and reaction model a physics aware approach |
| title_sub | a physics-aware approach |
| topic | System von partiellen Differentialgleichungen (DE-588)4116672-3 gnd Mehrgitterverfahren (DE-588)4038376-3 gnd |
| topic_facet | System von partiellen Differentialgleichungen Mehrgitterverfahren Hochschulschrift |
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