High Order Accurate Solution of Poisson's Equation in Infinite Domains for Smooth Functions

08/26/2021

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by   Christopher R. Anderson, et al.

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In this paper a method is presented for evaluating the convolution of the Green's function for the Laplace operator with a specified function ρ(x⃗) at all grid points in a rectangular domain Ω⊂R^d (d = 1,2,3), i.e. a solution of Poisson's equation in an infinite domain. 4th and 6th order versions of the method achieve high accuracy when ρ ( x⃗ ) possesses sufficiently many continuous derivatives. The method utilizes FFT's for computational efficiency and has a computational cost that is O (N log N) where N is the total number of grid points in the rectangular domain.