标题： 多尺度分析用于多尺度朗道-利夫希茨-吉尔伯特方程：理论与数值方法 显示英文标题

标题： Two-scale Analysis for Multiscale Landau-Lifshitz-Gilbert Equation: Theory and Numerical Methods

摘要： 本文讨论了复合铁磁材料中多尺度Landau-Lifshitz-Gilbert方程的两尺度分析的理论和数值方法。 这项工作的创新性可以总结为三个方面： 首先，考虑了更现实和复杂的模型，包括交换场、各向异性场、杂散场和外加磁场的影响。 得到了经典解与两尺度解在$H^1$范数下的显式收敛阶。 其次，我们提出了一种稳健的数值框架，并在多个综合实验中使用该框架来验证周期性和Neumann问题的收敛结果。 第三，我们设计了一种改进的隐式数值格式，以减少所需的迭代次数并放松对时间步长的限制，这可以显著提高计算效率。 具体来说，给出了投影和展开方法，以克服多尺度问题与均质化问题之间初始数据固有的不一致性。 显示英文摘要

摘要： This paper discusses the theory and numerical method of two-scale analysis for the multiscale Landau-Lifshitz-Gilbert equation in composite ferromagnetic materials. The novelty of this work can be summarized in three aspects: Firstly, the more realistic and complex model is considered, including the effects of the exchange field, anisotropy field, stray field, and external magnetic field. The explicit convergence orders in the $H^1$ norm between the classical solution and the two-scale solution are obtained. Secondly, we propose a robust numerical framework, which is employed in several comprehensive experiments to validate the convergence results for the Periodic and Neumann problems. Thirdly, we design an improved implicit numerical scheme to reduce the required number of iterations and relaxes the constraints on the time step size, which can significantly improve computational efficiency. Specifically, the projection and the expansion methods are given to overcome the inherent non-consistency in the initial data between the multiscale problem and homogenized problem.