Very promising approximate formula for the dynamical identification of small inhomogeneities embedded in a homogeneous medium has been developed in the present work for full time-depended Maxwell equation. The theoretical base for the precision reconstruction method of the small inhomogeneities dislocation has been confirmed by numerical simulations. The present reconstruction method could be easily adopted for the different geometry of the inhomogeneities as it was shown by the different numerical simulations. The numerical computational code has been developed. It could be divided in two principal parts, first of all, the numerical resolution of full time-depended Maxwell equation using a discontinuous Galerkin Method in space and Newmark scheme in time for the reconstruction problem's statement data simulation, and second part, the inversion using Fourier transforms algorithm of the constructed boundary integral, which give as the inclusion's centers reconstruction. All of them, the theoretical result and computational program have been validated by the modelling results.
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