Layer-Splitting Methods for Time-Dependent Schrodinger Equations of Incommensurate Systems
Wang, Ting1; Chen, Huajie1; Zhou, Aihui2,3; Zhou, Yuzhi4,5
AbstractThis work considers numerical methods for the time-dependent Schrodinger equation of incommensurate systems. By using a plane wave method for spatial discretization, the incommensurate problem is lifted to a higher dimension that results in semidiscrete differential equations with extremely demanding computational cost. We propose several fully discrete time stepping schemes based on the idea of "layer splitting", which decompose the semidiscrete problem into sub-problems that each corresponds to one of the periodic layers. Then these schemes handle only some periodic systems in the original lower dimension at each time step, which reduces the computational cost significantly and is natural to involve stochastic methods and parallel computing. Both theoretical analysis and numerical experiments are provided to support the reliability and efficiency of the algorithms.
KeywordIncommensurate system time-dependent Schrodinger equation time stepping scheme
Indexed BySCI
Funding ProjectNational Key R & D Program of China[2019YFA0709600] ; National Key R & D Program of China[2019YFA0709601] ; Natural Science Foundation of China[11971066] ; Key Research Program of Frontier Sciences of the Chinese Academy of Sciences[QYZDJ-SSW-SYS010] ; National Science Foundation of China[11671389] ; National Science Foundation of China[12004047]
WOS Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000711870700009
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Document Type期刊论文
Corresponding AuthorChen, Huajie
Affiliation1.Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
4.CAEP Software Ctr High Performance Numer Simulat, Beijing 100088, Peoples R China
5.Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China
Recommended Citation
GB/T 7714
Wang, Ting,Chen, Huajie,Zhou, Aihui,et al. Layer-Splitting Methods for Time-Dependent Schrodinger Equations of Incommensurate Systems[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2021,30(5):1474-1498.
APA Wang, Ting,Chen, Huajie,Zhou, Aihui,&Zhou, Yuzhi.(2021).Layer-Splitting Methods for Time-Dependent Schrodinger Equations of Incommensurate Systems.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,30(5),1474-1498.
MLA Wang, Ting,et al."Layer-Splitting Methods for Time-Dependent Schrodinger Equations of Incommensurate Systems".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 30.5(2021):1474-1498.
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