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Extended Brauer model for ferromagnetic materials: analysis and computation

Timo Hülsmann (Bergische Universität Wuppertal, Wuppertal, Germany)
Andreas Bartel (Bergische Universität Wuppertal, Wuppertal, Germany)
Sebastian Schöps (Graduate School of Computational Engineering, Technische Universität Darmstadt, Darmstadt, Germany)
Herbert De Gersem (Wave Propagation and Signal Processing Research Group, KU Leuven, Kortrijk, Belgium)



The purpose of this paper is to develop a fast and accurate analytic model function for the single-valued H-B curve of ferromagnetic materials, where hysteresis can be disregarded (normal magnetization curve). Nonlinear magnetoquasistatic simulations demand smooth monotone material models to ensure physical correctness and good convergence in Newton's method.


The Brauer model has these beneficial properties, but is not sufficiently accurate for low and high fields in the normal magnetization curve. The paper extends the Brauer model to better fit material behavior in the Rayleigh region (low fields) and in full saturation. Procedures for obtaining optimal parameters from given measurement points are proposed and tested for two technical materials. The approach is compared with cubic spline and monotonicity preserving spline interpolation with respect to error and computational effort.


The extended Brauer model is more accurate and even maintains the computational advantages of the classical Brauer model. The methods for obtaining optimal parameters yield good results if the measurement points have a distinctive Rayleigh region.


The model function for ferromagnetic materials enhances the precision of the classical Brauer model without notable additional simulation cost.



The authors are very grateful for the valuable discussions on single valued material curves with Luc Dupré. The first author is supported by the “BLP-Projekt Die Studieneingangsphase” of the German Federal and State Governments. The third author is supported by the “Excellence Initiative” of the German Federal and State Governments and the Graduate School of Computational Engineering at Technische Universität Darmstadt.


Hülsmann, T., Bartel, A., Schöps, S. and De Gersem, H. (2014), "Extended Brauer model for ferromagnetic materials: analysis and computation", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 33 No. 4, pp. 1251-1263.



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