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In this article we consider model reduction via proper orthogonal decomposition (POD) and its application to parameter estimation problems constrained by parabolic PDEs. We use a first discretize then optimize approach to solve the parameter estimation problem and show that the use of derivative information in the reduced-order model is important. We include directional derivatives directly in the POD snapshot matrix and show that, equivalently to the stationary case, this extension yields a more robust model with respect to changes in the parameters. Moreover, we propose an algorithm that uses derivative-extended POD models together with a Gauss--Newton method. We give an a posteriori error estimate that indicates how far a suboptimal solution obtained with the reduced problem deviates from the solution of the high dimensional problem. Finally we present numerical examples that showcase the efficiency of the proposed approach.
A design of a 3-phase inductive power and data transfer for multiple stationary loads is proposed. It focuses on stable load voltages while minimizing electromagnetic interference. Loads are contactless charging units of electric vehicles at car parks. Physical properties of the inductive couplers are modelled via 3-D FEM and lumped parameters are used for system studies. Design principles are verified at laboratory scale with a purpose built test stand.