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978-3-8439-0021-8, Reihe Mathematik

Oliver Tse
SPn-systems in Radiative Heat Transfer and Natural Convection-Radiation Models: Parameter Identification and Optimal Control

121 Seiten, Dissertation Technische Universität Kaiserslautern (2011), Softcover, A5

Zusammenfassung / Abstract

This thesis deals with optimal control problems for hydrodynamic and thermodynamic models coupled with the simplified spherical harmonic approximations of the radiative transfer equation. Two cases in which radiation plays a central role in the physics of the problem are considered. In the field of radiation therapy planning the identification of parameters and, possibly, functions that are responsible for the changes in optical parameters during radiation therapy is studied. In the field of glass manufacturing the controllability of the flow and temperature distribution within the glass melt by controlling the temperature on the boundary is studied. For this cause, the existence and uniqueness of solutions of their respective state system under certain regularity assumptions on the domain and data is shown. Next, the solvability of the linearized system and characterization of the adjoint states are established, thereby allowing the derivation of the corresponding first-order optimality system (KKT system). Numerical schemes exploiting the adjoint-based derivative for optimization are introduced and the numerical results are shown and explained. The independence of the adjoint-based derivative with respect to spacial and temporal grid is studied. Finally, the dependence of optimal solutions on variations in the regularization parameter is discussed.