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USING REDUCED MESHES FOR SIMULATIONS OF THE LOCALIZATION OF SMALL ELECTROMAGNETIC INHOMOGENEITIES IN A 3

We are concerned in this work with simulations of the localization of a finite number of small electromagnetic inhomogeneities contained in a three-dimensional bounded domain. Typically, the underlying inverse problem considers the time-harmonic Maxwell equations formulated in electric field in this domain and attempts, from a finite number of boundary measurements, to localize these inhomogeneities. Our simulations are based on an approach that combines an asymptotic formula for perturbations in the electromagnetic fields, a suited inversion process, and finite element meshes derived from a non-standard discretization process of the domain. As opposed to a recent work, where the usual discretization process of the domain was employed in the computations, here we localize inhomogeneities that are one order of magnitude smaller.