WIAS Preprint No. 963, (2004)

Shape optimization for 3D electrical impedance tomography



Authors

  • Eppler, Karsten
  • Harbrecht, Helmut

2010 Mathematics Subject Classification

  • 49Q10 49M37 65N38 49K20

Keywords

  • Electrical impedance tomography, Newton method, regularization, shape calculus, boundary integral equations, wavelets

Abstract

In the present paper we consider the identification of an obstacle or void of different conductivity included in a three-dimensional domain by measurements of voltage and currents at the boundary. We reformulate the given identification problem as a shape optimization problem. Since the Hessian is compact at the given hole we apply a regularized Newton scheme as developed by the authors (WIAS-Preprint No. 943). All information of the state equation required for the optimization algorithm can be derived by boundary integral equations which we solve numerically by a fast wavelet Galerkin scheme. Numerical results confirm that the proposed regularized Newton scheme yields a powerful algorithm to solve the considered class of problems.

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