Fast Poisson solvers for MIMD computers

The methods of cyclic reduction, Fourier analysis and the resulting hybrid algorithm FACR( l) are formulated for a shared memory multiprocessor and applied to the two-dimensional Poisson equation. The complexity of the algorithms is analyzed, performance curves are given and optimal values of the parameter l are determined for various problem sizes and degrees of parallelism. The algorithms are implemented on a shared memory multiprocessor and performance results are discussed.