Mathematics Colloquium, Fall 2009
David Nicholls
University of Illinois at Chicago
Boundary Perturbation Methods for Electromagnetic Scattering
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.