Open AccessParallel Implementations of FGMRES for Solving Large, Sparse Non-symmetric Linear Systems
Author(s) -
Byron DeVries,
Joe Iannelli,
Christian Trefftz,
Kurt A. O’Hearn,
Greg Wolffe
Publication year - 2013
Publication title -
procedia computer science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.334
H-Index - 76
ISSN - 1877-0509
DOI - 10.1016/j.procs.2013.05.213
Subject(s) - computer science , speedup , linear system , parallel computing , cuda , implementation , system of linear equations , thread (computing) , solver , multi core processor , range (aeronautics) , graphics , computational science , mathematics , computer graphics (images) , mathematical analysis , materials science , geometry , composite material , programming language , operating system
The Flexible Generalized Minimal Residual method (FGMRES) is an attractive iterative solver for non-symmetric systems of linear equations. This paper presents several methods for parallelizing FGMRES for a variety of archi- tectures including multi-core CPU, Graphics Processing Units (GPU), and multi-GPU systems. The parallel imple- mentations utilize OpenMP and CUDA kernels, and are organized according to thread scope. The linear systems employed in this study correspond to the discrete analogues of realistic three-dimensional convection-diffusion problems, and range in size to nearly 107 linear equations. All of the parallel implementations, particularly the novel hybrid approach, show a significant speedup over the sequential version. Theoretical insight and perfor- mance data is provided to allow informed decisions as to the most effective parallelization method for a given architecture
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