Graph partitioning with matrix coefficients for symmetric positive definite linear systems

Details Graph partitioning with matrix coefficients for symmetric positive definite linear systems Graph partitioning with matrix coefficients for symmetric positive definite linear systems

2011-10-26

arxiv.org/abs/1110.5709v1

Mathematics

Numerical Analysis

Scientific paper

Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel matrix-vector multiplication, and typically disregard the information on the coefficients of the matrix. This information, however, may have a significant impact on the quality of the preconditioning procedure used within the chosen iterative scheme. In the present paper, we suggest a spectral partitioning algorithm, which takes into account the information on the matrix coefficients and constructs partitions with respect to the objective of increasing the quality of the additive Schwarz preconditioning for symmetric positive definite linear systems. Numerical results for a set of test problems demonstrate a noticeable improvement in the robustness of the resulting solution scheme when using the new partitioning approach.

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