Controllability Methods for the Computation of Time-Periodic Solutions; Application to Scattering

We discuss in this article the application of controllability techniques to the computation of the time-periodic solutions of evolution equations. The basic principles of the computational methods are presented in a fairly general context where the time discretization aspect is also discussed. Then this general methodology is applied to the solution of scattering problems for harmonic planar waves by two- and three-dimensional purely reflecting nonconvex 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.