Analysis and Applied Mathematics Seminar
David Nicholls
UIC
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.
Monday November 7, 2022 at 4:00 PM in 1227 SEO