Browsing by Author "Eppler, Karsten"

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    A new fictitious domain method in shape optimization
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Eppler, Karsten; Harbrecht, Helmut; Mommer, Mario
    The present paper is concerned with investigating the capability of the smoothness preserving fictitious domain method from [22] to shape optimization problems. We consider the problem of maximizing the Dirichlet energy functional in the class of all simply connected domains with fixed volume, where the state equation involves an elliptic second order differential operator with non-constant coefficients. Numerical experiments in two dimensions validate that we arrive at a fast and robust algorithm for the solution of the considered class of problems. The proposed method keeps applicable for three dimensional shape optimization problems.
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    A shape calculus analysis for tracking type formulations for tracking type formulations in electrical impedance tomography
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Eppler, Karsten
    In the paper [17], the authors investigated the identification of an obstacle or void of perfectly conducting material in a two-dimensional domain by measurements of voltage and currents at the boundary. In particular, the reformulation of the given nonlinear identification problem was considered as a shape optimization problem using the Kohn and Vogelius criterion. The compactness of the complete shape Hessian at the optimal inclusion was proven, verifying strictly the ill-posedness of the identification problem. The aim of the paper is to present a similar analysis for the related least square tracking formulations. It turns out that the two-norm-discrepancy is of the same principal nature as for the Kohn and Vogelius objective. As a byproduct, the necessary first order optimality condition are shown to be satisfied if and only if the data are perfectly matching. Finally, we comment on possible consequences of the two-norm-discrepancy for the regularization issue.