Year: 2021
Author: Zhicheng Hu, Lei Yang, Guanghui Hu, Yedan Shen, Zhicheng Hu, Guanghui Hu
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 1 : pp. 261–284
Abstract
The implicit numerical methods have the advantages on preserving the physical properties of the quantum system when solving the time-dependent Kohn-Sham equation. However, the efficiency issue prevents the practical applications of those implicit methods. In this paper, an implicit solver based on a class of Runge-Kutta methods and the finite element method is proposed for the time-dependent Kohn-Sham equation. The efficiency issue is partially resolved by three approaches, i.e., an $h$-adaptive mesh method is proposed to effectively restrain the size of the discretized problem, a complex-valued algebraic multigrid solver is developed for efficiently solving the derived linear system from the implicit discretization, as well as the OpenMP based parallelization of the algorithm. The numerical convergence, the ability on preserving the physical properties, and the efficiency of the proposed numerical method are demonstrated by a number of numerical experiments.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2020-0040
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 1 : pp. 261–284
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Time-dependent Kohn-Sham equation implicit midpoint scheme finite element methods h-adaptive mesh methods complex-valued algebraic multigrid methods.