Loading [MathJax]/jax/output/HTML-CSS/config.js
full
search.png

Search

close.png

Cancel

arrow
Volume 16, Issue 3
A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model

Yedan Shen, Ting Wang, Jie Zhou & Guanghui Hu

DOI: 10.4208/nmtma.OA-2022-0195

Numer. Math. Theor. Meth. Appl., 16 (2023), pp. 597-621.

Published online: 2023-08

Preview Purchase PDF 2221 26066

Cited by

google scholar semantic scholar
Export citation
  • Abstract

In [Dai et al., Multi. Model. Simul. 18(4) (2020)], a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn-Sham density functional theory, based on which a linearized method was developed in [Hu et al., EAJAM. 13(2) (2023)] for further improving the numerical efficiency. In this paper, a complete convergence analysis is delivered for such a linearized method for the all-electron Kohn-Sham model. Temporally, the convergence, the asymptotic stability, as well as the structure-preserving property of the linearized numerical scheme in the method is discussed following previous works, while spatially, the convergence of the $h$-adaptive mesh method is demonstrated following [Chen et al., Multi. Model. Simul. 12 (2014)], with a key study on the boundedness of the Kohn-Sham potential for the all-electron Kohn-Sham model. Numerical examples confirm the theoretical results very well.

  • Keywords

Kohn-Sham density functional theory, gradient flow model, structure-preserving, linear scheme, convergence analysis.

  • AMS Subject Headings

35Q41, 81Q05, 65M60, 65M12, 65M50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{NMTMA-16-597, author = {Shen , YedanWang , TingZhou , Jie and Hu , Guanghui}, title = {A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2023}, volume = {16}, number = {3}, pages = {597--621}, abstract = {

In [Dai et al., Multi. Model. Simul. 18(4) (2020)], a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn-Sham density functional theory, based on which a linearized method was developed in [Hu et al., EAJAM. 13(2) (2023)] for further improving the numerical efficiency. In this paper, a complete convergence analysis is delivered for such a linearized method for the all-electron Kohn-Sham model. Temporally, the convergence, the asymptotic stability, as well as the structure-preserving property of the linearized numerical scheme in the method is discussed following previous works, while spatially, the convergence of the $h$-adaptive mesh method is demonstrated following [Chen et al., Multi. Model. Simul. 12 (2014)], with a key study on the boundedness of the Kohn-Sham potential for the all-electron Kohn-Sham model. Numerical examples confirm the theoretical results very well.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2022-0195}, url = {http://global-sci.org/intro/article_detail/nmtma/21959.html} }
TY - JOUR T1 - A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model AU - Shen , Yedan AU - Wang , Ting AU - Zhou , Jie AU - Hu , Guanghui JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 597 EP - 621 PY - 2023 DA - 2023/08 SN - 16 DO - http://doi.org/10.4208/nmtma.OA-2022-0195 UR - https://global-sci.org/intro/article_detail/nmtma/21959.html KW - Kohn-Sham density functional theory, gradient flow model, structure-preserving, linear scheme, convergence analysis. AB -

In [Dai et al., Multi. Model. Simul. 18(4) (2020)], a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn-Sham density functional theory, based on which a linearized method was developed in [Hu et al., EAJAM. 13(2) (2023)] for further improving the numerical efficiency. In this paper, a complete convergence analysis is delivered for such a linearized method for the all-electron Kohn-Sham model. Temporally, the convergence, the asymptotic stability, as well as the structure-preserving property of the linearized numerical scheme in the method is discussed following previous works, while spatially, the convergence of the $h$-adaptive mesh method is demonstrated following [Chen et al., Multi. Model. Simul. 12 (2014)], with a key study on the boundedness of the Kohn-Sham potential for the all-electron Kohn-Sham model. Numerical examples confirm the theoretical results very well.

Shen , YedanWang , TingZhou , Jie and Hu , Guanghui. (2023). A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model. Numerical Mathematics: Theory, Methods and Applications. 16 (3). 597-621. doi:10.4208/nmtma.OA-2022-0195
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard