Recent developments in the modeling, analysis, and numerics of ferromagnetism

Micromagnetics is a continuum variational theory describing magnetization patterns in ferromagnetic media. Its multiscale nature due to different inherent spatiotemporal physical and geometric scales, together with nonlocal phenomena and a nonconvex side- constraint, leads to rich behavior and pattern formation. This variety of effects is also the reason for severe problems in analysis, model validation, reductions, and numerics, which have only recently been accessed and are reviewed in this work.