Stephane Durand

Analysis of a Nondestructive Evaluation Technique for Defect Characterization in Magnetic Materials Using Local Magnetic Measurements

We study a method for nondestructive testing of laminated strips of a nonlinear magnetic material. Based on local measurements of the magnetic induction at the surface, we are able to reconstruct the proper position of defects inside the material, by solving an inverse problem. This inverse problem is solved by minimizing a suitable cost function using a gradient-based optimization procedure. Calculation of the gradient is done either by the standard method of small perturbations or by solving the sensitivity equation. The latter method yields a significant reduction of the computational time. The validity of the proposed algorithm is confirmed by experimental results.

A numerical scheme for the Maxwell equations in the quasi-static regime with a non-local source

In this paper we study a non-linear evolution equation, based on quasi-static electromagnetic fields, with a non-local field-dependent source. This model occurs in transformer driven active magnetic shielding. We present a numerical scheme for both time and space discretization and prove convergence of this scheme. We also derive the corresponding error estimates.