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Performance of the Block Jacobi-Davidson Method for the Solution of Large Eigenvalue Problems on Modern Clusters

Röhrig-Zöllner, Melven and Thies, Jonas and Basermann, Achim (2015) Performance of the Block Jacobi-Davidson Method for the Solution of Large Eigenvalue Problems on Modern Clusters. SIAM LA15, 26.-30. Okt 2015, Atlanta. (Unpublished)

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Abstract

We investigate a block Jacobi-Davidson method for computing a few exterior eigenpairs of a large sparse matrix. The block method typically requires more matrix-vector and vector-vector operations than the standard algorithm. However, this is more than compensated by the performance gains through better data reusage on modern CPUs, which we demonstrate by detailed performance engineering and numerical experiments. The key ingredients to achieving high performance consist in both kernel optimizations and a careful design of the algorithm that allows using blocked operations in most parts of the computation. We show the performance gains of the block algorithm with our hybrid parallel implementation for a variety of matrices on up to 5\,120 CPU cores. A new development we discuss in this context is a highly accurate and efficient block orthogonalization scheme that exploits modern hardware features and mixed precision arithmetic.

Item URL in elib:https://elib.dlr.de/100266/
Document Type:Conference or Workshop Item (Speech)
Title:Performance of the Block Jacobi-Davidson Method for the Solution of Large Eigenvalue Problems on Modern Clusters
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Röhrig-Zöllner, MelvenMelven.Roehrig-Zoellner (at) dlr.deUNSPECIFIED
Thies, JonasJonas.Thies (at) dlr.deUNSPECIFIED
Basermann, Achimachim.basermann (at) dlr.deUNSPECIFIED
Date:26 October 2015
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Status:Unpublished
Keywords:sparse eigenvalue problems, Jacobi-Davidson, block methods, performance engineering, high performance computing, multi-core processors, hybrid parallel implementation
Event Title:SIAM LA15
Event Location:Atlanta
Event Type:international Conference
Event Dates:26.-30. Okt 2015
Organizer:SIAM
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:09 Dec 2015 16:15
Last Modified:31 Jul 2019 19:57

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