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The Jacobi-Davidson Eigensolver on GPU Clusters

Thies, Jonas and Ernst, Dominik and Röhrig-Zöllner, Melven (2018) The Jacobi-Davidson Eigensolver on GPU Clusters. 6th European Seminar on Computing (ESCO 2018), 3.-8. Juni 2018, Pilsen, Tschechien.

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Abstract

Compared to multi-core processors, GPUs typically offer a higher memory bandwidth, which makes them attractive for memory-bounded codes like sparse linear and eigenvalue solvers. The fundamental performance issue we encounter when implementing such methods for modern GPUs is that the ratio between memory bandwidth and memory capacity is significantly higher than for CPUs. When solving large-scale problems one therefore has to use more compute nodes and is quickly forced into the strong scaling limit. In this paper we consider an advanced eigensolver (the block Jacobi-Davidson QR method [1]), implemented in the PHIST software (https://bitbucket.org/essex/phist/). We aim to provide a blueprint and a framework for implementing other iterative solvers like Krylov subspace methods for modern architectures that have relatively small high-bandwidth memory. The techniques we explore to reduce the memory footprint of our solver include mixed precision arithmetic and recalculating quantities `on-the-fly'. We use performance models to back our results theoretically and ensure performance portability.

Item URL in elib:https://elib.dlr.de/123327/
Document Type:Conference or Workshop Item (Speech)
Title:The Jacobi-Davidson Eigensolver on GPU Clusters
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Thies, JonasJonas.Thies (at) dlr.deUNSPECIFIED
Ernst, DominikDominik.Ernst (at) fau.deUNSPECIFIED
Röhrig-Zöllner, MelvenMelven.Roehrig-Zoellner (at) dlr.dehttps://orcid.org/0000-0001-9851-5886
Date:3 June 2018
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Status:Published
Keywords:eigenvalues, sparse matrices, graphics processing units (GPU), high performance computing
Event Title:6th European Seminar on Computing (ESCO 2018)
Event Location:Pilsen, Tschechien
Event Type:international Conference
Event Dates:3.-8. Juni 2018
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 > High Performance Computing
Deposited By: Thies, Jonas
Deposited On:03 Dec 2018 17:21
Last Modified:31 Jul 2019 20:21

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