NDLI: Sparse systems solving on GPUs with GMRES

Content Provider	Springer Nature Link
Author	Couturier, Raphaël Domas, Stéphane
Copyright Year	2011
Abstract	Scientific applications very often rely on solving one or more linear systems. When matrices are sparse, iterative methods are preferred to direct ones. Nevertheless, the value of nonzero elements and their distribution (i.e., the sketch of the matrix) greatly influence the efficiency of those methods (in terms of computation time, number of iterations, result precision) or simply prevent the convergence.Among iterative methods, GMRES (Saad, Iterative methods for sparse linear systems. PWS Publishing, New York, 1996) is often chosen when dealing with general nonsymmetric matrices. Indeed its convergence is very fast and more stable than the biconjugate gradient. Furthermore, it is mainly based on mathematical operations (matrix-vector and dot products, norms, etc.) that can be heavily parallelized and is thus a good candidate to implement a solver for sparse systems on Graphics Processing Units (GPU).This paper presents a GMRES method for such an architecture. It is based on the modified Gram–Schmidt approach and is very similar to that of Sparselib (Barrett et al., Templates for the solution of linear systems: building blocks for iterative methods, SIAM, Philadelphia, 1994). Our version uses restarting and a very basic preconditioning. For its implementation, we have based our code on CUBLAS (NVIDIA, http://developer.download.nvidia.com/compute/cuda/2_1/toolkit/docs/CUBLAS_Library_2.1.pdf , 2008) and SpMV (Bell and Garland, Efficient sparse matrix-vector multiplication on CUDA. NVIDIA technical report NVR-2008-004, 2008) libraries, in order to achieve a good performance whatever the matrix sizes and their sketch are. Our experiments exhibit encouraging results on the comparison between Central Processing Units (CPU) and GPU executions in double precision, obtaining a speedup ranging from 8 up to 23 for a large variety of problems.
Starting Page	1504
Ending Page	1516
Page Count	13
File Format	PDF
ISSN	09208542
Journal	The Journal of Supercomputing
Volume Number	59
Issue Number	3
e-ISSN	15730484
Language	English
Publisher	Springer US
Publisher Date	2011-02-10
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	GPU CUDA GMRES Iterative methods Processor Architectures Computer Science Programming Languages, Compilers, Interpreters
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Information Systems Hardware and Architecture Software

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