Application of the FEM with adaptivity for electromagnetic inverse medium scattering problems

The paper presents a study of solution of inverse medium scattering problems for 3D time-harmonic electromagnetics. The solution is based on minimization of the misfit function between the observed scattered fields and trial solutions of direct problems for the sought approximate distribution of electric permittivity. The sources of illuminating waves and the observation points of the scattered fields are located in the nearfield the scatterer. The simulations of the direct problems are performed with the Finite Element Method. Application of adaptive mesh refinement to improve accuracy of solutions is illustrated. Tests with real- and complex-valued distributions of electric permittivity, and with complete and incomplete measurement data are presented.