International Congress on Computational and Applied Mathematics location:Leuven date:5-9 July 2010
We present a multigrid method of the second kind to optimize time-periodic, parabolic, partial differential equations (PDE). We consider a quadratic tracking objective with a linear or a non-linear PDE constraint. In both cases the first order optimality conditions are given by a coupled system of boundary value problems. We present a derivation of the first and second order optimality conditions. In the linear case the first order conditions can be rewritten as an integral equation of the second kind, which is solved by multigrid of the second kind. The evaluation of the integral operator consists of solving sequentially a boundary value problem for respectively the state and the adjoints. Both are solved efficiently by a spacetime multigrid method. The nonlinear case is treated by applying a Hessian-free Newton method in the control space.