We develop efficient finite element methods for large multiscale problems described by Maxwell's equations using multiscale finite element methods or homogenisation with effective materials. To this end, underlying cell problems are exploited for the solution.

Multiscale finite element methods are developed for different potential formulations. The effective materials developed capture both the material properties and the fine structure. Non-linear materials are also considered with hysteresis. Further research topics are specific model order reductions and error estimators.

Application-oriented examples are eddy current and wave problems from electrical engineering such as laminated ferromagnetic cores of electrical devices, shielding with a thin layer or scattering and diffraction of electromagnetic waves on gratings.