Karsten Eppler, Helmut Harbrecht:

A regularized Newton method in EIT using shape Hessian information

The present paper is concerned with the identification of an obstacle or void of different conductivity included in a two-dimensional domain by measurements of voltage and currents at the boundary. We employ a reformulation of the given identification problem as a shape optimization problem as proposed by Sokolowski and Roche [1]. It turns out that the shape Hessian degenerates at the given hole which gives a further hint on the ill-posedness of the problem. For numerical methods, we propose a preprocessing for detecting the barycenter and a crude approximation of the void or hole. Then, we resolve the shape of the hole by a regularized Newton method.

[1] J.-R. Roche and J. Sokolowski

Numerical methods for shape identification problems.

Control Cybern. 25:867--894, 1996.

Erstveröffentlichung: Preprint WIAS-Preprint No. 943 (WIAS Berlin)

Mathematics Subject Classification (1991): 49Q10 49M37 65N38 49K20

Bibliographical note: Control Cybern. 34:203--225, 2005.

Keywords: shape optimization, boundary element methods, Newton scheme

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[Thu Feb 19 18:56:36 2009]

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