Parallel implementation of fast elliptic solver

A fast elliptic solver for separable elliptic equations on rectangular domains is considered. The method is referred to as FASV (fast algorithm for separation of variables) and is based on the odd-even block elimination technique in combination with the method for discrete separation of variables. The algorithm is connected with solving systems of algebraic equations with sparsity whose right-hand sides have only a few nonzero block components. The method is effective and stable by construction. Only a few of the block solution components are needed and hence these problems might be solved incompletely. Parallel implementation of the method proposed using the public domain PVM software is described in terms of decomposition of the original rectangular domain into a number of strips. Numerical results for a model problem on a cluster of a few IBM workstations are reported.