B-driven energy based model by using a modified Newton–Raphson algorithm

B-conform a and a − v formulations of magnetic problems are implemented in many software based on the Finite Element method (FEM). In order to take into account magnetic hysteresis, these formulations require that the hysteresis model is driven by the flux density b . Unfortunately the energy-based hysteresis model is intrinsically driven by the magnetic field h , and presently no inverted energy-based model (aka h -driven) is known. Thus one has to invert the model numerically, by using Newton–Raphson or other solvers, which are all prone to convergence issues. This paper proposes an implementation of Newton–Raphson algorithm in the case of uni- and multi-axial excitation, and presents some modifications which improves the convergence of the algorithm with respect to classical solutions like Armijo’s rule. This novel approach enables an enhanced initial estimate of the magnetic field for the NR iterations, achieving up to 68% reduction in calculation times.