On a Problem of Optimal Magnetization

Kristof Altmann, Serge Nicaise, Simon Stingelin and Fredi Tröltzsch^*

An optimal control problem is considered for a coupled Maxwell integrodifferential model that is of degenerate parabolic type. The problem is related to an industrial application, where a time-optimal switching between magnetic fields of different polarization is needed. The well-posedness of associated optimal control problems and necessary optimality conditions are discussed. We report on associated numerical results for the optimal control in a simplified 3D geometry and for a realistic industrial setting. Moreover, an application of model reduction by proper orthogonal decomposition (POD) to a realistic 3D model is presented.

Mathematics Subject Classification: 49J20 49M05 35K65 35Q60

Keywords: Optimal control; Maxwell evolution equation; integrodifferential system; optimal magnetization; model reduction

Minisymposion: Adaptivity and Model Order Reduction in PDE Constrained Optimization