Real-time adaptive finite element solution of time-dependent Kohn-Sham equation

Gang Bao, Guanghui Hu, Di Liu

    Research output: Contribution to journalArticle

    • 3 Citations

    Abstract

    In our previous paper (Bao et al., 2012 [1]), a general framework of using adaptive finite element methods to solve the Kohn-Sham equation has been presented. This work is concerned with solving the time-dependent Kohn-Sham equations. The numerical methods are studied in the time domain, which can be employed to explain both the linear and the nonlinear effects. A Crank-Nicolson scheme and linear finite element space are employed for the temporal and spatial discretizations, respectively. To resolve the trouble regions in the time-dependent simulations, a heuristic error indicator is introduced for the mesh adaptive methods. An algebraic multigrid solver is developed to efficiently solve the complex-valued system derived from the semi-implicit scheme. A mask function is employed to remove or reduce the boundary reflection of the wavefunction. The effectiveness of our method is verified by numerical simulations for both linear and nonlinear phenomena, in which the effectiveness of the mesh adaptive methods is clearly demonstrated.

    Original languageEnglish (US)
    Pages (from-to)743-758
    Number of pages16
    JournalJournal of Computational Physics
    Volume281
    DOIs
    StatePublished - Jan 5 2015

    Profile

    Wave functions
    Masks
    Numerical methods
    Finite element method
    Computer simulation
    mesh
    simulation
    eccentrics
    complex systems
    finite element method
    masks

    Keywords

    • Crank-Nicolson
    • Finite element methods
    • Mesh adaptive methods
    • Multigrid for complex system
    • Time-dependent Kohn-Sham

    ASJC Scopus subject areas

    • Computer Science Applications
    • Physics and Astronomy (miscellaneous)

    Cite this

    Real-time adaptive finite element solution of time-dependent Kohn-Sham equation. / Bao, Gang; Hu, Guanghui; Liu, Di.

    In: Journal of Computational Physics, Vol. 281, 05.01.2015, p. 743-758.

    Research output: Contribution to journalArticle

    Bao, Gang; Hu, Guanghui; Liu, Di / Real-time adaptive finite element solution of time-dependent Kohn-Sham equation.

    In: Journal of Computational Physics, Vol. 281, 05.01.2015, p. 743-758.

    Research output: Contribution to journalArticle

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