On the Landau-Lifshitz-Gilbert equation with magnetostriction
On the Landau-Lifshitz-Gilbert equation with magnetostriction
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关于具有磁致伸缩的 Landau-Lifshitz-Gilbert 方程
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
J. Rochat
中科院分区：
文献类型：
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作者：
L. Baňas;M. Page;D. Praetorius;J. Rochat
为了描述和模拟动态微磁现象，我们考虑非线性 Landau-Lifshitz-Gilbert 方程和动量守恒方程的耦合系统。这种耦合允许将磁致伸缩效应纳入模拟中。最近在[12]中证明了弱解的存在。在我们的贡献中，我们给出了另一种证明，它还提供了一个有效的数值积分器。后者基于空间中的最低阶有限元和线性隐式欧拉时间步长。尽管存在非线性，但每个时间步只需求解两个线性系统，并且积分器完全解耦两个方程。最后，我们证明了耦合系统弱解的无条件收敛（至少是子序列），因此存在，因为时间步长大小和空间网格大小趋于零。数值实验总结了这项工作，并为微磁模拟中爆炸的存在提供了新的线索。
To describe and simulate dynamic micromagnetic phenomena, we consider a coupled system of the nonlinear Landau-Lifshitz-Gilbert equation and the conservation of momentum equation. This coupling allows to include magnetostrictive effects into the simulations. Existence of weak solutions has recently been shown in [12]. In our contribution, we give an alternate proof which additionally provides an effective numerical integrator. The latter is based on lowest-order finite elements in space and a linear-implicit Euler time-stepping. Despite the nonlinearity, only two linear systems have to be solved per timestep, and the integrator fully decouples both equations. Finally, we prove unconditional convergence—at least of a subsequence—towards, and hence existence of, a weak solution of the coupled system, as timestep size and spatial mesh-size tend to zero. Numerical experiments conclude the work and shed new light on the existence of blow-up in micromagnetic simulations.