On Accelerating a Multilevel Correction Adaptive Finite Element Method for Kohn-Sham Equation (Hehu Xie)

　　Based on the numerical method proposed in Hu et al. (2018) [22] for Kohn-Sham equation, further improvement on the efficiency is obtained in this paper by i). designing a numerical method with the strategy of separately handling the nonlinear Hartree potential and exchange-correlation potential, and ii). parallelizing the algorithm in an eigenpairwise approach. The feasibility of two approaches is analyzed in detail, and the new algorithm is described completely. Compared with previous results, a significant improvement of numerical efficiency can be observed from plenty of numerical experiments, which make the new method more suitable for the practical problems.

　　Publication:

　　Journal of Computational Physics, Volume 472, 1 January 2023, 111674

　　Author:

　　Guanghui Hu

　　Department of Mathematics & Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications, Faculty of Science and Technology, University of Macau, Macao S.A.R., China

　　Zhuhai UM Science & Technology Research Institute, Zhuhai, Guangdong, China

　　Hehu Xie

　　LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

　　School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

　　Email: hhxie@lsec.cc.ac.cn

　　Fei Xu

　　Faculty of Science, Beijing University of Technology, Beijing 100124, China