On the Computation of the Free-Space Doubly-Periodic Green's Function of the Three-Dimensional Helmholtz Equation

Abstract

In a recent article [1] the performances of several methods used for the computation of the free-space doubly-periodic Green's function G_0Λ of the three-dimensional (3D) Helmholtz equation were investigated. The existence of an alternative method that is superior to those discussed in that article is pointed out. The alternative method can have accuracy close to machine precision and is more efficient (at least 12 times faster for an identical convergence test). It yields a fast convergent result for any z, i.e., also for z = 0, where the series discussed by Guérin, Enoch, and Tayeb are only conditionally convergent.