Highly scalable eigensolvers for Petaflop applications:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2012
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| Schlagworte: | |
| Online-Zugang: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130115-1115722-0-3 Inhaltsverzeichnis |
| Beschreibung: | VIII, 123 S. graph. Darst. |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 HIGH PERFORMANCE COMPUTING 1
1.2 EIGENSOLVERS: FIELDS OF APPLICATION 5
1.2.1 AB-INITIO MOLECULAR SIMULATIONS 5
1.2.2 INSPECTION OF LARGE NETWORKS 6
1.3 OVERVIEW OF THIS THESIS 7
2 SYMMETRIC EIGENSOLVERS 9
2.1 THE EIGENVALUE PROBLEM 9
2.2 DIRECT AND ITERATIVE EIGENSOLVERS 11
2.3 TRIDIAGONAL BASED (DIRECT) EIGENSOLVERS 11
2.3.1 TRIDIAGONALIZATION 12
2.3.2 TRIDIAGONAL EIGENSOLVERS 13
2.3.3 BACK TRANSFORMATION OF EIGENVECTORS 14
2.3.4 ALGORITHMIC KERNELS: ORTHOGONAL SIMILARITY TRANSFORMATIONS . . .
14 2.4 1-SIDED AND 2-SIDED FACTORIZATIONS 20
2.5 TRIDIAGONALIZATION APPROACHES 22
2.5.1 1-STEP TRIDIAGONALIZATION 22
2.5.2 2-STEP TRIDIAGONALIZATION 24
2.5.3 SUCCESSIVE BAND REDUCTION 27
2.6 EIGENSOLVERS IN THE CONTEXT OF HPC 29
3 T H E PARALLEL 2-STEP TRIDIAGONALIZATION 3 3
3.1 MODEL OF PARALLEL COMPUTATION 34
3.2 REDUCTION TO BANDED FORM USING QR-DECOMPOSITIONS 35
3.3 QR-DECOMPOSITION: ALGORITHMIC VARIANTS 41
3.3.1 CLASSIC HOUSEHOLDER QR-DECOMPOSITION 43
3.3.2 BLOCKED QR-DECOMPOSITION 45
3.4 TRIDIAGONALIZATION OF BANDED MATRICES 60
3.4.1 EXISTING PARALLELIZATION 60
3.4.2 FINE GRAINED DATA DEPENDENCY ANALYSIS 63
*
VII
HTTP://D-NB.INFO/1034860682
IMAGE 2
CONTENTS
3.5 TRIDIAGONAL-TO-BANDED BACK TRANSFORMATION 66
3.5.1 HIGH PERFORMANCE KERNELS 67
3.5.2 ID PARALLELIZATION 69
3.5.3 2D PARALLELIZATION 70
3.6 BANDED-TO-FULL BACK TRANSFORMATION 74
3.7 RUNTIME ANALYSIS 75
3.7.1 COMPARISON WITH 1-STEP TRIDIAGONALIZATION 76
3.7.2 STRONG SCALING AND EFFICIENCY 77
3.7.3 WEAK SCALING 79
3.8 OVERVIEW OF EXISTING IMPLEMENTATIONS 80
4 IMPLEMENTATION AND RESULTS 8 1
4.1 THE ELPA LIBRARY 81
4.2 TEST SETTINGS 83
4.2.1 HARDWARE OVERVIEW 83
4.2.2 TEST MATRICES 84
4.3 REDUCTION TO BANDED FORM 85
4.4 TRIDIAGONALIZATION OF BANDED MATRICES 89
4.5 REDUCTION OF BANDED MATRICES TO SMALLER BANDWIDTH 92
4.6 TRIDIAGONAL-TO-BANDED BACK TRANSFORMATION 95
4.6.1 HIGH PERFORMANCE KERNELS 95
4.6.2 PARALLEL PERFORMANCE 99
4.7 BANDED-TO-FULL BACK TRANSFORMATION 105
4.8 OVERALL RESULTS 106
5 CONCLUSION 1 1 3
BIBLIOGRAPHY 1 1 5
VIII
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| spelling | Auckenthaler, Thomas Verfasser aut Highly scalable eigensolvers for Petaflop applications Thomas Auckenthaler 2012 VIII, 123 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2013 Eigenwertproblem (DE-588)4013802-1 gnd rswk-swf Paralleler Algorithmus (DE-588)4193615-2 gnd rswk-swf Programmbibliothek (DE-588)4121521-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Eigenwertproblem (DE-588)4013802-1 s Paralleler Algorithmus (DE-588)4193615-2 s Programmbibliothek (DE-588)4121521-7 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20130115-1115722-0-3 http://mediatum.ub.tum.de/node?id=1115722 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130115-1115722-0-3 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025892530&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Auckenthaler, Thomas Highly scalable eigensolvers for Petaflop applications Eigenwertproblem (DE-588)4013802-1 gnd Paralleler Algorithmus (DE-588)4193615-2 gnd Programmbibliothek (DE-588)4121521-7 gnd |
| subject_GND | (DE-588)4013802-1 (DE-588)4193615-2 (DE-588)4121521-7 (DE-588)4113937-9 |
| title | Highly scalable eigensolvers for Petaflop applications |
| title_auth | Highly scalable eigensolvers for Petaflop applications |
| title_exact_search | Highly scalable eigensolvers for Petaflop applications |
| title_full | Highly scalable eigensolvers for Petaflop applications Thomas Auckenthaler |
| title_fullStr | Highly scalable eigensolvers for Petaflop applications Thomas Auckenthaler |
| title_full_unstemmed | Highly scalable eigensolvers for Petaflop applications Thomas Auckenthaler |
| title_short | Highly scalable eigensolvers for Petaflop applications |
| title_sort | highly scalable eigensolvers for petaflop applications |
| topic | Eigenwertproblem (DE-588)4013802-1 gnd Paralleler Algorithmus (DE-588)4193615-2 gnd Programmbibliothek (DE-588)4121521-7 gnd |
| topic_facet | Eigenwertproblem Paralleler Algorithmus Programmbibliothek Hochschulschrift |
| url | http://mediatum.ub.tum.de/node?id=1115722 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130115-1115722-0-3 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025892530&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT auckenthalerthomas highlyscalableeigensolversforpetaflopapplications |