Abstract

An adaptive finite element/finite difference domain decomposition method for solution of time-dependent Maxwell's equations for electric field in conductive media will be presented. This method is applied for reconstruction of dielectric permittivity  and conductivity functions using time-dependent scattered data of electric field at the boundary of the domain.All reconstruction algorithms are based on optimization approach for finding of stationary point of the Lagrangian. Theoretical results related to derivation of a posteriori error estimates for Lagrangian, Tikhonov's functional and regularized solution of Tikhonov's functional will be presented.  Based on these estimates adaptive  finite element reconstruction algorithms are developed.  Computational tests will show robustness of proposed algorithms in 3D.