Abstract
The performance of parallel algorithms implementing the block SOR iterative method, used for the solution of linear systems arising from the discretization of elliptic BVPs by the finite element collocation method, is investigated in this paper. By making use of a recently introduced block tridiagonal partitioning of the collocation matrix, which yields faster rates of convergence, and its associated modified red-black ordering of unknowns and equations, we succeeded to increase the scalability of the problem. The study of the communicational and computational needs of the problem on a virtual parallel machine made possible the mapping of the resulted SOR-algorithm on a fixed size distributed memory parallel system, utilizing a simple pipeline architecture among its processors, in an optimum way. The proposed parallel schemes are being realized on a Parsytec cognitive computer via an SPMD programming model. Speedup measurements are used to reveal the efficiency of our implementation.
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