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.

LanguageEnglish (US)
Pages743-758
Number of pages16
JournalJournal of Computational Physics
Volume281
DOIs
StatePublished - Jan 5 2015

Profile

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

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

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