Document Type

Article

Publication Date

2014

DOI

10.1137/120898760

Publication Title

SIAM Journal on Scientific Computing

Volume

36

Issue

1

Pages

A63-A87

Abstract

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 enhancing the quality of the nonoverlapping additive Schwarz (block Jacobi) preconditioning for symmetric positive definite linear systems. For a set of test problems with large variations in magnitudes of matrix coefficients, our numerical experiments demonstrate a noticeable improvement in the convergence of the resulting solution scheme when using the new partitioning approach. 2014 Society for Industrial and Applied Mathematics.

Comments

© Society for Industrial and Applied Mathematics.

"The Author may post the final published version of the Work on the Author's personal web site and on the web server of the Author's institution, provided that proper notice of the Publisher's copyright is included and that no separate or additional fees are collected for access to or distribution of the work."

Original Publication Citation

Vecharynski, E., Saad, Y., & Sosonkina, M. (2014). Graph partitioning using matrix values for preconditioning symmetric positive definite systems. SIAM Journal on Scientific Computing, 36(1), A63-A87. doi:10.1137/120898760

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