Improving the convergence of double series summation encountered in the analysis of curved frequency selective surfaces

Doubly curved frequency selective surfaces (FSS) represent a very difficult analysis problem due to the curvature itself and a large number of elements constituting the array. The analysis approach used here is based on the previously developed spectral domain - Method of Moments (MoM) algorithm which utilizes the Vilenkin´s addition theorem to enlarge the accuracy of the program and to decrease the needed computer time. However, for the efficient analysis of FSS further acceleration is required, and therefore here we concentrate on the acceleration of the double series summation encountered in the MoM analysis. Using Wynn´s series acceleration algorithm and applying it only to the extremes of the partial sums a significant calculation time and memory reductions are obtained. Furthermore, additional savings are gained by maximizing the precalculation steps in the program. The results of these techniques are demonstrated for a case of a circular-ring based spherical FSS and they show excellent agreement with the rigorous analysis approach.