A fast parallel algorithm for the Poisson equation on a disk

A parallel algorithm for solving the Poisson equation with either Dirichlet or Neumann conditions is presented. The solver follows some of the princip les introduced in a previous fast algorithm for evaluating singular integra l transforms by Daripa el al. Here we present recursive relations in Fourie r space together with fast Fourier transforms which lead to a fast and accu rate algorithm for solving Poisson problems within a unit disk. The algorit hm is highly parallelizable and our implementation is virtually architectur e-independent. Theoretical estimates show good parallel scalability of the algorithm, and numerical results show the accuracy of the method for proble ms with sharp variations on inhomogeneous term. Finally, performance result s for sequential and parallel implementations are presented. (C) 2001 Acade mic Press.