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Integral equation methods in inverse obstacle scattering

Published online by Cambridge University Press:  17 February 2009

Rainer Kress
Rainer Kress
Affiliation:
Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Lotzestr. 16–18, D-37083 Göttingen, Germany.
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Abstract

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In this survey we consider a regularized Newton method for the approximate solution of the inverse problem to determine the shape of an obstacle from a knowledge of the far field pattern for the scattering of time-harmonic acoustic or electromagnetic plane waves. Our analysis is in two dimensions and the numerical scheme is based on the solution of boundary integral equations by a Nyström method. We include an example of the reconstruction of a planar domain with a corner both to illustrate the feasibility of the use of radial basis functions for the reconstruction of boundary curves with local features and to connect the presentation to some of the research work of Professor David Elliott.

Type
Research Article
Information
The ANZIAM Journal , Volume 42 , Issue 1 , July 2000 , pp. 65 - 78
Copyright
Copyright © Australian Mathematical Society 2000

References

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