Numerical Solution of the Kohn-Sham Equation by Finite Element Methods with an Adaptive Mesh Redistribution Technique

被引：25

作者：

Bao, Gang ^{[1
,2
]}

Hu, Guanghui ^{[2
]}

Liu, Di ^{[2
]}

机构：

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China

[2] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2013年 / 55卷 / 02期

基金：

美国国家科学基金会;

关键词：

Adaptive mesh redistribution; Harmonic map; Finite element method; Kohn-Sham equation; Density functional theory; DENSITY-FUNCTIONAL THEORY; HARMONIC MAPS; ENERGY; FRAMEWORK;

D O I：

10.1007/s10915-012-9636-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A mesh redistribution method is introduced to solve the Kohn-Sham equation. The standard linear finite element space is employed for the spatial discretization, and the self-consistent field iteration scheme is adopted for the derived nonlinear generalized eigenvalue problem. A mesh redistribution technique is used to optimize the distribution of the mesh grids according to wavefunctions obtained from the self-consistent iterations. After the mesh redistribution, important regions in the domain such as the vicinity of the nucleus, as well as the bonding between the atoms, may be resolved more effectively. Consequently, more accurate numerical results are obtained without increasing the number of mesh grids. Numerical experiments confirm the effectiveness and reliability of our method for a wide range of problems. The accuracy and efficiency of the method are also illustrated through examples.

引用

页码：372 / 391

页数：20

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