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Title: Multigrid of the second kind for the optimal control of time-periodic, parabolic partial differential equations
Authors: Abbeloos, Dirk
Vandewalle, Stefan
Diehl, Moritz
Hinze, Michael
Issue Date: 7-Jul-2011
Conference: International Congress on Computational and Applied Mathematics location:Leuven date:5-9 July 2010
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 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.
Publication status: published
KU Leuven publication type: DI
Appears in Collections:Numerical Analysis and Applied Mathematics Section
ESAT - STADIUS, Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics

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