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Numerical integration of Landau-Lifshitz-Gilbert equation based on the midpoint rule

机译：基于中点规则的Landau-Lifshitz-Gilbert方程的数值积分

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摘要

The midpoint rule time discretization technique is applied to Landau-Lifshitz-Gilbert (LLG) equation. The technique is unconditionally stable and second-order accurate. It has the important property of preserving the conservation of magnetization amplitude of LLG dynamics. In addition, for typical forms of the micromagnetic free energy, the midpoint rule preserves the main energy balance properties of LLG dynamics. In fact, it preserves LLG Lyapunov structure and, in the case of zero damping, the system free energy. All the above preservation properties are fulfilled unconditionally, namely, regardless of the choice of the time step. The proposed technique is then tested on the standard micromagnetic problem No. 4. In the numerical computations, the magnetostatic field is computed by the fast Fourier transform method, and the nonlinear system of equations connected to the implicit time-stepping algorithm is solved by special and reasonably fast quasi-Newton technique.
机译：中点规则时间离散化技术应用于Landau-Lifshitz-Gilbert（LLG）方程。该技术是无条件稳定且二阶准确的。它具有保持LLG动力学磁化幅度守恒的重要特性。另外，对于典型形式的微磁自由能，中点法则保留了LLG动力学的主要能量平衡特性。实际上，它保留了LLG Lyapunov的结构，并且在零阻尼的情况下保留了系统的自由能。上述所有保存特性都是无条件满足的，即与时间步长的选择无关。然后在标准的微磁问题4上测试所提出的技术。在数值计算中，静磁场是通过快速傅立叶变换法计算的，而与隐式时间步长算法相连的方程组的非线性系统则是通过特殊方法求解的。和相当快的准牛顿技术。

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