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Parallel Choleski Factorization of Block-Diagonal-Bordered Sparse Matrices

D. P. Koester, S. Ranka, and G. C. Fox
School of Computer and Information Science and
The Northeast Parallel Architectures Center (NPAC)
Syracuse University
Syracuse, NY 13244-4100
dpk@npac.syr.edu, ranka@top.cis.syr.edu, gcf@npac.syr.edu

NPAC Technocal Report --- SCCS 604

Abstract:

This paper presents research into parallel block-diagonal-bordered sparse Choleski factorization algorithms developed with special consideration to irregular sparse matrices originating in the electrical power systems community. Direct block-diagonal-bordered sparse Choleski algorithms exhibit distinct advantages when compared to general direct parallel sparse Choleski algorithms. Task assignments for numerical factorization on distributed-memory multi-processors depend only on the assignment of data to blocks, and data communications are significantly reduced with uniform and structured communications. Choleski factorization algorithms for block-diagonal-bordered form matrices require a specialized ordering step coupled to an explicit load balancing step in order to generate this matrix form and to uniformly distribute the computational workload for an irregular matrix throughout a distributed-memory multi-processor. Matrix orderings are performed using a diakoptic technique based on node-tearing-nodal analysis, which permits load balancing on either the number of calculations in the factorization step or the number of calculations in the forward reduction and backward substitution phase. Empirical performance measurements for real power system load-flow matrices are presented for an implementation of a parallel block-diagonal-bordered Choleski algorithm run on a distributed memory Thinking Machines CM-5 multi-processor.





David P. Koester
Sun Oct 22 15:40:25 EDT 1995