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

Max-Planck-Institute for Mathematics in the Sciences
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  18th GAMM-Seminar
January, 24th-26th, 2002
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  Abstract A. Borzi, Fri, 10.00-10.40 Previous Contents Next  
  Multigrid techniques for distributed nonlinear parabolic optimal control problems
A. Borzi (Karl-Franzens-Universität Graz)

A standard approach to the solution of parabolic problems is by time-stepping methods. These methods require to treat time evolution in a strict sequential way which may be computationally disadvantageous. In fact, when solving optimal control problems governed by parabolic differential equations, the sequential approach makes it difficulty to implement time coupling between parabolic equations with opposite orientation. For these reasons we consider parabolic multigrid methods that solve distributed nonlinear parabolic optimal control systems in one shot in the whole space-time. To achieve this goal we introduce a new smoothing method and investigate three different coarsening strategies: standard coarsening, double time coarsening, and semicoarsening in space. Efficiency and robustness of the multigrid techniques considered here are discussed based on results of numerical experiments.

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