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General framework for re-assuring numerical reliability in parallel Krylov solvers: a case of bi-conjugate gradient stabilized methods
Umeå University, Faculty of Science and Technology, Department of Computing Science. Uppsala University, Uppsala, Sweden.
Sorbonne Université, CNRS, LIP6, Paris, France.
Universitat Jaime I, Castellón de la Plana, Spain.
2023 (English)In: The international journal of high performance computing applications, ISSN 1094-3420, E-ISSN 1741-2846Article in journal (Refereed) Epub ahead of print
Abstract [en]

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.

Place, publisher, year, edition, pages
Sage Publications, 2023.
Keywords [en]
accuracy, ExBLAS, HPC, Numerical reliability, PBiCGStab, pipelined PBiCGStab, reproducibility
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-216137DOI: 10.1177/10943420231207642Scopus ID: 2-s2.0-85174938956OAI: oai:DiVA.org:umu-216137DiVA, id: diva2:1809293
Available from: 2023-11-02 Created: 2023-11-02 Last updated: 2023-11-02

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Iakymchuk, Roman

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Citation style
  • apa
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