Preconditioned Krylov solvers on GPUs

被引：27

作者：

Anzt, Hartwig ^{[1
]}

Gates, Mark ^{[1
]}

Dongarra, Jack ^{[1
,2
,3
]}

Kreutzer, Moritz ^{[4
]}

Wellein, Gerhard ^{[4
]}

Koehler, Martin ^{[5
]}

机构：

[1] Univ Tennessee, Dept Elect Engn & Comp Sci, Innovat Comp Lab, Knoxville, TN 37996 USA

[2] Univ Manchester, Manchester, Lancs, England

[3] Oak Ridge Natl Lab, Oak Ridge, TN USA

[4] Friedrich Alexander Univ Nuermberg Erlangen, Erlangen, Germany

[5] Max Planck Inst Dynam Complex Tech Syst Magdeburg, Magdeburg, Germany

来源：

PARALLEL COMPUTING | 2017年 / 68卷

关键词：

Krylov solvers; Preconditioning; GPU; ILU; Jacobi; SUBSPACE METHODS; BI-CGSTAB; ALGORITHM; VARIANT; ILU;

D O I：

10.1016/j.parco.2017.05.006

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, we study the effect of enhancing GPU-accelerated Krylov solvers with pre-conditioners. 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. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：32 / 44

页数：13

共 42 条

[1]

[Anonymous], 2016, LIGHTHOUSE FRAMEWORK

[2]

Anzt H., 2014, 28 IEEE INT PAR DIST

[3]

Anzt H., 2015, P 2 INT WORKSH HARDW

[4]

Anzt H., 2016, VECP 2016 12 I UNPUB

[5] Optimization and performance evaluation of the IDR iterative Krylov solver on GPUs [J].

Anzt, Hartwig ;

Kreutzer, Moritz ;

Ponce, Eduardo ;

Peterson, Gregory D. ;

Wellein, Gerhard ;

Dongarra, Jack .

INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS, 2018, 32 (02) :220-230

[6] Efficiency of general Krylov methods on GPUs - An experimental study [J].

Anzt, Hartwig ;

Dongarra, Jack ;

Kreutzer, Moritz ;

Wellein, Gerhard ;

Koehler, Martin .

2016 IEEE 30TH INTERNATIONAL PARALLEL AND DISTRIBUTED PROCESSING SYMPOSIUM WORKSHOPS (IPDPSW), 2016, :683-691

[7]

Balay S., 2016, PETSC

[8]

Benzi M., 1999, ELECTRON T NUMER ANA, V8, P88

[9]

Brezinski C., 1991, Numerical Algorithms, V1, P261, DOI 10.1007/BF02142326

[10] Breakdowns in the implementation of the Lanczos method for solving linear systems [J].

Brezinski, C ;

RedivoZaglia, M ;

Sadok, H .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1997, 33 (1-2) :31-44

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