A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model

A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model

Year:    2023

Author:    Guanghui Hu, Yedan Shen, Ting Wang, Jie Zhou, Guanghui Hu

Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 3 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2022-0195

Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 3 : pp. 597–621

Published online:    2023-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

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

Author Details

Guanghui Hu

Yedan Shen

Ting Wang

Jie Zhou

Guanghui Hu