@Article{NMTMA-16-3,
author = {Hu, Guanghui and Yedan, Shen and Wang, Ting and Zhou, 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 = {<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>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2022-0195},
url = {https://global-sci.com/article/90220/a-convergence-analysis-of-a-structure-preserving-gradient-flow-method-for-the-all-electron-kohn-sham-model}
}