- AutorIn
- Dr. rer. nat. Uwe Prüfert
- Titel
- Solving optimal PDE control problems : optimality conditions, algorithms and model reduction
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:105-qucosa-204639
- Datum der Einreichung
- 18.12.2015
- Datum der Verteidigung
- 16.05.2016
- Abstract (EN)
- This thesis deals with the optimal control of PDEs. After a brief introduction in the theory of elliptic and parabolic PDEs, we introduce a software that solves systems of PDEs by the finite elements method. In the second chapter we derive optimality conditions in terms of function spaces, i.e. a systems of PDEs coupled by some pointwise relations. Now we present algorithms to solve the optimality systems numerically and present some numerical test cases. A further chapter deals with the so called lack of adjointness, an issue of gradient methods applied on parabolic optimal control problems. However, since optimal control problems lead to large numerical schemes, model reduction becomes popular. We analyze the proper orthogonal decomposition method and apply it to our model problems. Finally, we apply all considered techniques to a real world problem.
- Freie Schlagwörter (DE)
- Optimal Steuerung, partielle Differentialgleichungen, Algorithmen, Lack of adjointness, Smoothed projection
- Freie Schlagwörter (EN)
- optimal PDE control, algorithms, lack of adjointness, smoothed projection
- Klassifikation (DDC)
- 510
- Normschlagwörter (GND)
- Partielle Differentialgleichung, Optimale Kontrolle, Numerisches Verfahren, Algorithmus
- GutachterIn
- Prof. Dr. rer. nat habil. Michael Eiermann
- Prof. Dr. rer. nat. habil. Thomas Slawig
- Prof. Dr. rer. nat. Christian Meyer
- BetreuerIn
- Prof. Dr. rer. nat habil. Michael Eiermann
- Den akademischen Grad verleihende / prüfende Institution
- Technische Universität Bergakademie Freiberg, Freiberg
- URN Qucosa
- urn:nbn:de:bsz:105-qucosa-204639
- Veröffentlichungsdatum Qucosa
- 23.06.2016
- Dokumenttyp
- Habilitation
- Sprache des Dokumentes
- Englisch
- Inhaltsverzeichnis
Introduction The state equation Optimal control and optimality conditions Algorithms The \"lack of adjointness\" Numerical examples Efficient solution of PDEs and KKT- systems A real world application Functional analytical basics Codes of the examples