Comparison between differential and variational forms of an energy-based hysteresis model

This paper compares two implementations of an energy-based ferromagnetic hysteresis model for finite element computations. The first implementation is an approximated explicit solution of the non-linear differential equation that is obtained from the energy balance of the magnetic material. The second implementation borrows from the theory of plasticity a variational formulation to solve exactly this differential equation. Both implementations are quantitatively compared in terms of accuracy and computational cost. The differential approach turns out to be much faster than the variational one and to give in most situations a result very close to that of the exact variational approach.