Optimal control of PDEs has a crucial place in many parts of sciences and industry. Over the
last decade, there have been a great deal in, especially, control problems of elliptic problems.
Optimal control problems of Burgers equation that is as a simplifed model for turbulence
and in shock waves were recently investigated both theoretically and numerically. In this
thesis, we analyze the space-time simultaneous discretization of control problem for Burgers
equation. In literature, there have been two approaches for discretization of optimization
problems: optimize-then-discretize and discretize-then-optimize. In the first part, we follow
optimize-then-discretize appoproach. It is shown that both distributed and boundary time dependent
control problem can be transformed into an elliptic pde. Numerical results obtained
with adaptive and non-adaptive elliptic solvers of COMSOL Multiphysics are presented for
both the unconstrained and the control constrained cases. As for second part, we consider
discretize-then-optimize approach. Discrete adjoint concept is covered. Optimality conditions,
KKT-system, lead to a saadle point problem. We investigate the numerical treatment
for the obtained saddle point system. Both direct solvers and iterative methods are considered. For iterative mehods, preconditioners are needed. The structures of preconditioners for
both distributed and boundary control problems are covered. Additionally, an a priori error
analysis for the distributed control problem is given. We present the numerical results at the
end of each chapter.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/12613388/index.pdf |
| Date | 01 July 2011 |
| Creators | Yilmaz, Fikriye Nuray |
| Contributors | Karasozen, Bulent |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | Ph.D. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for public access |
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