Preconditioned Krylov solvers on GPUs

Hartwig Anzt; Mark Gates; Jack Dongarra; Moritz Kreutzer; Gerhard Wellein; Martin Köhler

doi:10.1016/j.parco.2017.05.006

Preconditioned Krylov solvers on GPUs

Hartwig Anzt, Mark Gates, Jack Dongarra, Moritz Kreutzer, Gerhard Wellein, Martin Köhler

Computer Science and Mathematics Div

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

Abstract

In this paper, we study the effect of enhancing GPU-accelerated Krylov solvers with preconditioners. We consider the BiCGSTAB, CGS, QMR, and IDR(s) Krylov solvers. For a large set of test matrices, we assess the impact of Jacobi and incomplete factorization preconditioning on the solvers’ numerical stability and time-to-solution performance. We also analyze how the use of a preconditioner impacts the choice of the fastest solver.

Original language	English
Pages (from-to)	32-44
Number of pages	13
Journal	Parallel Computing
Volume	68
DOIs	https://doi.org/10.1016/j.parco.2017.05.006
State	Published - Oct 2017

Keywords

GPU
ILU
Jacobi
Krylov solvers
Preconditioning

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10.1016/j.parco.2017.05.006

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title = "Preconditioned Krylov solvers on GPUs",

abstract = "In this paper, we study the effect of enhancing GPU-accelerated Krylov solvers with preconditioners. We consider the BiCGSTAB, CGS, QMR, and IDR(s) Krylov solvers. For a large set of test matrices, we assess the impact of Jacobi and incomplete factorization preconditioning on the solvers{\textquoteright} numerical stability and time-to-solution performance. We also analyze how the use of a preconditioner impacts the choice of the fastest solver.",

keywords = "GPU, ILU, Jacobi, Krylov solvers, Preconditioning",

author = "Hartwig Anzt and Mark Gates and Jack Dongarra and Moritz Kreutzer and Gerhard Wellein and Martin K{\"o}hler",

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AU - Anzt, Hartwig

AU - Gates, Mark

AU - Dongarra, Jack

AU - Kreutzer, Moritz

AU - Wellein, Gerhard

AU - Köhler, Martin

PY - 2017/10

Y1 - 2017/10

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AB - In this paper, we study the effect of enhancing GPU-accelerated Krylov solvers with preconditioners. We consider the BiCGSTAB, CGS, QMR, and IDR(s) Krylov solvers. For a large set of test matrices, we assess the impact of Jacobi and incomplete factorization preconditioning on the solvers’ numerical stability and time-to-solution performance. We also analyze how the use of a preconditioner impacts the choice of the fastest solver.

KW - GPU

KW - ILU

KW - Jacobi

KW - Krylov solvers

KW - Preconditioning

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VL - 68

SP - 32

EP - 44

JO - Parallel Computing

JF - Parallel Computing

ER -

Preconditioned Krylov solvers on GPUs

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Keywords

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