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Real-time adaptive finite element solution of time-dependent Kohn-Sham equation
Bao G.1,2; Hu G.3,4; Liu D.2
2015-01-05
Source PublicationJournal of Computational Physics
ISSN10902716 00219991
Volume281Pages:743-758
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.

KeywordCrank-nicolson Finite Element Methods Mesh Adaptive Methods Multigrid For Complex System Time-dependent Kohn-sham
DOI10.1016/j.jcp.2014.10.052
URLView the original
Indexed BySCI
Language英语
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000346429300036
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Cited Times [WOS]:6   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Michigan State University
2.Zhejiang University
3.Universidade de Macau
4.UM Zhuhai Research Institute
Recommended Citation
GB/T 7714
Bao G.,Hu G.,Liu D.. Real-time adaptive finite element solution of time-dependent Kohn-Sham equation[J]. Journal of Computational Physics,2015,281:743-758.
APA Bao G.,Hu G.,&Liu D..(2015).Real-time adaptive finite element solution of time-dependent Kohn-Sham equation.Journal of Computational Physics,281,743-758.
MLA Bao G.,et al."Real-time adaptive finite element solution of time-dependent Kohn-Sham equation".Journal of Computational Physics 281(2015):743-758.
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