计算机科学 ›› 2023, Vol. 50 ›› Issue (6): 81-85.doi: 10.11896/jsjkx.220500252

• 高性能计算 • 上一篇    下一篇

密度泛函微扰理论中响应密度矩阵的迭代求解算法研究

刘人僪1,2, 徐直前2,3, 商红慧2, 张云泉2   

  1. 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
  • 收稿日期:2022-05-27 修回日期:2022-09-22 出版日期:2023-06-15 发布日期:2023-06-06
  • 通讯作者: 商红慧(shanghonghui@ict.ac.cn)
  • 作者简介:(liurenyudlou@163.com)
  • 基金资助:
    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)

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

LIU Renyu1,2, XU Zhiqian2,3, SHANG Honghui2, ZHANG Yunquan2   

  1. 1 College of Information Engineering,Dalian Ocean University,Dalian,Liaoning 116023,China
    2 State Key Laboratory of Computer Archintecture,Institute of Computing Technology,Chinese Academy of Sciences,Beijing 100190,China
    3 School of Computer and Control Engineering,University of Chinese Academy of Sciences,Beijing 100190,China
  • Received:2022-05-27 Revised:2022-09-22 Online:2023-06-15 Published:2023-06-06
  • About author:LIU Renyu,born in 1997,postgraduate.His main research interests include computer application technology and so on.SHANG Honghui,born in 1984,Ph.D,associate professor.Her main research interests include the development of the first-principles methods and their applications on the high-performance computer systems.
  • Supported by:
    Research and Development of CAE Cloud Service Platform for Complex Equipment funded by National Key Research and Development Program of China(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。

关键词: 密度泛函, 线性方程, 迭代算法

Abstract: 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.

Key words: Density-functional theory, Linear equations, Iterative algorithm

中图分类号: 

  • TP311.5
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