Year: 2021
Author: Ting Wang, Huajie Chen, Aihui Zhou, Yuzhi Zhou
Communications in Computational Physics, Vol. 30 (2021), Iss. 5 : pp. 1474–1498
Abstract
This work considers numerical methods for the time-dependent Schrödinger 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2021-0070
Communications in Computational Physics, Vol. 30 (2021), Iss. 5 : pp. 1474–1498
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Incommensurate system time-dependent Schrödinger equation time stepping scheme.