# American Institute of Mathematical Sciences

November  2007, 1(4): 643-660. doi: 10.3934/ipi.2007.1.643

## Inverse scattering using finite elements and gap reciprocity

 1 Department of Mathematics, University of Delaware, Newark, DE 19716, United States 2 Department of Applied Mathematics and Theoretical Physics, Delaware State University, Dover, DE 19901,, United States

Received  August 2007 Published  October 2007

In this paper we consider the inverse scattering problem of determining the shape of one or more objects embedded in an inhomogeneous background from Cauchy data measured on the boundary of a domain containing the objects in its interior. Following [1], we use the reciprocity gap functional method. In an inhomogeneous background medium the use of a Herglotz wave function in the reciprocity gap functional is no longer permissable. Instead we propose to use a finite element representation. We provide analysis to support the method, and also describe implementation issues. Numerical examples are given showing the performance of the method.
Citation: Peter Monk, Jiguang Sun. Inverse scattering using finite elements and gap reciprocity. Inverse Problems & Imaging, 2007, 1 (4) : 643-660. doi: 10.3934/ipi.2007.1.643
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