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

^*Corresponding author for this work

Software Systems

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

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
Journal	Parallel Computing
Volume	68
Early online date	26 May 2017
DOIs	https://doi.org/10.1016/j.parco.2017.05.006
Publication status	Published - Oct 2017

Keywords

65Y05
65Y10
65Y20
68W10
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' numerical stability and time-to-solution performance. We also analyze how the use of a preconditioner impacts the choice of the fastest solver.",

keywords = "65Y05, 65Y10, 65Y20, 68W10, 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",

year = "2017",

month = oct,

doi = "10.1016/j.parco.2017.05.006",

language = "English",

volume = "68",

journal = "Parallel Computing",

issn = "0167-8191",

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TY - JOUR

T1 - Preconditioned Krylov solvers on GPUs

AU - Anzt, Hartwig

AU - Gates, Mark

AU - Dongarra, Jack

AU - Kreutzer, Moritz

AU - Wellein, Gerhard

AU - Köhler, Martin

PY - 2017/10

Y1 - 2017/10

N2 - 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.

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 - 65Y05

KW - 65Y10

KW - 65Y20

KW - 68W10

KW - GPU

KW - ILU

KW - Jacobi

KW - Krylov solvers

KW - Preconditioning

UR - http://www.scopus.com/inward/record.url?scp=85020001878&partnerID=8YFLogxK

U2 - 10.1016/j.parco.2017.05.006

DO - 10.1016/j.parco.2017.05.006

M3 - Article

AN - SCOPUS:85020001878

SN - 0167-8191

VL - 68

JO - Parallel Computing

JF - Parallel Computing

ER -

Preconditioned Krylov solvers on GPUs

Abstract

Keywords

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