Shifted Equivalent Sources and FFT acceleration for Periodic Scattering Problems including Wood Anomalies

TL;DR

This paper presents a fast, accurate algorithm for electromagnetic scattering by periodic surfaces, capable of handling challenging scenarios including Wood anomalies, using shifted equivalent sources and FFT acceleration.

Contribution

It introduces a novel Green function approach with shifted sources and FFT acceleration, enabling efficient solutions at Wood-anomaly resonant frequencies.

Findings

Algorithm remains accurate for challenging configurations.

Computing costs grow at most linearly with problem size.

Single-core computations take fractions of a second to a few seconds.

Abstract

This paper introduces a fast algorithm, applicable throughout the electromagnetic spectrum, for the numerical solution of problems of scattering by periodic surfaces in two-dimensional 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, Jour. Computat. Phys., 262--290, 2014). 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, single-core 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.