On Solving Parabolic Optimal Control Problems by Using Space-Time Discretization
Please always quote using this URN:urn:nbn:de:0296-matheon-5980
- In this paper we present a strategy to solve parabolic optimal control problems using available specialized elliptic PDE solvers. We aim at an indirect solution approach, i.e. developing optimality conditions in function spaces that are then discretized and solved. Classes of problems where optimality conditions can be derived as coupled systems of parabolic partial differential equations are considered. We consider a simultaneous space-time discretization. We verify that for our model problems the parabolic forward-backward system of PDEs can equivalently be expressed by a single elliptic boundary value problem in the space-time domain. This fact has been used as a motivation for space-time-multigrid solution approaches, which may also be an option in our context. The theoretical base developed for the example problems then allows to apply specialized elliptic PDE solvers to the optimality system without much implementational effort. Numerical experiments for some example problems are conducted and underline the applicability of this approach.
Author: | Ira Neitzel, Uwe Prüfert, Thomas Slawig |
---|---|
URN: | urn:nbn:de:0296-matheon-5980 |
Referee: | Fredi Tröltzsch |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2009/07/22 |
Release Date: | 2009/07/20 |
Institute: | Technische Universität Berlin |
Zuse Institute Berlin (ZIB) | |
Preprint Number: | 632 |