An SAV Method for Imaginary Time Gradient Flow Model in Density Functional Theory

作     者：Ting Wang Jie Zhou Guanghui Hu 

作者机构：Department of MathematicsFaculty of Science and TechnologyUniversity of MacaoMacao SARChina School of Mathematics and Computational ScienceXiangtan UniversityXiangtanHunan 411105China Zhuhai UM Science&Technology Research InstituteZhuhaiGuangdong 519030China Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering ApplicationsUniversity of MacaoMacao SARChina 

出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)

年 卷 期：2023年第15卷第3期

页      面：719-736页

核心收录：

学科分类：083002[工学-环境工程] 0830[工学-环境科学与工程（可授工学、理学、农学学位）] 08[工学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：The first author would like to thank the support from the UM-Funded PhD Assistantship from University of Macao The second author was partially supported by Macao Young Scholar Program(AM201919) excellent youth project of Hunan Education Department(19B543) Hunan National Applied Mathematics Center of Hunan Provincial Science and Technology Department(2020ZYT003) The third author would like to thank financial support from National Natural Science Foundation of China(Grant Nos.11922120,11871489) FDCT of Macao SAR(Grant No.0082/2020/A2) University of Macao(Grant No.MYRG2020-00265-FST) Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications(Grant No.2020B1212030001). 

主　　题：Density functional theory gradient flow scalar auxiliary variable unconditional energy stability orthonormalization free 

摘      要：In this paper,based on the imaginary time gradient flow model in the density functional theory,a scalar auxiliary variable(SAV)method is developed for the ground state calculation of a given electronic structure system.To handle the orthonormality constraint on those wave functions,two kinds of penalty terms are introduced in designing the modified energy functional in SAV,i.e.,one for the norm preserving of each wave function,another for the orthogonality between each pair of different wave functions.A numerical method consisting of a designed scheme and a linear finite element method is used for the discretization.Theoretically,the desired unconditional decay of modified energy can be obtained from our method,while computationally,both the original energy and modified energy decay behaviors can be observed successfully from a number of numerical experiments.More importantly,numerical results show that the orthonormality among those wave functions can be automatically preserved,without explicitly preserving orthogonalization operations.This implies the potential of our method in large-scale simulations in density functional theory.