An FFT Based Fast Poisson Solver on Spherical Shells

Abstract

We present a fast Poisson solver on spherical shells. With a special change of variable, the radial part of the Laplacian transforms to a constant coefficient differential operator. As a result, the Fast Fourier Transform can be applied to solve the Poisson equation with O(N³logN) operations. Numerical examples have confirmed the accuracy and robustness of the new scheme.