Application of the stereographic projection to studies of magnetization dynamics described by the Landau–Lifshitz–Gilbert equation

We present a comparative analysis of the calculation performance for several representations of the Landau–Lifshitz–Gilbert equation (spherical, Cartesian and stereographic), underlining good perspectives to use the stereographic projection for numerical simulations of magnetization dynamics. The advantages of this approach include a five-time calculation speed-up compared to the spherical coordinate representation together with unconditional preservation of the magnetization vector length. Slightly faster calculations are achievable with the Cartesian coordinate representation, which, however, require renormalization of the magnetization vector at each integration step.