ABSTRACT Finite element formulations using the magnetic vector potential are numerically inefficient for modelling 3‐D magnetic hysteresis, as they rely on computationally expensive inverse material models. This article presents a robust and efficient ‐formulation that overcomes this limitation by incorporating the direct form of the energy‐based hysteresis model. A detailed implementation that resolves key numerical challenges, ensuring a well‐conditioned system and a stable nonlinear solver via a quasi‐Newton scheme is provided. Through a comparative analysis in both magnetostatic and magnetoquasistatic cases, the results show that the ‐formulation achieves a significant performance gain. While maintaining the same level of accuracy as the ‐formulation, it reduces the required computation time by a factor of over five when energy‐based hysteresis models are used. This work establishes the ‐formulation as a viable alternative to accurately and efficiently perform 3‐D simulations where hysteretic effects are non‐negligible.
Domenig et al. (Thu,) studied this question.