A numerical method for a direct obstacle scattering problem

We consider a direct scattering problem for an impenetrable obstacle. This problem is solved numerically with the operator expansion method, that can be seen as a perturbative method with respect to the boundary of the considered obstacle. This method requires the solution of various linear systems having the same coefficient matrix. The main result of this paper is the efficient solution of such linear systems with a numerical linear algebra algorithm based on the well-known Sherman-Morrison formula.