报告题目 (Title)：Second-order Semi-implicit Projection Methods and Analysis for Micromagnetics Simulations（微磁模拟中的二阶半隐式投影方法与理论分析）
报告人 (Speaker)： 谢长健 (西交利物浦大学)
报告时间 (Time)：2025年4月19日（周六）15:00
报告地点 (Place)： 校本部Gj303
邀请人(Inviter)：秦晓雪
主办部门：8455新葡萄场网站数学系
报告摘要：The numerical approximation of the Landau-Lifshitz equation for ferromagnetic magnetization dynamics is considered. This highly nonlinear, non-convex constrained equation, with multiple equivalent forms and an infinite - domain auxiliary problem, poses challenges for numerical methods.
A fully discrete semi-implicit method based on second-order backward differentiation and one-sided extrapolation is introduced. A projection step preserves magnetization length. Rigorous convergence analysis shows unconditional stability and second-order accuracy in time and space when spatial and temporal step-sizes are of the same order, relaxing temporal step-size restrictions compared to implicit schemes. The unique solvability of the numerical solution, without step-size assumptions, is proven for the micromagnetics model. Numerical examples in 1D and 3D verify these theoretical properties.
