A radial basis function-finite difference method for solving Landau–Lifshitz–Gilbert equation including Dzyaloshinskii-Moriya interaction

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements Pub Date : 2024-09-20 DOI:10.1016/j.enganabound.2024.105966

Zhoushun Zheng, Sai Qi, Xinye Li

引用次数: 0

Abstract

This paper investigates a numerical method for solving the two-dimensional Landau–Lifshitz–Gilbert (LLG) equation, governing the dynamics of the magnetization in ferromagnetic materials. Specifically, we incorporate the Dzyaloshinskii–Moriya interaction into the LLG equation—a crucial factor for the creation and stabilization of magnetic skyrmions. We propose a local meshless method that utilizes radial basis function-finite difference (RBF-FD) for spatial discretization and the Crank–Nicolson scheme for temporal discretization, along with an extrapolation technique to handle the nonlinear terms. We demonstrate the method’s accuracy, efficiency, and adaptability through numerical tests on domains of various shapes, showcasing its practical utility in simulating real-world magnetic phenomena and advanced materials.

查看原文本刊更多论文

用于求解包含 Dzyaloshinskii-Moriya 相互作用的 Landau-Lifshitz-Gilbert 方程的径向基函数-有限差分法

本文研究了一种求解二维 Landau-Lifshitz-Gilbert (LLG) 方程的数值方法，该方程控制着铁磁材料中的磁化动力学。具体来说，我们将 Dzyaloshinskii-Moriya 相互作用纳入 LLG 方程--这是磁性天幕产生和稳定的关键因素。我们提出了一种局部无网格方法，利用径向基函数-有限差分（RBF-FD）进行空间离散化，利用 Crank-Nicolson 方案进行时间离散化，并采用外推法处理非线性项。我们通过对各种形状的域进行数值测试，证明了该方法的准确性、效率和适应性，展示了它在模拟现实世界的磁现象和先进材料方面的实用性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Engineering Analysis with Boundary Elements 工程技术-工程：综合

CiteScore

5.50

自引率

18.20%

发文量

368

审稿时长

56 days

期刊介绍： This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods. Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness. The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields. In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research. The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods Fields Covered: • Boundary Element Methods (BEM) • Mesh Reduction Methods (MRM) • Meshless Methods • Integral Equations • Applications of BEM/MRM in Engineering • Numerical Methods related to BEM/MRM • Computational Techniques • Combination of Different Methods • Advanced Formulations.