General framework for re-assuring numerical reliability in parallel Krylov solvers: A case of bi-conjugate gradient stabilized methods
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Otros documentos de la autoría: Iakymchuk, Roman; Graillat, Stef; Aliaga Estellés, José Ignacio
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Título
General framework for re-assuring numerical reliability in parallel Krylov solvers: A case of bi-conjugate gradient stabilized methodsFecha de publicación
2024-01-01Editor
SAGE Publications Inc.ISSN
1094-3420Cita bibliográfica
1. Iakymchuk R, Graillat S, Aliaga JI. General framework for re-assuring numerical reliability in parallel Krylov solvers: A case of bi-conjugate gradient stabilized methods. The International Journal of High Performance Computing Applications. 2024;38(1):17-33. doi:10.1177/10943420231207642Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://journals.sagepub.com/doi/full/10.1177/10943420231207642Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
Parallel implementations of Krylov subspace methods often help to accelerate the procedure of finding an approximate solution of a linear system. However, such parallelization coupled with asynchronous and out-of-order ... [+]
Parallel implementations of Krylov subspace methods often help to accelerate the procedure of finding an approximate solution of a linear system. However, such parallelization coupled with asynchronous and out-of-order execution often makes more visible the non-associativity impact in floating-point operations. These problems are even amplified when communication-hiding pipelined algorithms are used to improve the parallelization of Krylov subspace methods. Introducing reproducibility in the implementations avoids these problems by getting more robust and correct solutions. This paper proposes a general framework for deriving reproducible and accurate variants of Krylov subspace methods. The proposed algorithmic strategies are reinforced by programmability suggestions to assure deterministic and accurate executions. The framework is illustrated on the preconditioned BiCGStab method and its pipelined modification, which in fact is a distinctive method from the Krylov subspace family, for the solution of non-symmetric linear systems with message-passing. Finally, we verify the numerical behavior of the two reproducible variants of BiCGStab on a set of matrices from the SuiteSparse Matrix Collection and a 3D Poisson’s equation. [-]
Publicado en
The International Journal of High Performance Computing Applications. 2024;38(1)Entidad financiadora
Department of Computing Science at Umeå University | EU H2020 MSCA-IF | Universitat Jaume I
Código del proyecto o subvención
842528, ANR-20-CE46-0009 | MCIN/AEI/10.13039/501100011033, PID2020-113656RB-C21, UJI-B2021-58
Derechos de acceso
© The Author(s) 2023.
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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