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Scalable block methods and preconditioning for hardware efficient sparse eigensolutions

Basermann, Achim and Röhrig-Zöllner, Melven and Thies, Jonas (2015) Scalable block methods and preconditioning for hardware efficient sparse eigensolutions. Sparse Solvers for Exascale: From Building Blocks to Applications, 23.-25. März 2015, Greifswald, Deutschland.

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Abstract

Block variants of the Jacobi-Davidson method for computing a few extreme eigenpairs of a large sparse matrix are known to improve the robustness of the standard algorithm, but are generally shunned because the total number of floating-point operations increases. We present a scalable implementation of a block Jacobi-Davidson solver with blocked GMRES preconditioning. By detailed performance engineering and numerical experiments we demonstrate that the increase in operations is typically more than compensated by the performance gains of the block operations on modern parallel hardware architectures. Thus the block solver is both more efficient and robust than its single vector counterpart. Moreover, we discuss a row projection method for the solution of ill-conditioned linear systems encountered in the FEAST algorithm for computing inner eigenpairs. We introduce a novel hybridly parallel and fully iterative implementation of the eigenvalue solver which exploits parallelism on several levels and present numerical and performance results.

Item URL in elib:https://elib.dlr.de/100613/
Document Type:Conference or Workshop Item (Speech)
Title:Scalable block methods and preconditioning for hardware efficient sparse eigensolutions
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Basermann, AchimDLR-KP, SC-VSSUNSPECIFIED
Röhrig-Zöllner, MelvenDLR-KP, SC-VSSUNSPECIFIED
Thies, JonasDLR-KP, SC-VSSUNSPECIFIED
Date:23 March 2015
Refereed publication:No
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Status:Published
Keywords:Block methods; scalability; preconditioning; sparse eigenproblems; hardware efficiency; Jacobi-Davidson; blocked GMRES; MINRES; FEAST; CGMN; CARP; multi-coloring; interior eigenvalues; performance
Event Title:Sparse Solvers for Exascale: From Building Blocks to Applications
Event Location:Greifswald, Deutschland
Event Type:Workshop
Event Dates:23.-25. März 2015
Organizer:Institute of Physics of the University of Greifswald (IfP); DFG through Priority Programme “Software for Exascale Computing” (SPPEXA)
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: Basermann, Dr.-Ing. Achim
Deposited On:09 Dec 2015 16:22
Last Modified:31 Jul 2019 19:57

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