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## Abstract - In this paper we study the inverse scattering problem to determine the shape of a scatterer from either far field data for plane wave incidence or near field data for point sources as incident fields. As the simplest case of an absorbing medium we consider an impedance boundary condition with complex valued impedance λ on the boundary of the obstacle. We extend a new approach which characterizes the domain by those points z ∈R^3^ for which a certain function attains zero as its minimal value. This function is given as the cost functional of an optimization problem and depends explicitly on the data and the points z. An valuable feature of this approach is that it does not assume any a priori knowledge on the number of components of the obstacle or even the type of boundary condition. Some examples show the usefulness of this approach also from the numerical point of view.

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Author

N. Grinberg; A. Kirsch

Publisher

Walter de Gruyter GmbH

Published

2002

Language

EN

Field

Mathematics (Physical Sciences)