Invited Session Tue.2.MA 415

Tuesday, 13:15 - 14:45 h, Room: MA 415

Cluster 19: PDE-constrained optimization & multi-level/multi-grid methods [...]

Optimization applications in industry I


Chair: Dietmar Hömberg



Tuesday, 13:15 - 13:40 h, Room: MA 415, Talk 1

Juergen Sprekels
Optimal control problems arising in the industrial growth of bulk semiconductor single crystals


The industrial growth of bulk semiconductor crystals is a challenging technological problem that leads to control problems with pointwise state constraints for an extremely difficult system of nonlinearly coupled partial differential equations. Turbulent fluid flows, magnetic fields and quasilinear heat conduction problems with both nonlocal and nonlinear radiation boundary conditions occur. We report on recent progress that has been made in the treatment of such problems.



Tuesday, 13:45 - 14:10 h, Room: MA 415, Talk 2

Simon Stingelin
Applications of optimal control in electromagnetic flow measurement

Coauthor: Fredi Tröltzsch


Electromagnetic flow measurement has been in use around the world for more than 50 years, as witnessed by the popularity of these meters that continues unabated in virtually all sectors of industry. Electromagnetic flowmeters can be used to measure all electrically conductive liquids (>\!\!5 \muS/cm) with or without solids.
The volume flow measurement is performed differentially with a pulsed magnetic field to suppress noise voltages as efficiently as possible. The key question in the talk is: How should the coil voltage be controlled to switch as fast as possible from one field state to another?
Because we want to control the voltage in a induction coil, this question leads us to the optimal control of an eddy current problem coupled with an ordinary differential equation for the electrical current. The ordinary differential equation is derived from the induction law.
In the talk we present the necessary first order optimality conditions of the control system and mention the well-posedness. Then we discuss numerical methods used to calculate the optimal coil voltage. Finally we present computations based on industrial flow meter geometries.



Tuesday, 14:15 - 14:40 h, Room: MA 415, Talk 3

Oliver Tse
Optimal boundary control of natural convection-radiation model in melting furnaces

Coauthor: René Pinnau


In this paper we present a comprehensive analysis of an optimal boundary control for a combined natural convection-radiation model, which has applications in the design of combustion chambers or for the control of melting processes in glass production or crystal growth. The model under investigation consists of the transient Boussinesq system coupled with a nonlinear heat equation and the SP3 model for radiation. We present existence, uniqueness and regularity results of bounded states. We further state an analysis of an optimal control problem, where we show the existence of an optimal control, derive the first-order optimality system and analyze the adjoint system. To underline the feasibility of the approach, we present numerical results based on a descent method using adjoint information.


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