Homogenization of Multiscale Eddy Current Problem by Localized Orthogonal Decomposition Method

A homogenization approach for the solution of multiscale eddy current problem is proposed. The method is based on the subspace decomposition and it involves a coarse space and a nested fine space. The homogenized problem is posed in the coarse space with the help of a projection operator acting between the coarse space and a space of rapidly oscillating functions. A Helmholtz decomposition is applied to treat the null-space of the curl operator so that the projection can be locally calculated. The results are illustrated in a 2-D numerical example.