Comparison of parallel-plate Green's function acceleration techniques

Abstract

A comparative study of acceleration methods for computing the infinite series summation arising in parallelplate Green's functions is performed. The spectral summation, the application of the Shanks-transformed spatial summation, and the Ewald method are examined. Results are presented which show that, although the convergence rates of Ewald's method and the spectral summation are generally largest (i.e. less number of terms), the total series evaluation time for reaching a certain specified accuracy -which is ultimately of more practical importance -is shortest for the Shanks accelerated spatial summation for most of the cases we considered.

Fast analysis of gap waveguides using the characteristic basis function method and the parallel-plate Green's function

“…We concluded that the double Shanks tranformation on the orignal spatial Green's function series represents the best trade off between the solution accuracy and the total series evaluation time [3].…”

“…However, the field of a line array can be computed rapidly using the Shanksaccelerated spatial Green's function method. Other methods, such as the Ewald summation method, or the spectral-domain summation method, were found to be less efficient for our type of problems [3]. For instance, the Ewald summation method requires very few terms in the near-field region of the source, but the computation time of a single term is orders larger than that of a spatial Green's function term.…”

“…In this paper, we propose to employ the Characteristic Basis Function Method (CBFM, [2]) in conjunction with the parallel-plate Green's function [3]. This methodology enhances the computational efficiency of conventional method of moment (MoM) codes significantly.…”

Fast Analysis of Periodic Antennas and Metamaterial-Based Waveguides

“…The above capacitive gap in the so-called "gap waveguide" not only emulates a perfect magnetic conductor (PMC) boundary condition, but represents a mechanical advantage as well. As explained above, the CBFM is an enhancement technique for the method of moments and is very well suited to deal with large periodic struc- [42]. Consequently, we will only need to discretize and solve for the electric currents on the pins and probes in Fig.…”

“…(32) are known to be slowly convergent, however, each summation can be computed rapidly using the Shanks transformation [38]. This method is easy to implement and very fast if only a few digits of accuracy is required, which is sufficient in most practical cases [42]. For example, when considering the new series G 1 xx , G 2 xx , .…”