The linear sampling method for solving the electromagnetic inverse scattering problem

We consider the inverse scattering problem of determining the shape of an obstacle in ℝ from knowledge of the time harmonic incident electromagnetic wave and the far-field pattern of the scattered wave with frequency in the resonance region. The approach used is the linear sampling method which does not require a priori knowledge of either the boundary condition or the connectivity of the scattering obstacle. Numerical examples are given for the case of both a simply connected perfect conductor and multiply connected obstacles satisfying an impedance boundary condition on the boundary of one component and satisfying a perfect conducting boundary condition on the boundary of another component.