Natural vectorial extension of the preisach operator

In this paper, we give the formal definition of a new vector Preisach operator, in order to show that it naturally extends the classical scalar Preisach operator. We present a geometric representation for the 2-D operator, which allows for visualization of some properties of the operator summarized here. Finally, we present two finite-element simulations of the operator within electromagnetic field computations exhibiting hysteresis. The first simulation aims at analytical verification of the computations. The second simulation, where the fields are largely rotating, exploits the fully vectorial nature of the hysteresis operator. Here, a hysteresis effect experimentally observed is qualitatively reproduced well in the simulations.