Shifted equivalent sources and FFT acceleration for periodic scattering problems, including Wood anomalies

Abstract

This paper introduces a fast algorithm, applicable throughout the electromagnetic spectrum, for the numerical solution of problems of scattering by periodic surfaces in twodimensional space. The proposed algorithm remains highly accurate and efficient for challenging configurations including randomly rough surfaces, deep corrugations, large periods, near grazing incidences, and, importantly, Wood-anomaly resonant frequencies. The proposed approach is based on use of certain “shifted equivalent sources” which enable FFT acceleration of a Wood-anomaly-capable quasi-periodic Green function introduced recently (Bruno and Delourme (2014) [4]). The Green-function strategy additionally incorporates an exponentially convergent shifted version of the classical spectral series for the Green function. While the computing-cost asymptotics depend on the asymptotic configuration assumed, the computing costs rise at most linearly with the size of the problem for a number of important rough-surface cases we consider. In practice, singlecore runs in computing times ranging from a fraction of a second to a few seconds suffice for the proposed algorithm to produce highly-accurate solutions in some of the most challenging contexts arising in applications.