The Ewald method is applied to accelerate the evaluation of the Green’s function of an infinite periodic phased linear array of point sources. Only a few terms are needed to evaluate Ewald sums, which are cast in terms of error functions and exponential integrals, to high accuracy.

An alternative direct procedure for applying the Ewald approach to obtain the Green's function for an array of line sources with 1D periodicity is presented. Furthermore, an algorithm for choosing the Ewald splitting parameter E that extends the efficiency of the method when the periodicity is somewhat larger than a wavelength is derived. In particular, the dyadic Green's function formalism is combined with the Ewald method.

The Ewald method is applied to accelerate the evaluation of the Green's function (GF) of an infinite equispaced linear array of point sources with linear phasing. Only a few terms are needed to evaluate Ewald sums, which are cast in terms of error functions and exponential integrals, to high accuracy. It is shown analytically that the choice of the standard "optimal" Ewald splitting parameter E0 causes overflow errors at high frequencies (period large compared to the wavelength), and convergence rates are analyzed. A recipe for selecting the Ewald splitting parameter is provided. © 2006 Elsevier Inc. All rights reserved.