A high-accuracy algorithm for solving problems of electrostatics in a nonhomogeneous spatially periodic dielectric medium

A high-accuracy economical iterative method is proposed for calculating the potential and the strength of the electric field in a three-dimensional inhomogeneous spatially periodic dielectric placed in an initially uniform electric field. The idea underlying the algorithm is that the potential is represented as a sum of a linear function and a spatially periodic correction, which can be expressed as an expansion in eigenfunctions of the Laplace operator that satisfy the appropriate periodicity conditions. The fast Fourier transform is used for an efficient numerical implementation of the proposed algorithm.