A High-Accuracy Algorithm for Solving Problems of Electrostatics in a Nonhomogeneous Spatially Periodic Dielectric Medium

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