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GRADIENT FLOW BASED KOHN-SHAM DENSITY FUNCTIONAL THEORY MODEL

文献类型：期刊论文

作者Dai, Xiaoying1,2; Wang, Qiao3; Zhou, Aihui1,2
刊名MULTISCALE MODELING & SIMULATION
出版日期2020
卷号18期号:4页码:1621-1663
关键词density functional theory dynamical system gradient flow orthogonality preserving eigenvalue problem energy minimization
ISSN号1540-3459
DOI10.1137/19M1276170
英文摘要In this paper, we propose and analyze a gradient flow based model for electronic structure calculations. First, based on an extended gradient flow proposed in this paper, we propose a Kohn-Sham gradient flow based model. We prove that our gradient flow based model is orthogonality preserving, the extended gradient has an exponential decay over time t, and the equilibrium point is a local minimizer of the Kohn-Sham energy functional. Then we propose a midpoint scheme to carry out the temporal discretization, which is proven to be orthogonality preserving, too. Based on the midpoint scheme, we design a practical orthogonality preserving iteration scheme which can deal with the propagation of the gradient flow based model and prove that the scheme produces approximations that converge to a local minimizer with some convergence rate under some reasonable assumptions. Finally, we report a number of numerical experiments that validate our theoretical results.
资助项目National Key Research and Development Program of China[2019YFA0709601] ; National Natural Science Foundation of China[91730302] ; National Natural Science Foundation of China[11671389] ; Key Research Program of Frontier Sciences of the Chinese Academy of Sciences[QYZDJ-SSW-SYS010]
WOS研究方向Mathematics ; Physics
语种英语
WOS记录号WOS:000600667900009
出版者SIAM PUBLICATIONS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/57907]  
专题中国科学院数学与系统科学研究院
通讯作者Dai, Xiaoying
作者单位1.Chinese Acad Sci, LSEC, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.Beijing Univ Civil Engn & Architecture, Sch Sci, Beijing 102616, Peoples R China
推荐引用方式
GB/T 7714		 Dai, Xiaoying,Wang, Qiao,Zhou, Aihui. GRADIENT FLOW BASED KOHN-SHAM DENSITY FUNCTIONAL THEORY MODEL[J]. MULTISCALE MODELING & SIMULATION,2020,18(4):1621-1663.
APA Dai, Xiaoying,Wang, Qiao,&Zhou, Aihui.(2020).GRADIENT FLOW BASED KOHN-SHAM DENSITY FUNCTIONAL THEORY MODEL.MULTISCALE MODELING & SIMULATION,18(4),1621-1663.
MLA Dai, Xiaoying,et al."GRADIENT FLOW BASED KOHN-SHAM DENSITY FUNCTIONAL THEORY MODEL".MULTISCALE MODELING & SIMULATION 18.4(2020):1621-1663.

入库方式： OAI收割

来源：数学与系统科学研究院

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