密度泛函微扰理论中响应密度矩阵的迭代求解算法研究  

Study of Iterative Solution Algorithm of Response Density Matrix in Density Functional Perturbation Theory

作　　者：刘人僪 徐直前 商红慧 张云泉[2] LIU Renyu;XU Zhiqian;SHANG Honghui;ZHANG Yunquan(College of Information Engineering,Dalian Ocean University,Dalian,Liaoning 116023,China;State Key Laboratory of Computer Archintecture,Institute of Computing Technology,Chinese Academy of Sciences,Beijing 100190,China;School of Computer and Control Engineering,University of Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]大连海洋大学信息工程学院,辽宁大连116023 [2]中国科学院计算技术研究所计算机体系结构国家重点实验室,北京100190 [3]中国科学院大学计算机与控制学院,北京100190

出　　处：《计算机科学》2023年第6期81-85,共5页Computer Science

基　　金：国家重点研发计划资助:“面向复杂装备的CAE云服务平台研发”项目(2020YFB1709500)。

摘　　要：针对密度泛函微扰理论中响应密度矩阵的计算问题,提出了一种全新的Sternheimer方程的并行求解方法,即通过共轭梯度算法和矩阵直接分解算法对Sternheimer方程进行求解,并且在第一性原理的分子模拟软件FHI-aims中实现了这两种算法。实验结果表明采用共轭梯度算法和矩阵直接分解算法的计算结果精度较高,相比传统方法的计算结果误差较小,且具有可扩展性,验证了新的Sternheimer方程中线性方程求解的正确性和有效性。For the problem of calculating the response density matrix in density-functional perturbation theory(DFPT),a new parallel solution method for the Sternheimer equation is proposed,i.e.,the Sternheimer equation is solved by the conjugate gra-dient algorithm and the matrix direct decomposition algorithm,and the two algorithms are implemented in the first-principles molecular simulation software FHI-aims.Experimental results show that the computational results using conjugate gradient algorithm and matrix direct decomposition algorithm are more accurate,with less error than those of traditional methods,and scalable,which verifies the correctness and validity of the solution of linear equations in the new Sternheimer equation.

关 键 词：密度泛函 线性方程 迭代算法 

分 类 号：TP311.5[自动化与计算机技术—计算机软件与理论]