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V. Hanser:
"Numerical computation of the Eddy Current problem in ferromagnetic sheets by the multiscale finite element method using the vector preisach model";
Supervisor: J. Schöberl, K. Hollaus; E101, 2021; final examination: 2021-03-11.

To facilitate the design of electrical machines and transformers and to meet today´s economic as well as ecological requirements, an efficient simulation of the electromagnetic fields using the finite element method (FEM) is indispensable. The iron core of electrical machines and transformers is composed of many very thin sheets with excellent magnetic properties in order to keep the eddy currents and the associated losses as small as possible and to optimally guide the magnetic flux. Modelling of each single sheet by finite elements requires the solution of huge nonlinear equation systems which would make routine simulations of practically relevant problems impossible. In the present work, a mixed multiscale finite element method (MMSFEM) was used to cope with the problem of laminated cores. A vector Preisach model was developed to account for hysteresis of ferromagnetic materials as accurately as possible with little computational effort. The integration of hysteresis into the FEM is carried out by a differential permeability to avoid singular points occurring in case of the permeability.