Comparison of multiscale models for eddy current computation in granular magnetic materials

In this paper, two multiscale numerical techniques are applied to the study of eddy current phenomena in magnetic granular materials. In particular, the Multiscale Finite Element Method and the Variational Multiscale Method are compared in terms of accuracy and computational efficiency with respect to a standard Finite Element approach and to a homogenization technique with second-order correctors. The numerical analysis is carried on focusing on specific conditions arising in the simulation of actual granular materials, such as soft ferrites and composite materials. In particular, depending on the working frequency and domain size, the electromagnetic phenomena may have a mainly local or global behavior, resulting in a different numerical response of the considered techniques. The results show that the Variational Multiscale Method is more accurate than the Multiscale Finite Element Method, but less efficient from a computational point of view. Moreover, the Multiscale Finite Element Method is found to have a complementary behavior with respect to the homogenization approach with local correctors.