Inverse scattering using finite elements and gap reciprocity

Peter Monk; Jiguang Sun

doi:10.3934/ipi.2007.1.643

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2007, Volume 1, Issue 4: 643-660. Doi: 10.3934/ipi.2007.1.643

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Inverse scattering using finite elements and gap reciprocity

Peter Monk^1, and
Jiguang Sun^2,

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

Received: July 31, 2007

Published: October 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 65N30.

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