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 - <p style="text-align: justify;">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.</p>