2025/02/07 by Yunjie Gong, Chen, Jingrun, Gong, Yunjie +4
Engineering · Mathematics · #35K51 #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #G.1.8 #Numerical Analysis (math.NA) #Numerical methods for differential equations #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2502.04871
openalex publication_date 2025/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 provide the approximation error in space and depict the energy law when the FVEM is adopted. Owing to the GSPM for time-marching, the discrete system is decoupled component by component, making the computational complexity comparable to that of solving the scalar heat equation implicitly. This significantly accelerates real simulations. We present several numerical experiments to validate the theoretical analysis and the efficiency gain. Additionally, we study the blow-up solution and efficiently simulate the 2D magnetic textures using the proposed method.