State-constrained optimization for identification of small inclusions

The inverse problem of identification of small geometric objects (defects, inclusions) of unknown topological properties is under the investigation. This problem is treated within the state-constrained optimization framework. Using topological sensitivity analysis and methods of singular perturbations, a proper approximation by the asymptotic model is justified rigorously. The underlying parametric optimization problem is solved semi-analytically by a variational calculus. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)