Optimization approach for the simultaneousreconstruction of the dielectric permittivity and magnetic permeability functions from limited observations

We consider the inverse problem of the simultaneous reconstruction of the dielectricpermittivity and magnetic permeability functions of the Maxwell's system in3D with limited boundary observations of the electric field. Thetheoretical stability for the problem is provided by the Carleman estimates.For the numerical computations the problem is formulated as anoptimization problem and hybrid finite element/difference method isused to solve the parameter identification problem.