2024/12/13 by Panchi Li, Xiaoping Wang, Li, Panchi +1
Computer Science · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2412.10025
openalex publication_date 2024/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The dynamics of magnetization in ferromagnetic materials are modeled by the\nLandau-Lifshitz equation, which presents significant challenges due to its\ninherent nonlinearity and non-convex constraint. These complexities necessitate\nefficient numerical methods for micromagnetics simulations. The Gauss-Seidel\nProjection Method (GSPM), first introduced in 2001, is among the most efficient\ntechniques currently available. However, existing GSPMs are limited to\nfirst-order accuracy. This paper introduces two novel second-order accurate\nGSPMs based on a combination of the biharmonic equation and the second-order\nbackward differentiation formula, achieving computational complexity comparable\nto that of solving the scalar biharmonic equation implicitly. The first\nproposed method achieves unconditional stability through Gauss-Seidel updates,\nwhile the second method exhibits conditional stability with a\nCourant-Friedrichs-Lewy constant of 0.25. Through consistency analysis and\nnumerical experiments, we demonstrate the efficacy and reliability of these\nmethods. Notably, the first method displays unconditional stability in\nmicromagnetics simulations, even when the stray field is updated only once per\ntime step.\n