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Parallel LU 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 550

22 August 1993

Abstract:

Research is being performed to examine the applicability of parallel direct block-diagonal-bordered sparse matrix solvers for irregular sparse matrix problems derived from the electrical power systems community. Moreover, we believe that this research also has utility for irregular sparse matrix factorization for applications where the data is hierarchical. Direct block-diagonal-bordered sparse matrix algorithms exhibit distinct advantages when compared to current general parallel direct sparse matrix solvers. Task assignments for numerical factorization on distributed-memory multi-processors depend only on the assignment of independent blocks to processors and the processor assignments of data in the last diagonal block. In addition, data communications are significantly reduced and those remaining communications are generally uniform and structured. Parallel block-diagonal-bordered sparse matrix algorithms require modifications to the traditional sparse matrix preprocessing phase that include an explicit load balancing step coupled to a specialized ordering step to uniformly distribute the workload throughout a distributed-memory multi-processor. In this paper, we propose a new preprocessing phase that includes specialized ordering and load balancing techniques, we describe in detail the mathematics of block-diagonal-bordered sparse matrix solvers, and we present implementation details and empirical parallel performance data for a prototype direct block-diagonal-bordered sparse matrix solver running on a Thinking Machines CM-5 using message passing.





David P. Koester
Sun Oct 22 16:27:33 EDT 1995