Towards Translational Invariance of Total Energy with Finite Element Methods for Kohn-Sham Equation

Gang Bao, Guanghui Hu, Di Liu

    Research output: Research - peer-reviewArticle

    • 1 Citations

    Abstract

    Numerical oscillation of the total energy can be observed when the Kohn- Sham equation is solved by real-space methods to simulate the translational move of an electronic system. Effectively remove or reduce the unphysical oscillation is crucial not only for the optimization of the geometry of the electronic structure, but also for the study of molecular dynamics. In this paper, we study such unphysical oscillation based on the numerical framework in [G. Bao, G. H. Hu, and D. Liu, An h-adaptive finite element solver for the calculations of the electronic structures, Journal of Computational Physics, Volume 231, Issue 14, Pages 4967-4979, 2012], and deliver some numerical methods to constrain such unphysical effect for both pseudopotential and all-electron calculations, including a stabilized cubature strategy for Hamiltonian operator, and an a posteriori error estimator of the finite element methods for Kohn-Sham equation. The numerical results demonstrate the effectiveness of our method on restraining unphysical oscillation of the total energies.

    LanguageEnglish (US)
    Pages1-23
    Number of pages23
    JournalCommunications in Computational Physics
    Volume19
    Issue number1
    DOIs
    StatePublished - Jan 15 2016

    Profile

    invariance
    finite element method
    oscillations
    energy
    electronic structure
    estimators
    pseudopotentials
    molecular dynamics
    operators
    physics
    optimization
    geometry
    electronics
    electrons

    Keywords

    • adaptive finite element methods
    • Kohn-Sham equation
    • Translational invariance
    • unstructured mesh

    ASJC Scopus subject areas

    • Physics and Astronomy (miscellaneous)

    Cite this

    Towards Translational Invariance of Total Energy with Finite Element Methods for Kohn-Sham Equation. / Bao, Gang; Hu, Guanghui; Liu, Di.

    In: Communications in Computational Physics, Vol. 19, No. 1, 15.01.2016, p. 1-23.

    Research output: Research - peer-reviewArticle

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