A convergence analysis of a structure-preserving gradient flow method for the all-electron Kohn-Sham model
Abstract
In [Dai et al, Multi. Model. Simul., 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, accepted] 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., 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
Cite
@article{arxiv.2303.03878,
title = {A convergence analysis of a structure-preserving gradient flow method for the all-electron Kohn-Sham model},
author = {Yedan Shen and Ting Wang and Jie Zhou and Guanghui Hu},
journal= {arXiv preprint arXiv:2303.03878},
year = {2023}
}