Shape optimization for 3D electrical impedance tomography
- Eppler, Karsten
- Harbrecht, Helmut
2010 Mathematics Subject Classification
- 49Q10 49M37 65N38 49K20
- Electrical impedance tomography, Newton method, regularization, shape calculus, boundary integral equations, wavelets
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.