A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model  

作　　者：Yedan Shen Ting Wang Jie Zhou Guanghui Hu 

机构地区：[1]School of Mathematics and Information Science,Guangzhou University,Guangzhou,China [2]Faculty of Science and Technology,University of Macao,Macao SAR,China [3]Hunan Key Laboratory for Computation and Simulation in Science and Engineering,Xiangtan University,Xiangtan,China [4]School of Mathematical Computational Sciences,Xiangtan University,Xiangtan,China [5]Zhuhai UM Science&Technology Research Institute,Zhuhai,China [6]Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications,University of Macao,Macao SAR,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2023年第3期597-621,共25页高等学校计算数学学报（英文版）

基　　金：partially funded by the Hunan National Applied Mathematics Center of Hunan Provincial Science and Technology Department(Grant No.2020ZYT003);by the RSF-NSFC Cooperation project(Grant No.12261131501);by the Excellent youth project of the Hunan Education Department(Grant No.19B543);partially supported by the National Natural Science Foundation of China(Grant Nos.11922120 and 11871489);by the FDCT of Macao SAR(Grant No.0082/2020/A2);by the MYRG of the University of Macao(Grant No.MYRG2020-00265-FST);by the Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications(Grant No.2020B1212030001).

摘　　要：In[Dai et al.,Multi.Model.Simul.18(4)(2020)],a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn-Sham density functional theory,based on which a linearized method was developed in[Hu et al.,EAJAM.13(2)(2023)]for further improving the numerical efficiency.In this paper,a complete convergence analysis is delivered for such a linearized method for the all-electron Kohn-Sham model.Temporally,the convergence,the asymptotic stability,as well as the structure-preserving property of the linearized numerical scheme in the method is discussed following previous works,while spatially,the convergence of the h-adaptive mesh method is demonstrated following[Chen et al.,Multi.Model.Simul.12(2014)],with a key study on the boundedness of the Kohn-Sham potential for the all-electron Kohn-Sham model.Numerical examples confirm the theoretical results very well.

关 键 词：Kohn-Sham density functional theory gradient flow model structure-preserving linear scheme convergence analysis 

分 类 号：O17[理学—数学]