A novel tetrahedral spectral element method for Kohn-Sham model

Zhan, Hongfei; Hu, Guanghui

doi:10.1016/j.jcp.2022.111831

Cited by 1 publication

(1 citation statement)

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“…For the ground state calculation, concerned with the nonlinearity of the Kohn-Sham equation caused by the Hamiltonian operator, the self consistent field (SCF) iteration is a classical choice [22,24]. Several types of numerical methods are employed in the simulation of Kohn-Sham equation, such as finite element methods [2,4,12,20], finite difference methods [30], spectral methods [18,25,35], discontinuous Galerkin methods [23], finite volume methods [9], plane-wave methods [17], etc. Besides directly solving the Kohn-Sham equation, minimizing the total energy is also a popular way to obtain the ground state of the quantum system.…”

Section: Introductionmentioning

confidence: 99%

A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model

Guanghui Hu,

Yedan Shen,

Ting Wang

et al. 2023

NMTMA

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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.

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