Mathematics and its Applications Seminar
David Nicholls
University of Illinois at Chicago
Boundary Perturbation Methods for Electromagnetic Scattering
Abstract: The scattering of electromagnetic waves by irregular obstacles arises
in a wide array of applications including remote sensing,
nondestructive testing, and imaging. In this talk we will discuss a
class of highly accurate numerical methods for the simulation of
rough-surface scattering based upon the classical approach of Lord
Rayleigh from the early 1900's. While these methods feature rapid
execution times and exponentially fast convergence, subtle
cancellations in the underlying recursions render them unreliable for
very challenging problems (e.g., non-smooth surfaces). We will show
how a simple change of variables produces not only a robust and highly
accurate numerical procedure applicable to the most difficult
configurations, but also delivers a proof of the algorithm's
convergence. Furthermore, we will illustrate how these ideas can be
adapted to the multi-scale problem of high-frequency scattering where
the wavelength of the electromagnetic radiation is many orders of
magnitude smaller than the features of the scattering obstacle.
Wednesday October 28, 2009 at 4:00 PM in SEO 636