Residual correction techniques for the efficient solution of inverse scattering problems

We consider the scattering of time-harmonic electromagnetic waves by penetrable inhomogeneous obstacles. In particular, we study the numerical solution of an inverse scattering problem, where the refractive index of the obstacle is computed from some knowledge of the scattered waves, generated by the obstacle itself, and known incident waves. This problem can be formulated by a pair of non-linear integral equations, and its numerical solution is usually a time-consuming computation. We propose an efficient solution of this problem by taking into account a linearization of the integral equation under consideration. The proposed method is tested by a numerical experiment, where the inverse scattering problem is numerically solved for different obstacles.