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Abstract:

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 PDE constraint. The first order optimality conditions are given by a coupled system of boundary value problems. These 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 effciently by a space-­time multigrid method.