UTA Department of Mathematics

Mathematics and Statistics Colloquium

Date/Time/Room: Friday (10/17/2008) at 2:30pm in 304 Pickard Hall

Speaker: Dr. Thomas Hagstrom, Professor
Department of Mathematics
SMU
(Local host: J. Zhu)


"Efficient Representations of Wave Fields and Algorithms for Time-Domain Scattering Problems"

Abstract: The fundamental feature of waves is their ability to propagate long distances relative to their wavelength. Efficient algorithms for simulating waves deal with this fact by:
i. Employing high-resolution discretizations;
ii. Avoiding the sampling of wave fields where possible via the use of accurate radiation boundary conditions and fast far-field propagation algorithms.

In this talk we will focus on the second issue, reviewing the disparate representations which have been proposed and developing a new technique, the complete plane wave representation, which we prove leads to local radiation boundary conditions of optimal complexity for isotropic systems. We will also discuss the prospects for the development of fast propagation algorithms using the complete plane wave representation as well as issues which arise in its generalization to more complex models.