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Inverse impedance boundary problem via the conformal mapping method: the case of small impedances

Abstract : 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.
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F. Ben Hassen, Y. Boukari, H. Haddar. Inverse impedance boundary problem via the conformal mapping method: the case of small impedances. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2010, Volume 13 - 2010 - Special issue TAMTAM'09, pp.47-62. ⟨10.46298/arima.1936⟩. ⟨hal-00739330v2⟩

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