Two-Dimensional Modeling of Soft Ferromagnetic Films
  We examine the response of a soft ferromagnetic film to an in-plane applied magnetic field. Our theory, based on asymptotic analysis of the micromagnetic energy in the thin-film limit, proceeds in two steps: first we determine the magnetic charge density by solving a convex variational problem; then we construct an associated magnetization field using a robust numerical method. Experimental results show good agreement with the theory. Our analysis is consistent with prior work by van den Berg and by Bryant and Suhl, but it goes much further; in particular it applies even for large fields which penetrate the sample. 
Antonio DeSimone, Robert V. Kohn, Stefan Mueller, Felix Otto, and   Rudolf Schaefer