18th GAMM-Seminar Leipzig on
Multigrid and related methods for optimization problems

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
Phone: +49.341.9959.752, Fax: +49.341.9959.999

  18th GAMM-Seminar
January, 24th-26th, 2002
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  Abstract K. Kunisch, Fri, 09.00-09.50 Previous Contents Next  
  Some Aspect of Multigrid Methods for Optimal Control of Partial Differential Equations
K. Kunisch (Universität Graz)

Within the last years investigations focusing on numerical realisations of open loop optimal control for partial differential equations have significantly increased in number. First and second order optimisation based techniques have reached a high level of maturity. Solution techniques based on multigrid methods appear to be less developed in the context of optimal control. In the first part of the talk I shall present some of our experience with multigrid methods for two concrete problems: Optimal control for the solid fuel iginition model, where the state variable appears within an exponential nonlinearity, and an optimal control-based formulation of the optical flow problem. In the second part I turn to accuracy, convergence and rate of convergence properties of finite difference multigrid solutions of optimality systems governed by linear elliptic pds. Sharp convergence factor estimates are obtained by means of local Fourier analysis as well as by functional analysis techniques.

This is joint work with Dr. Alfio Borzi.

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Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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