This work deals with the inverse problem associated to 3D crack identification inside a conductive material using eddy current measurements. In order to accelerate the time-consuming direct optimization, the reconstruction is provided by the minimization of a last-square functional of the data-model misfit using space mapping (SM) methodology. This technique enables to shift the optimization burden from a time consuming and accurate model to the less precise but faster coarse surrogate model. In this work, the finite element method (FEM) is used as a fine model while the model based on the volume integral method (VIM) serves as a coarse model. The application of the proposed method to the shape reconstruction allows to shorten the evaluation time that is required to provide the proper parameter estimation of surface defects.
In this paper we present the results of simulations of the Magnetic Induction Tomography (MIT) forward problem. Two complementary calculation techniques have been implemented and coupled, namely: the finite element method (applied in commercial software Comsol Multiphysics) and the second, algebraic manipulations on basic relationships of electromagnetism in Matlab. The developed combination saves a lot of time and makes a better use of the available computer resources.