An Adaptive Moving Mesh Method for Simulating Finite-time Blowup Solutions of the Landau-Lifshitz-Gilbert Equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-01 DOI:10.4208/eajam.2023-322.250224

Zheyue Fang, Xiaoping Wang

引用次数: 0

Abstract

We present a moving mesh finite element method to study the finite-time blowup solution of the Landau-Lifshitz-Gilbert (LLG) equation, considering both the heat flow of harmonic map and the full LLG equation. Our approach combines projection methods for solving the LLG equation with an iterative grid redistribution method to generate adaptive meshes. Through iterative remeshing, we successfully simulate blowup solutions with maximum gradient magnitudes up to $10^4$ and minimum mesh sizes of $10^{−5}.$ We investigate the self-similar patterns and blowup rates of these solutions, and validate our numerical findings by comparing them to established analytical results from a recent study

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模拟兰道-利夫希茨-吉尔伯特方程有限时间炸毁解的自适应移动网格法

我们提出了一种移动网格有限元方法，用于研究 Landau-Lifshitz-Gilbert (LLG) 方程的有限时间放大解，同时考虑谐波图的热流和完整的 LLG 方程。我们的方法结合了求解 LLG 方程的投影方法和迭代网格重分布方法，以生成自适应网格。通过迭代重网格化，我们成功地模拟出了最大梯度幅值高达 10^4 美元、最小网格尺寸为 10^{-5} 美元的炸裂解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.