SIAM Journal on Scientific Computing
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.
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
Vecharynski, Eugenr; Saad, Yousef; and Sosonkina, Masha, "Graph Partitioning Using Matrix Values for Preconditioning Symmetric Positive Definite Systems" (2014). Modeling, Simulation & Visualization Engineering Faculty Publications. 13.