论文标题
部分可观测时空混沌系统的无模型预测
Length preserving numerical schemes for Landau-Lifshitz equation based on Lagrange multiplier approaches
论文作者
论文摘要
我们在本文中开发了基于两种不同的拉格朗日乘数方法的Landau-Lifshitz方程的两类长度保留方案。在第一种方法中，Lagrange乘数$λ（\ bx，t）$等于$ | \ nabla m（\ bx，t）|^2 $在连续水平上，而在第二种方法中，Lagrange乘数$λ（\ bx，t）$被引入以识别级别的层次级别的级别，并在IS ISCERATIATS IS齐平级别上进行了限制。通过使用预测器 - 矫正器方法，我们构建了为Landau-Lifshitz方程保留高阶方案的有效且稳健的长度，其计算成本以预测变量步骤为主，这只是一个半图像方案。此外，通过引入另一个独立于空间的拉格朗日乘数，我们构建了能量耗散，除了保留长度，landau-lifshitz方程的方案，以求解一个非线性代数方程。我们提供了足够的数值实验，以验证所提出的方案的稳定性和准确性，并提供与某些现有方案的性能比较。
We develop in this paper two classes of length preserving schemes for the Landau-Lifshitz equation based on two different Lagrange multiplier approaches. In the first approach, the Lagrange multiplier $λ(\bx,t)$ equals to $|\nabla m(\bx,t)|^2$ at the continuous level, while in the second approach, the Lagrange multiplier $λ(\bx,t)$ is introduced to enforce the length constraint at the discrete level and is identically zero at the continuous level. By using a predictor-corrector approach, we construct efficient and robust length preserving higher-order schemes for the Landau-Lifshitz equation, with the computational cost dominated by the predictor step which is simply a semi-implicit scheme. Furthermore, by introducing another space-independent Lagrange multiplier, we construct energy dissipative, in addition to length preserving, schemes for the Landau-Lifshitz equation, at the expense of solving one nonlinear algebraic equation. We present ample numerical experiments to validate the stability and accuracy for the proposed schemes, and also provide a performance comparison with some existing schemes.
