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We consider a multiscale strategy addressing the disparate scales in theLandau-Lifschitz equations in micro-magnetism. At the microscopic scale, thedynamics of magnetic moments are driven by a high frequency field. On themacroscopic scale we are interested in simulating the dynamics of themagnetisation without fully resolving the microscopic scales.  The method follows the framework of heterogeneous multiscale methods and ithas two main ingredients: a micro- and a macroscale model. The microscopicmodel is assumed to be known exactly whereas the macro model is incomplete asit lacks effective quantities. The two models use different temporal andspatial scales and effective parameter values for the macro model are computedon the fly, allowing for improved efficiency over traditional one-scaleschemes.  For the analysis, we consider a single spin under a high frequency field andshow that effective quantities can be obtained accurately with step-sizes muchlarger than the size of the microscopic scales required to resolve themicroscopic features. Numerical results both for a single magnetic particle aswell as a chain of interacting magnetic particles are given to validate thetheory.

Temporal upscaling in micro magnetism via heterogeneous multiscale methods