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Full-Text Articles in Physical Sciences and Mathematics
Graph Partitioning Using Matrix Values For Preconditioning Symmetric Positive Definite Systems, Eugenr Vecharynski, Yousef Saad, Masha Sosonkina
Graph Partitioning Using Matrix Values For Preconditioning Symmetric Positive Definite Systems, Eugenr Vecharynski, Yousef Saad, Masha Sosonkina
Computational Modeling & Simulation Engineering Faculty Publications
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 …