Nested multigrid methods for time-periodic,parabolic optimal control problems |
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Authors: | Dirk Abbeloos Moritz Diehl Michael Hinze Stefan Vandewalle |
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Affiliation: | 1.Department of Computer science,K. U. Leuven,Heverlee,Belgium;2.Electrical Engineering Department ESAT,K. U. Leuven,Heverlee,Belgium;3.Fachbereich Mathematik,Universit?t Hamburg,Hamburg,Germany |
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Abstract: | We present a nested multigrid method to optimize time-periodic, parabolic, partial differential equations (PDE). We consider a quadratic tracking objective with a linear parabolic PDE constraint. The first order optimality conditions, given by a coupled system of boundary value problems can be rewritten as an Fredholm integral equation of the second kind, which is solved by a 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 problems are solved efficiently by a time-periodic space-time multigrid method. |
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