Seminar in Numerical Analysis: Ulrich Römer (TU Darmstadt)

On Uncertainties in Low-Frequency Electromagnetics

Simulation results of magnetic devices with ferromagnetic materials are highly sensitive to the nonlinear material law and the geometry. Due to uncertainties inherent to measurements and the fabrication process, the precise knowledge of model input data cannot be assumed to be given. Therefore, in recent years, methods of uncertainty quantification have become more and more important. In this talk a short overview over application examples (magnets, machines) will be given and the PDEs for the magnetic fields will be discussed. Under some simplifications these are 2D nonlinear elliptic interface equations of monotone type. We will introduce a stochastic collocation method based on generalized polynomial chaos to quantify the uncertainties. Furthermore, we will discuss a worst-case scenario analysis to cover cases where the statistics of the inputs is not available. Since for the worst-case analysis gradient information is especially important, sensitivity analysis techniques, e.g., adjoint equations and shape calculus are required.

Joint work with Sebastian Schöps and Thomas Weiland.

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