A multilevel correction adaptive finite element method for Kohn–Sham equation
A multilevel correction adaptive finite element method for Kohn–Sham equation
复制标题
Kohn-Sham方程的多级修正自适应有限元方法
DOI：
10.1016/j.jcp.2017.11.024
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发表时间：
2017
影响因子：
4.1
通讯作者：
Fei Xu
中科院分区：
文献类型：
--
作者：
Guanghui Hu;Hehu Xie;Fei Xu
本文提出了一种求解Kohn-Sham方程的自适应有限元方法，该方法采用多层修正技术。在该方法中，Kohn-Sham方程在一个固定的适当粗网格上用有限元法求解，其中有限元空间通过在一系列自适应和逐次加密的网格上求解导出的边值问题而不断改进。该方法的一个主要特点是有效地避免了求解大规模Kohn-Sham方程组，并且可以用多重网格法等经典方法有效地求解导出的边值问题。因此，所提出的多层校正技术可以显著地加快求解Kohn-Sham方程的速度。各种数值实验的方法的性能进行检查。
In this paper, an adaptive finite element method is proposed for solving Kohn–Sham equation with the multilevel correction technique. In the method, the Kohn–Sham equation is solved on a fixed and appropriately coarse mesh with the finite element method in which the finite element space is kept improving by solving the derived boundary value problems on a series of adaptively and successively refined meshes. A main feature of the method is that solving large scale Kohn–Sham system is avoided effectively, and solving the derived boundary value problems can be handled efficiently by classical methods such as the multigrid method. Hence, the significant acceleration can be obtained on solving Kohn–Sham equation with the proposed multilevel correction technique. The performance of the method is examined by a variety of numerical experiments.