Model hierarchy-based optimal control of radiative heat transfer

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 (PDAE) and additional control constraints. We consider a sequence of model approximations given by spacetime 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.