A Conformal Mapping Method in Inverse Obstacle Scattering

s of MMA2013 & AMOE2013, May 27–30, 2013, Tartu, Estonia c © 2013 University of Tartu A CONFORMAL MAPPING METHOD IN INVERSE OBSTACLE SCATTERING RAINER KRESS Institut für Numerische und Angewandte Mathematik, Universität Göttingen Lotzestraße 16–18, 37083 Göttingen, Germany E-mail: [email protected] In a series of papers Akduman [1], Haddar [2] and Kress [5] have employed a conformal mapping technique for the inverse problem to reconstruct a perfectly conducting inclusion in a homogeneous background medium from Cauchy data for electrostatic imaging, i.e., for solving an inverse boundary value problem for the Laplace equation. An extension to impedance tomography also has been considered [3]. In a joint work [4] with Houssem Haddar, Palaiseau, France, we present an extension of this approach to inverse obstacle scattering for time-harmonic waves, i.e., 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 obtain 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.