Vector Preisach model and Maxwell's equations

Abstract

We represent processes in highly anisotropic, nonhomogeneous, either ferromagnetic or ferrimagnetic materials, by coupling the Maxwell equations with a vector extension of the standard rectangular hysteresis loop. We then derive a two-length-scale vector model via a homogenization procedure. Here, the fine-scale magnetization M depends on the fine-scale magnetic field H , at variance with the corresponding scalar problem. This amends the usual formulation of the vector Preisach model, which is not consistent with the law ∇· B =0 .