The efficient solution of direct medium problems by using translation techniques.

We consider a Fredholm integral equation arising from a time-harmonic electromagnetic scattering problem for inhomogeneous media. The discretization of this equation usually produces a large dense linear system that must be solved by iterative methods. To speed up these methods we propose an efficient computation of the action of the corresponding coefficient matrix on a generic vector. This computation is mainly based on the well known addition formula for the Hankel functions and a simple translation argument. We present some numerical examples to show the efficiency of the proposed method.