FFTs and three-dimensional Poisson solvers for hypercubes

This paper investigates the implementation of fast direct methods for solving the three-dimensional Poisson equation on loosely coupled hypercube multiprocessors. As a preliminary step, the problem of computing multiple FFTs is considered and two different algorithms are compared. These algorithms are then used to implement two FFT-based fast Poisson solvers. Proceeding both with experiments and with performance models, these two solvers are studied and compared. No single algorithm is superior in all ranges of the parameters and the best choice depends upon problem size, number of processors and communication costs. In closing, two additional parallel algorithms for solving the Poisson equation are proposed, both of which appear to be competitive.