Multi-atomic young measure and artificial boundary in approximation of micromagnetics

Some micromagnetic phenomena can be modelled by a minimization problem of a nonconvex energy. A numerical method to compute the micromagnetic field, which gives rise to a finite dimensional unconstrained minimization problem, is given and analyzed. In our method, the Maxwell's equation defined on the whole space is solved by a finite element method using artificial boundary, and the highly oscillatory magnetization structure is approximated by an element-wise constant Young measure supported on a finite number of unknown points on the unit sphere. Numerical experiments on some uniaxial and cubic anisotropic energy densities show that the method is efficient.