Numerical Analysis Seminar

Date: October 12, 2022

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: David Nicholls, University of Illinois Chicago

Title: A Stable High-Order Perturbation of Surfaces/Asymptotic Waveform Evaluation Method for the Numerical Solution of Grating Scattering Problems

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.