Incomplete block-factorization preconditioners for solving three-dimensional elliptic difference equations on systolic processors^∗

Research supported in part by Bulgarian Committee for Science under Grant #938-9-5-88 and under Grant # 10-17-3-87.

^∗∗

First presented at the Conference on Numerical Methods and Applications, Sofia, August 22-27, 1988.

Abstract

An architecture of a parallel computing system for matrix computations based on a systolic array of processors is considered and a version of incomplete block-factorizations of sparse matrices that arise in finite difference solution of three dimensional elliptic differential equations of second order is studied. The parallelization, both of factorization and solution processes, is investigated and the implementation of a stationary preconditioned iterative method on the considered computer architecture is described. Representative numerical tests for the efficiency of the consecutive version of the method for solving three-dimensional finite difference approximations to the Poisson equation are presented.

Keywords:

• Parallel algorithm
• systolic array
• sparse linear system
• preconditioned iterative method
• incomplete block-factorization
• finite differences
• three dímensional elliptic problem

Subject Classifications: AMS(MOS)::

• 65F10
• 65N20
• 65N30

C.R. CATEGORIES::

• G1.3.
• G1.8.

Research supported in part by Bulgarian Committee for Science under Grant #938-9-5-88 and under Grant # 10-17-3-87.

First presented at the Conference on Numerical Methods and Applications, Sofia, August 22-27, 1988.

Research supported in part by Bulgarian Committee for Science under Grant #938-9-5-88 and under Grant # 10-17-3-87.

First presented at the Conference on Numerical Methods and Applications, Sofia, August 22-27, 1988.

Notes

Research supported in part by Bulgarian Committee for Science under Grant #938-9-5-88 and under Grant # 10-17-3-87.

First presented at the Conference on Numerical Methods and Applications, Sofia, August 22-27, 1988.