A fast 3D Poisson solver of arbitrary order accuracy

We present a direct solver for the Poisson and Laplace equations in a 3D rectangular box. The method is based on the application of the discrete Fourier transform accompanied by a subtraction technique which allows reducing the errors associated with the Gibbs phenomenon and achieving any prescribed rate of convergence. The algorithm requires O (N-3 log N) operations, where N is the number of grid points in each direction. We show that our approach allows accurate treatment of singular cases which arise when the boundary function is discontinuous or incompatible with the differential equation. (C) 1998 Academic Press.