Finite volume element method for Landau-Lifshitz equation

Abstract: The Landau-Lifshitz equation describes the dynamics of magnetization in ferromagnetic materials. Due to the essential nonlinearity and nonconvex constraint, it is typically solved numerically. In this paper, we developed a finite volume element method (FVEM) with the Gauss-Seidel projection method (GSPM) for the micromagnetics simulations. We give the error estimate for FVEM in space and depict the discretized energy dissipation. Owing to the application of the GSPM, the nonlinear vector system is decoupled and the computational complexity is comparable to that of implicitly solving the scalar heat equation, which accelerates the real simulations significantly. We present several numerical experiments to verify the theoretical analysis. Furthermore, we study the blow-up solution and efficiently simulate the 2D magnetic textures using the proposed method.