Röhrig-Zöllner, Melven und Thies, Jonas und Kreutzer, Moritz und Alvermann, Andreas und Pieper, Andreas und Basermann, Achim und Hager, Georg und Wellein, Gerhard und Fehske, Holger (2015) Increasing the performance of the Jacobi-Davidson method by blocking. SIAM Journal on Scientific Computing, 37 (6), C697-C722. SIAM - Society for Industrial and Applied Mathematics. doi: 10.1137/140976017. ISSN 1064-8275.
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Offizielle URL: http://epubs.siam.org/doi/10.1137/140976017
Kurzfassung
Block variants of the Jacobi-Davidson method for computing a few eigenpairs of a large sparse matrix are known to improve the robustness of the standard algorithm when it comes to computing multiple or clustered eigenvalues. In practice, however, they are typically avoided because the total number of matrix-vector operations increases. In this paper we present the implementation of a block Jacobi-Davidson solver. By detailed performance engineering and numerical experiments we demonstrate that the increase in operations is typically more than compensated by performance gains through better cache usage on modern CPUs, resulting in a method that is both more efficient and robust than its single vector counterpart. The steps to be taken to achieve a block speed-up involve both kernel optimizations for sparse matrix and block vector operations, and algorithmic choices to allow using blocked operations in most parts of the computation. We discuss the aspect of avoiding synchronization in the algorithm and show by numerical experiments with our hybrid parallel implementation that a significant speed-up through blocking can be achieved for a variety of matrices on up to 5120 CPU cores as long as at least about 20 eigenpairs are sought.
elib-URL des Eintrags: | https://elib.dlr.de/108424/ | ||||||||||||||||||||||||||||||||||||||||
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Dokumentart: | Zeitschriftenbeitrag | ||||||||||||||||||||||||||||||||||||||||
Titel: | Increasing the performance of the Jacobi-Davidson method by blocking | ||||||||||||||||||||||||||||||||||||||||
Autoren: |
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Datum: | 15 Dezember 2015 | ||||||||||||||||||||||||||||||||||||||||
Erschienen in: | SIAM Journal on Scientific Computing | ||||||||||||||||||||||||||||||||||||||||
Referierte Publikation: | Ja | ||||||||||||||||||||||||||||||||||||||||
Open Access: | Nein | ||||||||||||||||||||||||||||||||||||||||
Gold Open Access: | Nein | ||||||||||||||||||||||||||||||||||||||||
In SCOPUS: | Ja | ||||||||||||||||||||||||||||||||||||||||
In ISI Web of Science: | Ja | ||||||||||||||||||||||||||||||||||||||||
Band: | 37 | ||||||||||||||||||||||||||||||||||||||||
DOI: | 10.1137/140976017 | ||||||||||||||||||||||||||||||||||||||||
Seitenbereich: | C697-C722 | ||||||||||||||||||||||||||||||||||||||||
Verlag: | SIAM - Society for Industrial and Applied Mathematics | ||||||||||||||||||||||||||||||||||||||||
Name der Reihe: | SIAM Journal on Scientific Computing | ||||||||||||||||||||||||||||||||||||||||
ISSN: | 1064-8275 | ||||||||||||||||||||||||||||||||||||||||
Status: | veröffentlicht | ||||||||||||||||||||||||||||||||||||||||
Stichwörter: | sparse eigenvalue problems, Jacobi-Davidson, block methods, performance engineering, high performance computing, multi-core processors, hybrid parallel implementation | ||||||||||||||||||||||||||||||||||||||||
HGF - Forschungsbereich: | Luftfahrt, Raumfahrt und Verkehr | ||||||||||||||||||||||||||||||||||||||||
HGF - Programm: | Raumfahrt | ||||||||||||||||||||||||||||||||||||||||
HGF - Programmthema: | Technik für Raumfahrtsysteme | ||||||||||||||||||||||||||||||||||||||||
DLR - Schwerpunkt: | Raumfahrt | ||||||||||||||||||||||||||||||||||||||||
DLR - Forschungsgebiet: | R SY - Technik für Raumfahrtsysteme | ||||||||||||||||||||||||||||||||||||||||
DLR - Teilgebiet (Projekt, Vorhaben): | R - Vorhaben SISTEC (alt) | ||||||||||||||||||||||||||||||||||||||||
Standort: | Köln-Porz | ||||||||||||||||||||||||||||||||||||||||
Institute & Einrichtungen: | Institut für Simulations- und Softwaretechnik > Verteilte Systeme und Komponentensoftware | ||||||||||||||||||||||||||||||||||||||||
Hinterlegt von: | Röhrig-Zöllner, Melven | ||||||||||||||||||||||||||||||||||||||||
Hinterlegt am: | 20 Dez 2016 13:01 | ||||||||||||||||||||||||||||||||||||||||
Letzte Änderung: | 20 Jun 2024 13:39 |
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