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Inverse scattering using finite elements and gap reciprocity

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


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