We discuss in this article the application of controllability techniques to the calculation of the time-periodic solutions of evolution equations. The basic principles of the computational methods are presented in a fairly general context where we discuss the time discretization aspect. We apply then this general methodology to the solution of scattering problems for harmonic planar waves by two and three dimensional purely reflecting non-convex obstacles. Numerical results obtained by the above method and comparisons with the results obtained by more classical methods show the superiority of the former ones. In annexe A, we give some details on the Radar Cross Section computation.