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Increasing the performance of the Jacobi-Davidson method by blocking

Röhrig-Zöllner, Melven and Thies, Jonas and Kreutzer, Moritz and Alvermann, Andreas and Pieper, Andreas and Basermann, Achim and Hager, Georg and Wellein, Gerhard and 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 ISBN 1095-7197 ISSN 1064-8275

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Official URL: http://epubs.siam.org/doi/10.1137/140976017

Abstract

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.

Item URL in elib:https://elib.dlr.de/108424/
Document Type:Article
Title:Increasing the performance of the Jacobi-Davidson method by blocking
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Röhrig-Zöllner, Melvenmelven.roehrig-zoellner (at) dlr.deUNSPECIFIED
Thies, Jonasjonas.thies (at) dlr.deUNSPECIFIED
Kreutzer, MoritzErlangen Regional Computing CenterUNSPECIFIED
Alvermann, AndreasErnst-Moritz-Arndt University of GreifswaldUNSPECIFIED
Pieper, AndreasErnst-Moritz-Arndt University of GreifswaldUNSPECIFIED
Basermann, Achimachim.basermann (at) dlr.dehttps://orcid.org/0000-0003-3637-3231
Hager, GeorgErlangen Regional Computing CenterUNSPECIFIED
Wellein, GerhardErlangen Regional Computing CenterUNSPECIFIED
Fehske, HolgerErnst-Moritz-Arndt University of GreifswaldUNSPECIFIED
Date:15 December 2015
Journal or Publication Title:Siam Journal on Scientific Computing
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:37
DOI :10.1137/140976017
Page Range:C697-C722
Publisher:SIAM - Society for Industrial and Applied Mathematics
Series Name:SIAM Journal on Scientific Computing
ISSN:1064-8275
ISBN:1095-7197
Status:Published
Keywords:sparse eigenvalue problems, Jacobi-Davidson, block methods, performance engineering, high performance computing, multi-core processors, hybrid parallel implementation
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Technik für Raumfahrtsysteme
DLR - Research theme (Project):R - Vorhaben SISTEC
Location: Köln-Porz
Institutes and Institutions:Institut of Simulation and Software Technology > Distributed Systems and Component Software
Deposited By: Röhrig-Zöllner, Melven
Deposited On:20 Dec 2016 13:01
Last Modified:06 Sep 2019 15:20

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