An Unconditionally Energy-Stable and Orthonormality-Preserving Scheme for the Kohn-Sham Gradient Flow Based Model Based on a Tetrahedral Spectral Element Method
Year: 2025
Author: Hongfei Zhan, Ting Wang, Guanghui Hu
Communications in Computational Physics, Vol. 37 (2025), Iss. 4 : pp. 921–941
Abstract
In this paper, the unconditionally energy-stable and orthonormality-preserving iterative scheme proposed in [X. Wang et al. (2024), J. Comput. Phys., 498:112670] is extended both theoretically and numerically, including (i) the exchange-correlation energy is introduced into the model for a more comprehensive description of the quantum system, utilizing the local density approximation used by the National Institution of Science and Technology Standard Reference Database; (ii) both the unconditional energy-stability and orthonormality-preservation are attained in the newly derived scheme; (iii) a $C^0$ tetrahedral spectral element method is adopted for the quality spatial discretization, of which a quality initial condition can be designed using low order one for effectively accelerating the simulation. A series of numerical experiments validate the effectiveness of our method, encompassing various atoms and molecules. All the computations successfully reveal the anticipated spectral accuracy and the exponential error dependence to the cubic root of the degree of freedom number. Moreover, the efficiency of the extended framework is discussed in detail on updating schemes.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2024-0053
Communications in Computational Physics, Vol. 37 (2025), Iss. 4 : pp. 921–941
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Kohn-Sham density functional theory gradient flow model structure-preserving scheme energy stability tetrahedral spectral element method.