The Structure of Parallel Sparse Matrix Algorithms for Solving Partial Differential Equations on Hypercubes

A complete PDE sparse matrix solver consists of several components. Its overall performance strongly depends on their mutual interactions and the effect of application properties, especially when exploiting the parallelism of a distributed memory, message passing multiprocessor. This paper systematically investigates various aspects of the structure and performance of direct methods for solving sparse, nonsymmetric linear systems from PDE applications on hypercube machines. a geometric approach is. used to construct and test these POE solvers. The performance data on the NCUBE are reported which provide the guidance for blending algorithm components to achieve high performance and for creating new, efficient POE solvers. IWork supported in part by National Science Foundation grant CCR-8619817. 2Work supported in part by lhe Air Force Office of scientific Research grant, 88-0243 and the Strategic Ddense Initiative Office contracl DAAL03-86·J(-Ol06.