F. Ben Hassen ; Y. Boukari ; H. Haddar - Inverse impedance boundary problem via the conformal mapping method: the case of small impedances

arima:1936 - Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, August 26, 2010, Volume 13 - 2010 - Special issue TAMTAM'09 - https://doi.org/10.46298/arima.1936
Inverse impedance boundary problem via the conformal mapping method: the case of small impedances

Authors: F. Ben Hassen ; Y. Boukari ; H. Haddar

Haddar and Kress [9] extended the use of the conformal mapping approach [2, 8] to reconstruct the internal boundary curve Ti of a doubly connected domain from the Cauchy data on the external boundary of a harmonic function satisfying a homogeneous impedance boundary condition on Ti. However, the analysis of this scheme indicates non convergence of the proposed algorithm for small values of the impedance. In this paper, we modify the algorithm proposed in [9] in order to obtain a convergent and stable inversion process for small impedances. We illustrate the performance of the method through some numerical examples that also include the cases of variable impedances.


Volume: Volume 13 - 2010 - Special issue TAMTAM'09
Published on: August 26, 2010
Submitted on: February 12, 2010
Keywords: electric impedance tomography, inverse problems, conformal mapping.,omographie électrique,problèmes inverses,applications conformes,[INFO] Computer Science [cs],[MATH] Mathematics [math]


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