Revisited implementation of the spectral kummer-poisson's method for the efficient computation of 2-D periodic Green's functions in homogeneous media

This paper presents a new algorithm to accelerate the computation of the series that lead to the determination of the 2-D periodic Green's functions with 1-D and 2-D periodicities in homogeneous media. The algorithm is based on a novel implementation of the spectral Kummer-Poisson's method. In this novel implementation every original series is split into two fast converging series, one with exponential convergence and the other with algebraic convergence of arbitrarily large order. The CPU times required by the new algorithm to obtain the 2-D periodic Green's functions have been compared with those required by Ewald's method, and the new algorithm has been found to be between 2 and 5 times faster than Ewald's method.