A conformal mapping method in inverse obstacle scattering - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Complex Variables and Elliptic Equations Year : 2013

A conformal mapping method in inverse obstacle scattering

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.
Fichier principal
Vignette du fichier
HaKr2012.pdf (253.87 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00768726 , version 1 (23-12-2012)

Identifiers

  • HAL Id : hal-00768726 , version 1

Cite

Houssem Haddar, Rainer Kress. A conformal mapping method in inverse obstacle scattering. Complex Variables and Elliptic Equations, 2013. ⟨hal-00768726⟩
272 View
593 Download

Share

Gmail Facebook X LinkedIn More