Efficient computation of the 3D Green's function with one dimensional periodicity using the Ewald method

F Capolino,D.R Wilton,W.A Johnson

doi:10.1109/aps.2006.1711199

Abstract

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

Highlights

In applying numerical full wave methods like the Method of Moments (MoM) to periodic structures, fast and accurate means for evaluating the periodic Green’s function are often needed
The percentage relative error is plotted versus summation limit parameters ±N, ±P in sums (6) and (7) resulting in a total number of terms of 2N +1 and 2P +1, respectively
The n = 0 point source is at (x, y, z ) = (0, 0, 0), and the two curves are related to two observation points at (x, y, z) = (0.01, 0, 0.1)λ0 and (x, z) = (0.1, 0, 0.1)λ0, respectively, where λ0 = 2π/k is the free space wavelength

Summary

Introduction

In applying numerical full wave methods like the Method of Moments (MoM) to periodic structures, fast and accurate means for evaluating the periodic Green’s function are often needed. Terms in the spatial series representation of G An alternative spectral series representation of this Green’s function, in terms of cylindrical waves, exists, G r, r e−jkzqz H0(2)

Results

Conclusion