The potential limitations of the Quasi-Newton based method primarily arise from the assumptions made regarding the material models and the geometrical configurations of the problem. One significant limitation is the reliance on the smoothness of the material behavior. While the method is designed to handle nonsmooth material laws, such as those exhibiting hysteresis, extreme cases of non-differentiability or highly complex material responses may lead to convergence issues or require additional modifications to the algorithm.
In terms of problem geometries, the method may face challenges when applied to highly irregular or complex geometries where the finite-element mesh becomes excessively refined. The local Quasi-Newton updates, while efficient, may struggle to maintain the required conditions for convergence if the mesh is not adequately designed to capture the material behavior across all elements. Furthermore, the performance of the method could degrade in scenarios involving significant geometric nonlinearity or when the magnetic field exhibits strong spatial variations, necessitating careful mesh design and possibly more sophisticated numerical techniques.