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Conformal mapping and inverse conductivity problem withone measurement

Published online by Cambridge University Press:  14 February 2007

Marc Dambrine  and
Djalil Kateb
Marc Dambrine
Affiliation:
Laboratoire de Mathématiques Appliquées de Compiègne. Université de Technologie de Compiègne. Centre de Recherche de Royalieu 60200 Compiègne, France; [email protected]
Djalil Kateb
Affiliation:
Laboratoire de Mathématiques Appliquées de Compiègne. Université de Technologie de Compiègne. Centre de Recherche de Royalieu 60200 Compiègne, France; [email protected]
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Abstract

This work deals with a two-dimensional inverse problem in the field of tomography. The geometry of an unknown inclusion has to be reconstructed from boundary measurements. In this paper, we extend previous results of R. Kress and his coauthors: the leading idea is to use the conformal mapping function as unknown. We establish an integrodifferential equation that the trace of the Riemann map solves. We write it as a fixed point equation and give conditions for contraction. We conclude with a series of numerical examples illustrating the performance of the method.

Keywords

Inverse conductivity problemconformal mapping.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 1 , January 2007 , pp. 163 - 177
Copyright
© EDP Sciences, SMAI, 2007

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References

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