938 research outputs found
Graph partitioning using matrix values for preconditioning symmetric positive definite systems
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
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