Table of Contents
International Journal of Partial Differential Equations
Volume 2015, Article ID 968529, 9 pages
http://dx.doi.org/10.1155/2015/968529
Research Article

Direct and Inverse Scattering Problems for Domains with Multiple Corners

1Department of Mathematics and Statistics and Center of Applied Physics, Louisiana Tech University, Ruston, LA 71272, USA
2Department of Mathematics and Statistics, Louisiana Tech University, Ruston, LA 71272, USA

Received 31 August 2014; Accepted 1 January 2015

Academic Editor: Chi K. Lin

Copyright © 2015 Songming Hou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We proposed numerical methods for solving the direct and inverse scattering problems for domains with multiple corners. Both the near field and far field cases are considered. For the forward problem, the challenges of logarithmic singularity from Green’s functions and corner singularity are both taken care of. For the inverse problem, an efficient and robust direct imaging method is proposed. Multiple frequency data are combined to capture details while not losing robustness.