A Linearized Structure-Preserving Numerical Scheme for a Gradient Flow Model of the Kohn-Sham Density Functional Theory

被引：5

作者：

Hu, Guanghui ^{[1
,2
,3
]}

Wang, Ting ^{[1
]}

Zhou, Jie ^{[4
]}

机构：

[1] Univ Macau, Fac Sci & Technol, Dept Math, Taipa, Macao Sar, Peoples R China

[2] Zhuhai UM Sci & Technol Res Inst, Zhuhai, Guangdong, Peoples R China

[3] Univ Macau, Guangdong Hong Kong Macao Joint Lab Data Driven Fl, Taipa, Macao Sar, Peoples R China

[4] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan, Hunan, Peoples R China

来源：

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2023年 / 13卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Kohn-Sham density functional theory; gradient flow model; structure-preserving; linear scheme; adaptive strategy;

D O I：

10.4208/eajam.2022-134.081022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Dai et al. [Multiscale Model. Simul. 18 (2020)] proposed a gradient flow model and a numerical scheme for ground state calculations in Kohn-Sham density functional theory. It is a feature that orthonormality of all wave functions can be preserved automatically during the simulation which makes such a method attractive towards simulations for large scale systems. In this paper, two extensions are proposed for further improving the efficiency of the method. The first one is a linearization of the original nonlinear scheme. It is shown analytically that both the orthonormality of wave functions and the decay of the total energy can be preserved well by this linear scheme, while a significant acceleration can be observed from the numerical experiments due to the removal of an iteration process in the nonlinear scheme. The second one is the introduction of the adaptivity in the algorithm both temporally and spatially - i.e. an h-adaptive mesh method is employed to control the total amount of mesh grids, and an adaptive stop criterion in time propagation process is designed based on an observation that total energy always decays much faster at the beginning. Plenty of numerical experiments successfully demonstrate effectiveness of our method.

引用

页码：299 / 319

页数：21

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