一种基于迭代子空间直接求逆算法的高效子空间混合算法

doi:10.19596/j.cnki.1001-246x.8301

计算物理 ›› 2021, Vol. 38 ›› Issue (4): 418-422.DOI: 10.19596/j.cnki.1001-246x.8301

一种基于迭代子空间直接求逆算法的高效子空间混合算法

丁永龙¹(), 胡琳萍², 张瑞勤¹^,²^,³^,*()

1. 北京计算科学研究中心, 北京 100193
2. 深圳京鲁计算科学应用研究院, 广东深圳 518110
3. 香港城市大学物理学系, 香港

收稿日期:2020-11-10 出版日期:2021-07-25 发布日期:2021-12-21
通讯作者: 张瑞勤
作者简介:丁永龙(1993-), 男, 安徽, 硕士研究生, 研究方向为凝聚态物理, E-mail: ylding@csrc.ac.cn
基金资助:
国家自然科学基金(11874081);国家自然科学基金委员会—中国工程物理研究院（NSAF）联合基金(U1930402)

An Efficient Subspace Hybrid Algorithm Based on Direct Inversion in Iterative Subspace Algorithm

Yonglong DING¹(), Linping HU², Ruiqin ZHANG¹^,²^,³^,*()

1. Beijing Computational Science Research Center, Beijing 100193, China
2. Shenzhen JL Computational Science and Applied Research Institute, Shenzhen, Guangdong 518110, China
3. Department of Physics, City University of Hong Kong, Hong Kong, China

Received:2020-11-10 Online:2021-07-25 Published:2021-12-21
Contact: Ruiqin ZHANG

摘要/Abstract

摘要：

发展一种基于迭代子空间直接求逆（DIIS）算法的可用于快速求解原子和分子Hartree-Fock方程的子空间混合算法。该算法利用不同大小的子空间的混合将更接近收敛的Fock矩阵的权重增大，混合后的Fock矩阵作为新的迭代起点能有效减少自洽场迭代（SCF）过程中的迭代次数。与DIIS算法进行对比，发现该算法优于两种不同子空间的DIIS算法，并有效减少了计算量。

关键词: 迭代子空间, 自洽场迭代, 混合算法, 加速收敛

Abstract:

A hybrid algorithm based on Direct Inversion in Iterative Subspace (DIIS) algorithm is developed for rapid solution of atomic and molecular Hartree-Fock equations. The improved algorithm uses mixing of subspaces with different sizes to increase the weight of Fock matrix closer to convergence, and the mixed Fock matrix is used as a starting point of new iteration. This algorithm reduces effectively the number of iterations in SCF process. Compared with DIIS algorithm before mixing, it is found that this algorithm is superior to the DIIS algorithm with two different subspaces, and the computational cost is effectively reduced.

Key words: DIIS, SCF, hybrid algorithm, accelerated convergence

中图分类号:

O561

丁永龙, 胡琳萍, 张瑞勤. 一种基于迭代子空间直接求逆算法的高效子空间混合算法[J]. 计算物理, 2021, 38(4): 418-422.

Yonglong DING, Linping HU, Ruiqin ZHANG. An Efficient Subspace Hybrid Algorithm Based on Direct Inversion in Iterative Subspace Algorithm[J]. Chinese Journal of Computational Physics, 2021, 38(4): 418-422.

图/表 2

参考文献 16

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分子	E/Hartree
分子	Gaussian程序结果	自编程结果
H₂	-1.120 018 013 45	-1.120 018 013 71
H₂O	-75.161 772 436 6	-75.161 772 323 7
NH₃	-55.567 472 491 8	-55.567 472 473 6
CH₄	-39.764 712 736 1	-39.764 712 727 0

分子	E/Hartree
分子	Gaussian程序结果	自编程结果
H₂	-1.120 018 013 45	-1.120 018 013 71
H₂O	-75.161 772 436 6	-75.161 772 323 7
NH₃	-55.567 472 491 8	-55.567 472 473 6
CH₄	-39.764 712 736 1	-39.764 712 727 0

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一种基于迭代子空间直接求逆算法的高效子空间混合算法

An Efficient Subspace Hybrid Algorithm Based on Direct Inversion in Iterative Subspace Algorithm

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分子	无加速的SCF	混合算法	DIIS(3)	DIIS(5)
H₂O	13	6	7	7
CH₃CHO	不收敛	15	16	20
C₂H₆	65	30	40	47