Multiprocessor Schemes for Solving Block Tridiagonal Linear Systems

Abstract

The solution of large, banded diagonally dominant or symmetric positive definite linear systems constitutes one of the most common computational tasks asso ciated with implementations of the finite element method in applications such as fluid dynamics and structural analysis. Thus, designing multiprocessor algorithms for solving large block tridiagonal systems becomes of paramount importance for efficient imple mentation of these applications on vector and parallel machines. We present such schemes here, along with specific performance results on the Alliant FX/8 and CRAY X-MP/48. We particularly emphasize the speedups obtained with these schemes over popular direct band solvers. The development of a candidate scheme for the multicluster CEDAR machine is our goal.