A conformal mapping method in inverse obstacle scattering

Houssem Haddar 1 Rainer Kress 2
1 DeFI - Shape reconstruction and identification
Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
Abstract : Akduman, Haddar and Kress [1, 5, 11] have employed a conformal map- ping technique for the inverse problem to reconstruct a perfectly conducting inclusion in a homogeneous background medium from Cauchy data for elec- trostatic imaging, that is, for solving an inverse boundary value problem for the Laplace equation. We propose an extension of this approach to inverse obstacle scattering for time-harmonic waves, that is, to the solution of an inverse boundary value problem for the Helmholtz equation. The main idea is to use the conformal mapping algorithm in an iterative procedure to ob- tain Cauchy data for a Laplace problem from the given Cauchy data for the Helmholtz problem. We present the foundations of the method together with a convergence result and exhibit the feasibility of the method via numerical examples.
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Houssem Haddar, Rainer Kress. A conformal mapping method in inverse obstacle scattering. Complex Variables and Elliptic Equations, Taylor & Francis, 2013. ⟨hal-00768726⟩

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