Two-Scale Homogenization of the Nonlinear Eddy Current Problem with FEM

An efficient and accurate computation of the eddy current losses in laminated iron cores of electric devices is of great interest. Modeling each laminate individually by the finite element method requires many elements and leads to large systems of equations. Homogenization represents a promising method to overcome this problem. A two-scale finite element method is proposed to efficiently compute the eddy current losses in laminated media with nonlinear material properties. A rather coarse finite element grid suffices to approximate the losses accurately. The method based on the magnetic vector potential is described. The laminates are basically considered individually in the finite element assembly taking account of the nonlinearity. This is computationally very intensive. Some adapted integration rules are introduced and studied to accelerate the finite element assembly. The accuracy and the computational costs of the proposed method are shown by a numerical example.