A Comparative Analysis of an H⃗‐Formulation for the 3‐D Magnetostatic and Magnetoquasistatic Case Considering Hysteretic Effects

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.