A framework for the numerical solution of the Landau-Lifshitz-Gilbert equation is developed in this paper. The numerical framework is based on the finite element method on tetrahedral meshes for the spatial discretization and the implicit midpoint scheme for the temporal discretization. The computational complexity for calculating the demagnetization field is effectively reduced by using a PDE approach, in which a gradient recovery technique is used for preserving the numerical accuracy. The numerical convergence of the proposed method is studied in detail for the μMAG standard problem #3, from which a limit is predicted for the desired side length. The capability of the proposed method on handling problems defined on complex domains is successfully demonstrated by several examples, in which the computational domains are thin films with irregular defects.

本文为Landau-Lifshitz-Gilbert方程的数值解建立了框架。数值框架基于四面体网格上的有限元方法进行空间离散化，隐式中点方案基于时间离散化。通过使用PDE方法有效地减少了计算退磁场的计算复杂性，在该方法中，使用了梯度恢复技术来保持数值精度。对于μ，详细研究了所提出方法的数值收敛性。MAG标准问题3，由此可以预测所需边长的极限。通过计算实例成功地证明了所提方法处理复杂域问题的能力，其中计算域是具有不规则缺陷的薄膜。