A general transient simulation method accurately models the magnetic state of a device containing a ferromagnetic core by incorporating a scalar hysteresis model into the standard finite element framework. The method numerically implements the Jiles-Atherton hysteresis model to simulate hysteresis without introducing additional parameters to simulate minor loops. Additionally, it extends the finite element geometry to two-dimensional space by predefining directional vectors or element coordinate systems that specify the local field directions for which the scalar material model applies. The method is verified by applying it to a rotationally symmetric ferromagnetic core with a time harmonic current excitation. Finally, the verified technique is applied to model a square-shaped inductor core having a more general two-dimensional magnetic field distribution.
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Toms et al. (2001) studied this question.