In this paper, we present a finite difference heterogeneous multiscale method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient. The approach combines a higher order discretization and artificial damping in the so-called micro problem to obtain an efficient implementation. The influence of different parameters on the resulting approximation error is discussed. Numerical examples for both periodic as well as more general coefficients are given to demonstrate the functionality of the approach.

翻译：在本文中,我们为Landau-Lifshitz等式提出了一个有高度随机扩散系数的有限差异的多尺度多尺度方法,该方法结合了在所谓的微观问题中更高层次的分解和人为阻塞,以获得有效的执行。讨论了不同参数对由此产生的近似误差的影响。给出了定期和更一般性系数的数值示例,以证明该方法的功能。