  We consider a multiscale strategy addressing the disparate scales in the
Landau-Lifschitz equations in micro-magnetism. At the microscopic scale, the
dynamics of magnetic moments are driven by a high frequency field. On the
macroscopic scale we are interested in simulating the dynamics of the
magnetisation without fully resolving the microscopic scales.
  The method follows the framework of heterogeneous multiscale methods and it
has two main ingredients: a micro- and a macroscale model. The microscopic
model is assumed to be known exactly whereas the macro model is incomplete as
it lacks effective quantities. The two models use different temporal and
spatial scales and effective parameter values for the macro model are computed
on the fly, allowing for improved efficiency over traditional one-scale
schemes.
  For the analysis, we consider a single spin under a high frequency field and
show that effective quantities can be obtained accurately with step-sizes much
larger than the size of the microscopic scales required to resolve the
microscopic features. Numerical results both for a single magnetic particle as
well as a chain of interacting magnetic particles are given to validate the
theory.

Numerical Analysis