Scholarlink

<p>This paper discusses the theory and numerical methods 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, a 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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10915_2025_3026_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(H^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation> norm between the classical solution and the two-scale approximation are obtained. Secondly, we propose a robust numerical framework, 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 relax the constraints on the time step size, which can significantly improve computational efficiency. Specifically, the projection and expansion methods are given to overcome the inherent non-consistency in the initial data between the multiscale problem and homogenized problem.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

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

  • 期刊论文

  • 发表日期：

    2025年8月19日

查看全文
  • Xiaofei Guan,
  • Hang Qi,
  • Zhiwei Sun

摘要

This paper discusses the theory and numerical methods 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, a 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 \(H^1\) H 1 norm between the classical solution and the two-scale approximation are obtained. Secondly, we propose a robust numerical framework, 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 relax the constraints on the time step size, which can significantly improve computational efficiency. Specifically, the projection and expansion methods are given to overcome the inherent non-consistency in the initial data between the multiscale problem and homogenized problem.