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Author: Sprekels, Jürgen × Author: Tröltzsch, Fredi × End date: 2019 × Start date: 2019 × Type: Text ×

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Now showing 1 - 3 of 3
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    Optimal control of semiconductor melts by traveling magnetic fields
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Nestler, Peter; Schlömer, Nico; Klein, Olaf; Sprekels, Jürgen; Tröltzsch, Fredi
    In this paper, the optimal control of traveling magnetic fields in a process of crystal growth from the melt of semiconductor materials is considered. As controls, the phase shifts of the voltage in the coils of a heater-magnet module are employed to generate Lorentz forces for stirring the crystal melt in an optimal way. By the use of a new industrial heater-magnet module, the Lorentz forces have a stronger impact on the melt than in earlier technologies. It is known from experiments that during the growth process temperature oscillations with respect to time occur in the neighborhood of the solid-liquid interface. These oscillations may strongly influence the quality of the growing single crystal. As it seems to be impossible to suppress them completely, the main goal of optimization has to be less ambitious, namely, one tries to achieve oscillations that have a small amplitude and a frequency which is sufficiently high such that the solid-liquid interface does not have enough time to react to the oscillations. In our approach, we control the oscillations at a finite number of selected points in the neighborhood of the solidification front. The system dynamics is modeled by a coupled system of partial differential equations that account for instationary heat condution, turbulent melt flow, and magnetic field. We report on numerical methods for solving this system and for the optimization of the whole process. Different objective functionals are tested to reach the goal of optimization.
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    Extensions of the control variational method : dedicated to Prof. Dr. Fredi Tröltzsch on the occasion of his 60th birthday
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Sprekels, Jürgen; Tiba, Dan; Tröltzsch, Fredi
    The control variational method is a development of the variational approach, based on optimal control theory. In this work, we give an application to a variational inequality arising in mechanics and involving unilateral conditions both in the domain and on the boundary, and we explore the extension of the method to time-dependent problems
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    Optimal control of 3D state constrained induction heating problems with nonlocal radiation effects
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Druet, Pierre-Étienne; Klein, Olaf; Sprekels, Jürgen; Tröltzsch, Fredi; Yousept, Irwin
    The paper is concerned with a class of optimal heating problems in semiconductor single crystal growth processes. To model the heating process, time-harmonic Maxwell equations are considered in the system of the state. Due to the high temperatures characterizing crystal growth, it is necessary to include nonlocal radiation boundary conditions and a temperature-dependent heat conductivity in the description of the heat transfer process. The first goal of this paper is to prove the existence and uniqueness of the solution to the state equation. The regularity analysis associated with the time harmonic Maxwell equations is also studied. In the second part of the paper, the existence and uniqueness of the solution to the corresponding linearized equation is shown. With this result at hand, the differentiability of the control-to-state mapping operator associated with the state equation is derived. Finally, based on the theoretical results, first oder necessary optimality conditions for an associated optimal control problem are established.