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Compressed basis GMRES on high-performance graphics processing units

Aliaga, José I.; Anzt, Hartwig ORCID iD icon 1; Grützmacher, Thomas 1; Quintana-Ortí, Enrique S.; Tomás, Andrés E.
1 Scientific Computing Center (SCC), Karlsruher Institut für Technologie (KIT)

Abstract:

Krylov methods provide a fast and highly parallel numerical tool for the iterative solution of many large-scale sparse linear systems. To a large extent, the performance of practical realizations of these methods is constrained by the communication bandwidth in current computer architectures, motivating the investigation of sophisticated techniques to avoid, reduce, and/or hide the message-passing costs (in distributed platforms) and the memory accesses (in all architectures). This article leverages Ginkgo’s memory accessor in order to integrate a communication-reduction strategy into the (Krylov) GMRES solver that decouples the storage format (i.e., the data representation in memory) of the orthogonal basis from the arithmetic precision that is employed during the operations with that basis. Given that the execution time of the GMRES solver is largely determined by the memory accesses, the cost of the datatype transforms can be mostly hidden, resulting in the acceleration of the iterative step via a decrease in the volume of bits being retrieved from memory. Together with the special properties of the orthonormal basis (whose elements are all bounded by 1), this paves the road toward the aggressive customization of the storage format, which includes some floating-point as well as fixed-point formats with mild impact on the convergence of the iterative process. ... mehr


Verlagsausgabe §
DOI: 10.5445/IR/1000150042
Veröffentlicht am 25.08.2022
Originalveröffentlichung
DOI: 10.1177/10943420221115140
Scopus
Zitationen: 2
Dimensions
Zitationen: 2
Cover der Publikation
Zugehörige Institution(en) am KIT Scientific Computing Center (SCC)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2022
Sprache Englisch
Identifikator ISSN: 1094-3420, 1078-3482, 1741-2846
KITopen-ID: 1000150042
HGF-Programm 46.21.02 (POF IV, LK 01) Cross-Domain ATMLs and Research Groups
Erschienen in The International Journal of High Performance Computing Applications
Verlag SAGE Publications
Band 37
Heft 2
Seiten 82-100
Vorab online veröffentlicht am 05.08.2022
Schlagwörter Sparse linear systems, mixed precision, Krylov solvers, compressed basis GMRES, graphics processing units
Nachgewiesen in Dimensions
Web of Science
Scopus
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