Applied Mathematics Seminar

Speaker: David Nicholls, Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago

Title: Numerical Solution of Diffraction Problems: A High-Order Perturbation of Surfaces/Asymptotic Waveform Evaluation Method

Abstract: The rapid and robust simulation of linear waves interacting with layered periodic media is a crucial capability in many areas of scientific and engineering interest. High–Order Perturbation of Surfaces (HOPS) algorithms are interfacial methods which recursively estimate scattering quantities via perturbation in the interface shape heights/slopes. For a single incidence wavelength such methods are the most efficient available in the parameterized setting we consider here. In this talk we describe a generalization of one of these HOPS schemes by incorporating a further expansion in the wavelength about a base configuration which constitutes an "Asymptotic Waveform Evaluation" (AWE). We not only provide a detailed specification of the algorithm, but also verify the scheme and point out its benefits and shortcomings. With numerical experiments we show the remarkable efficiency, fidelity, and high–order accuracy one can achieve with an implementation of this algorithm.