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

The method of Accelerated Cartesian Expansions (ACE) is an O(N) tree-based algorithm similar to the well-known Fast Multipole Method (FMM). Recent work 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.