Speaker: 

Carlos Perez-Arancibia

Institution: 

Caltech

Time: 

Monday, February 22, 2016 - 4:00pm to 5:00pm

Host: 

Location: 

RH 306

In this talk we present a novel boundary integral equation method for the numerical solution of problems of scattering by obstacles and defects in the presence of layered media. This new approach, that we refer to as the windowed Green function method (WGFM), is based on use of smooth windowing functions and integral kernels that can be expressed directly in terms of the free-space Green function. The WGFM is fast, accurate, flexible and easy to implement. In particular straightforward modifications of existing (accelerated or unaccelerated) solvers suffice to incorporate the WGF capability. The mathematical basis of the method is simple: the method relies on a certain integral equation that is smoothly windowed by means of a low-rise windowing function, and is thus supported on the union of the obstacle and a small flat section of the interface between the two penetrable media. Various numerical experiments demonstrate that both the near- and far-field errors resulting from the proposed approach, decrease faster than any negative power of the window size. In some of those examples the proposed method is up to thousands of times faster, for a given accuracy, than an integral equation method based on use of the layer Green function and the numerical approximation of Sommerfeld integrals. Generalizations of the WGFM to problems of scattering by obstacles in layered media composed by any finite number of layers as well as wave propagation and radiation in open dielectric waveguides are also included in this presentation.