Title: Model hierarchy-based optimal control of radiative heat transfer

Authors: Debora Clever; Jens Lang; Dirk Schröder

Addresses: Department of Mathematics, Graduate School of Computational Engineering, Technische Universität Darmstadt, Dolivostr. 15, D-64293 Darmstadt, Germany ' Department of Mathematics, Center of Smart Inferfaces, Graduate School of Computational Engineering, Technische Universität Darmstadt, Dolivostr. 15, D-64293 Darmstadt, Germany ' Department of Mathematics, Technische Universität Darmstadt, Dolivostr. 15, D-64293 Darmstadt, Germany

Abstract: We present a model hierarchy multilevel optimisation approach to solve an optimal boundary control problem in glass manufacturing. The process is modelled by radiative heat transfer and formulated as an optimal control problem restricted by partial differential algebraic equations (PDAEs) and additional control constraints. We consider a sequence of model approximations given by space-time dependent non-linear PDAEs of ascending accuracy. The different models allow for a model hierarchy-based optimisation approach, where the models are shifted automatically as the optimisation proceeds. We present a realisation of a multilevel generalised SQP method within the fully space-time adaptive optimisation environment Kardos using linearly implicit methods of Rosenbrock type and multilevel finite elements. We apply the optimal control algorithm to a glass cooling problem and present numerical experiments for the model hierarchy-based approach in two spatial dimensions and for a fully space-time adaptive optimisation in three spatial dimensions.

Keywords: optimal boundary control; multilevel optimisation; SQP methods; control constraints; adaptivity; Rosenbrock methods; 3D FEM; finite element method; model hierarchy; partial differential algebraic equations; PDAEs; radiative heat transfer; model-based control; optimal control; glass manufacturing; glass cooling; sequential quadratic programming.

DOI: 10.1504/IJCSE.2014.064536

International Journal of Computational Science and Engineering, 2014 Vol.9 No.5/6, pp.509 - 525

Received: 22 Dec 2011
Accepted: 14 Sep 2012

Published online: 22 Sep 2014 *

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