Applications of periodic Accelerated Cartesian Expansions to the analysis of electrically dense frequency selective structures

Abstract

The method of Accelerated Cartesian Expansions (ACE) is an O(N ) tree-based algorithm similar to the wellknown Fast Multipole Method (FMM) [1]. Recent work [2]has demonstrated the extension of this method to problems with periodic kernels, with a focus on demonstrating convergence with respect to the reconstruction of the Green's function as well as linear scaling in the evaluation of potentials. In this work, the integration of the periodic ACE algorithm into a fast solver for the EFIE is demonstrated, including a discussion of algorithmic changes necessary to the construction of trees on periodic domains, its break-even point relative to direct methods, and a few token applications illustrating the analysis of frequency selective structures (FSS) with electrically dense unit cells. We conclude with a discussion of further extensions and applications that will be presented at the conference.