A parallel solver using block fourier decompositions

Authors:
Hsin-Chu Chen;Shinn-Yih Tzeng
Affiliations:
Dept. of Computer and Information Science, Clark Atlanta University, Atlanta, GA;Dept. of Computer and Information Science, Clark Atlanta University, Atlanta, GA
Venue:
ISPA'03 Proceedings of the 2003 international conference on Parallel and distributed processing and applications
Year:
2003

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Abstract

The block Fourier decomposition method recently proposed by the first author is a special method for decoupling any block tridiagonal matrix of the form K = block-tridiag [B, A, B], where A and B are square submatrices, into diagonal blocks. Unlike the traditional fast Poisson solver, block cyclic reductions, or the FACR algorithm, this approach does not require A and B be symmetric or commute. Presented in this paper is a parallel solver using this block decomposition method to solve linear systems whose coefficient matrices are of the form of K. We describe the computational procedure and implementation for parallel executions on distributed workstations. The performance from our numerical experiments is reported to demonstrate the usefulness of this approach.