论文标题
计算微磁学的质量中点方案：牛顿线性化和应用于磁性的Skyrmion动力学
The mass-lumped midpoint scheme for computational micromagnetics: Newton linearization and application to magnetic skyrmion dynamics
论文作者
论文摘要
我们讨论了质量集中的中点方案，用于Landau-Lifshitz-Gilbert方程的数值近似，该方程模拟了铁磁材料中磁化的动力学。除了经典的微磁场贡献外，我们的设置还涵盖了非标准的dzyaloshinskii-moriya相互作用，这是磁性天空敏化和稳定化的必不可少的成分。我们的分析还包括出现的非线性系统的不精确解决方案，为此，我们讨论了从文献中保留固定点求解器的约束和基于牛顿方法的新方法。我们从数值上比较了两种线性化技术，并表明牛顿求解器导致非线性迭代次数较低。此外，在一项关于磁性天际的数值研究中，我们证明，对于对能量扰动非常敏感的磁化动力学，由于其保护特性，中点方案优于文献中的耗散性切线平面方案。
We discuss a mass-lumped midpoint scheme for the numerical approximation of the Landau-Lifshitz-Gilbert equation, which models the dynamics of the magnetization in ferromagnetic materials. In addition to the classical micromagnetic field contributions, our setting covers the non-standard Dzyaloshinskii-Moriya interaction, which is the essential ingredient for the enucleation and stabilization of magnetic skyrmions. Our analysis also includes the inexact solution of the arising nonlinear systems, for which we discuss both a constraint preserving fixed-point solver from the literature and a novel approach based on the Newton method. We numerically compare the two linearization techniques and show that the Newton solver leads to a considerably lower number of nonlinear iterations. Moreover, in a numerical study on magnetic skyrmions, we demonstrate that, for magnetization dynamics that are very sensitive to energy perturbations, the midpoint scheme, due to its conservation properties, is superior to the dissipative tangent plane schemes from the literature.
