  We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation
with a highly oscillatory diffusion coefficient, a simple model for a
ferromagnetic composite. A finite element macro scheme is combined with a
finite difference micro model to approximate the effective equation
corresponding to the original problem. This makes it possible to obtain
effective solutions to problems with rapid material variations on a small
scale, described by $\varepsilon \ll 1$, which would be too expensive to
resolve in a conventional simulation.
