A Strategy for Parametrization Refinement in the Solution of a Geometric Inverse Problem

This paper treats the problem of identifying a single inclusion in a conductor domain based on the knowledge of measured electrical potentials on the external boundary of the conductor body due to known injected electrical currents. The inclusion boundary is approximated by an Extended X-Spline, that allows identify inclusions with smooth or sharp boundary. In this work, the forward problem is solved by an implementation of the direct formulation of the Boundary Element Method (BEM) and the inverse one is solved by Levenberg-Marquardt method, which requires the evaluation of the objective function derivatives, here approximated by finite differences. This work presents a methodology to increase the number of optimization variables during the solution of the inverse problem in order to improve the quality of the results.