Computational methods for quantum chromodynamics:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2013
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| Schlagworte: | |
| Online-Zugang: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:355-epub-282815 Inhaltsverzeichnis |
| Beschreibung: | XI, 181 S. Ill., graph. Darst. |
Internformat
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| 502 | |a Regensburg, Univ., Diss., 2013 | ||
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Datensatz im Suchindex
| _version_ | 1804150443254743040 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
INTRODUCTION VII
I INVERTERS AND PRECONDITIONERS 1
1 SCHWARZ METHODS 3
1.1 INTRODUCTION 3
1.2 SCHWARZ METHODS 3
1.2.1 OVERLAPPING DOMAIN DECOMPOSITIONS 5
1.2.2 ADDITIVE SCHWARZ 6
1.2.3 MULTIPLICATIVE SCHWARZ 6
1.2.4 HYBRID SCHWARZ 8
1.2.5 SCHWARZ METHOD AS A PRECONDITIONER 8
1.2.6 A NOTE ON OVERLAP 9
1.3 IMPLEMENTATION 11
1.3.1 EVEN/ODD PRECONDITIONING 11
1.3.2 D A T A LAYOUT 12
1.3.3 D A T A FLOW 15
1.3.4 IMPLEMENTATION VARIANTS OF MULTIPLICATIVE SCHWARZ 17
1.4 NUMERICAL STUD,Y OF SCHWARZ METHODS WITH VARYING OVERLAP 18
1.4.1 PERFORMANCE OF THE SCHWARZ METHOD 19
1.4.2 PERFORMANCE OF THE SCHWARZ METHOD AS PRECONDITIONER 24
1.5 CONCLUSIONS 28
2 OPTIMIZED SCHWARZ METHODS 3 1
2.1 INTRODUCTION 31
2.2 INTRODUCTORY STUDY OF OPTIMIZED SCHWARZ METHODS 31
2.2.1 BOUNDARY CONDITION CLASSIFICATION 31
2.2.2 DISCRETIZATION OF BOUNDARY CONDITIONS 33
2.2.3 DISCRETIZATION OF BOUNDARY CONDITIONS WITH DERIVATIVES ALONG T H E
BOUNDARY 35
2.2.4 TOPOLOGIES 38
2.2.5 DOMAIN SPLITTING IN TWO DIRECTIONS 40
2.2.6 ITERATIVE INVERSIONS 40
2.3 OPTIMIZED SCHWARZ METHODS FOR QCD 42
2.3.1 BOUNDARY CONDITIONS FOR GAUGE THEORIES 42
2.3.2 RESULTS 45
III
HTTP://D-NB.INFO/1037454421
IMAGE 2
CONTENTS
2.4 CONCLUSIONS 50
3 SCHUR COMPLEMENT INVERTER FOR NON-OVERLAPPING SUBDOMAINS 5 1
3.1 INTRODUCTION 51
3.2 SCHUR COMPLEMENT 52
3.3 NEUMANN-NEUMANN PRECONDITIONER FOR THE SCHUR COMPLEMENT 54
3.4 TECHNICAL DETAILS 55
3.4.1 FINITE-ELEMENT METHODS AND SUBDOMAIN MATRICES 55
3.4.2 D A T A LAYOUT 59
3.4.3 COMMUNICATION 61
3.4.4 ALGORITHMS 62
3.5 COARSE GRIDS AND DEFLATION 63
3.6 NUMERICAL RESULTS 63
3.6.1 IMPLEMENTATION AND SIMULATION DETAILS 63
3.6.2 PARAMETER TUNING PART 1: BLOCK VOLUME AND GEOMETRY 64
3.6.3 PARAMETER TUNING PART 2: CHOICE OF THE KRYLOV INVERTER FOR OUTER
INVERSION 67
3.6.4 PARAMETER TUNING P A R T 3: ITERATION COUNT OF THE PRECONDITIONER
74 3.6.5 PARAMETER TUNING PART 4: PRECISION OF BLOCK INVERSIONS IN T H E
PRECONDITIONER 76
3.6.6 MULTIPLE RIGHT-HAND SIDES BLOCK INVERSIONS 77
3.6.7 LOWERED KAPPA PRECONDITIONER 78
3.6.8 DEPENDENCE ON CONFIGURATION 81
3.6.9 COMPARISON WITH SCHWARZ METHODS 85
3.7 CONCLUSIONS 87
II SIGN FUNCTION A N D OVERLAP OPERATOR 9 1
4 NESTED KRYLOV SUBSPACE METHOD FOR THE SIGN FUNCTION 9 3
4.1 INTRODUCTION 93
4.2 OVERLAP OPERATOR AND THE MATRIX SIGN FUNCTION 95
4.3 KRYLOV-RITZ APPROXIMATIONS FOR MATRIX FUNCTIONS 96
4.4 NESTED KRYLOV SUBSPACE METHOD FOR THE SIGN FUNCTION 99
4.4.1 NESTING AND PRECONDITIONING 99
4.4.2 CONVERGENCE 104
4.4.3 BENCHMARKS 107
4.4.4 NOTE ON THE MEMORY USAGE 108
4.4.5 MULTI-LEVEL NESTING 110
4.5 CONCLUSIONS 112
5 DOUBLE-PASS VARIANTS FOR MULTI-SHIFT BICGSTAB(L) 113
5.1 INTRODUCTION AND MOTIVATION 113
5.2 DOUBLE-PASS ALGORITHM 114
I V
IMAGE 3
CONTENTS
5.3 COST ANALYSIS AND BENCHMARKS 115
5.4 ALGORITHM DETAILS 118
5.5 CONCLUSIONS 119
III HYBRID M O N T E CARLO 1 2 1
6 HYBRID MONTE CARLO WITH COARSE MOMENTUM FIELD 123
6.1 INTRODUCTION 123
6.1.1 HYBRID MONTE CARLO 124
6.1.2 AUTOCORRELATIONS 127
6.2 HYBRID MONTE CARLO WITH COARSE MOMENTUM FIELD 130
6.2.1 COARSE MOMENTUM HOLD WITH MODIFIED MASS 130
6.2.2 COARSE-MOMENTUM HMC SHOWCASE 133
6.2.3 A MODEL PROBLEM: THE .RY-MODEL 136
6.2.4 COST ANALYSIS 140
6.2.5 RECURSIVE ALGORITHM 141
6.3 RESULTS 142
6.3.1 PARAMETER DETERMINATION 142
6.3.2 VOLUME DEPENDENCE 147
6.3.3 RECURSIVE METHOD 148
6.3.4 OTHER INTEGRATORS 149
6.4 COARSE-MOMENTUM HMC FOR QCD 149
6.4.1 HMC WITH MODIFIED KINETIC TERM 150
6.4.2 GENERALIZED HYBRID MONTE CARLO FOR QCD 153
6.5 CONCLUSIONS 160
7 SCHUR COMPLEMENT WITH NON-OVERLAPPING SUBDOMAINS FOR HMC 161
8 CONCLUSIONS 163
9 ACKNOWLEDGEMENTS 165
A MEMORY CONSUMPTION FOR DOMAIN DECOMPOSITIONS 167
B PROPAGATION O F ERROR: QUADRATIC CASE 169
C ALGORITHMS FOR NESTED KRYLOV SUBSPACE METHODS 171
C . L LANCZOS ALGORITHM 171
C.2 TWO-SIDED LANCZOS ALGORITHM 171
C.3 NESTED ALGORITHM 172
REFERENCES 175
V
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| spelling | Heybrock, Simon Verfasser aut Computational methods for quantum chromodynamics Simon Heybrock 2013 XI, 181 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Regensburg, Univ., Diss., 2013 Quantenchromodynamik (DE-588)4128082-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Quantenchromodynamik (DE-588)4128082-9 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:355-epub-282815 http://epub.uni-regensburg.de/28281/ Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:355-epub-282815 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026052153&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Heybrock, Simon Computational methods for quantum chromodynamics Quantenchromodynamik (DE-588)4128082-9 gnd |
| subject_GND | (DE-588)4128082-9 (DE-588)4113937-9 |
| title | Computational methods for quantum chromodynamics |
| title_auth | Computational methods for quantum chromodynamics |
| title_exact_search | Computational methods for quantum chromodynamics |
| title_full | Computational methods for quantum chromodynamics Simon Heybrock |
| title_fullStr | Computational methods for quantum chromodynamics Simon Heybrock |
| title_full_unstemmed | Computational methods for quantum chromodynamics Simon Heybrock |
| title_short | Computational methods for quantum chromodynamics |
| title_sort | computational methods for quantum chromodynamics |
| topic | Quantenchromodynamik (DE-588)4128082-9 gnd |
| topic_facet | Quantenchromodynamik Hochschulschrift |
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