Numerical approximation of ferromagnetic materials

In previous works, we have obtained several results on the numerical analysis of magnetostrictive materials at microscopic scale. These studies, based on the minimization of the total energy functional of the system, include the existence and the approximation of solutions and the associated numerical experiments on two-dimensional samples. Next, we have considered the numerical analysis of two-dimensional cubic crystals of ferromagnetic materials with emphasis on the thickness of the walls and their evolution under an incremental magnetic field and the effect of nonmagnetic inclusions. This contribution discusses more specifically two extensions i) to three dimensional ferromagnetic materials (computation and representation of magnetic domains and Bloch walls) and ii) to the case of two-dimensional polycrystals, in particular, the magnetic domains for adjacent rectangular crystals whose easy lines of magnetization have different orientations.