Next: Introduction
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