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. (C) 1998 Academic Press.