Optimal Control of Parameter-Dependent Convection-Diffusion Problems around Rigid Bodies

Authors:
Timo Tonn;Karsten Urban;Stefan Volkwein
Affiliations:
timo.tonn@uni-ulm.de and karsten.urban@uni-ulm.de;-;Stefan.Volkwein@uni-konstanz.de
Venue:
SIAM Journal on Scientific Computing
Year:
2010

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Abstract

This paper is concerned with optimal control problems of elliptic partial differential equations. In particular, parametrized convection-diffusion problems are considered, where the parameter appears in the coefficients of the partial differential equation. Moreover, the presence of one or more rigid bodies is assumed inside the domain. Both the theory (existence, differentiability, optimality criteria) is investigated and the numerical solution (projected gradient scheme) of such problems is carried out. Finally, it is shown that optimizing the efficiency of a rotating propeller fits into the presented framework, and the results of corresponding numerical experiments are given.