Theoretical formulation of a time-domain finite element method for nonlinear magnetic problems in three dimensions

In this work, a numerical solution of nonlinear ferromagnetic problems is formulated using the three-dimensional time-domain finite element method (TDFEM) combined with the inverse Jiles- Atherton (J-A) vector hysteresis model. After a brief introduction of the J-A constitutive model, the second-order nonlinear partial differential equation (PDE) is constructed through the magnetic vector potential in the time domain, which is then discretized by employing the Newmark-β scheme, and solved by applying the Newton-Raphson method. Different Newton-Raphson schemes are constructed and compared. The capability of the proposed methods is demonstrated by several numerical examples including the simulation of the physical demagnetization process, the prediction of the magnetic remanence in the ferromagnetic material, and the generation of higher-order harmonics.