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PATTERNS FOR PARALLEL PROGRAMMING ON GPUS
Edited by: F. Magoulès
Solving Sparse Linear Systems with CG and GMRES Methods on a GPU and GPU Clusters
R. Couturier and L. Ziane Khodja
FEMTO-ST Institute, University of Franche-Comte, Belfort, France
R. Couturier, L. Ziane Khodja, "Solving Sparse Linear Systems with CG and GMRES Methods on a GPU and GPU Clusters", in F. Magoulès, (Editor), "Patterns for Parallel Programming on GPUs", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 10, pp 227-248, 2014. doi:10.4203/csets.34.10
Keywords: sparse linear systems, CG and GMRES methods, CUDA, GPU clusters.
In this chapter, we aim to exploit the computing power of GPUs for solving sparse linear systems. Therefore, we have chosen two different iterative solutions to implement and to test their performances on GPUs. The conjugate gradient method is used for solving symmetric linear systems, and the generalized minimal residual method is used, more precisely, for solving unsymmetric linear systems. First, we have adapted the sequential algorithm of each method to the GPU architecture, by using the CUDA programming environment. We noticed that computations of both methods were faster on a GPU than on a CPU. Then, we parallelized algorithms of both iterative methods on a GPU cluster in order to solve large sparse linear systems. The performances of these parallel algorithms were tested on GPU clusters and on CPU clusters. We can notice that a GPU cluster is faster than a CPU cluster for solving sparse linear systems, but it is more efficient when these linear systems are large size ones.
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