2023/03/07 by Yedan Shen, Shen, Yedan, Ting Wang +5
Earth and Planetary Sciences · Materials Science · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Applied mathematics #Balanced flow #Catalytic Processes in Materials Science #Computer science #Convergence (economics) #Density functional theory #Electron #FOS: Mathematics #Flow (mathematics) #Geometry #Kohn–Sham equations #Mathematical analysis #Mathematics #Numerical Analysis (math.NA) #Physics #Quantum mechanics #Stability (learning theory) #nanoparticles nucleation surface interactions
paper · pdf · doi:10.48550/arxiv.2303.03878
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/03/07 · openalex created_date 2023/03/10 · openalex updated_date 2026/07/28
In [Dai et al, Multi. Model. Simul., 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, accepted] 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., 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.