@Article{CiCP-30-5,
author = {Wang, Ting and Huajie, Chen and Zhou, Aihui and Zhou, Yuzhi},
title = {Layer-Splitting Methods for Time-Dependent Schrödinger Equations of Incommensurate Systems},
journal = {Communications in Computational Physics},
year = {2021},
volume = {30},
number = {5},
pages = {1474--1498},
abstract = {<p style="text-align: justify;">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 &quot;layer-splitting&quot;, 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2021-0070},
url = {https://global-sci.com/article/79610/layer-splitting-methods-for-time-dependent-schrodinger-equations-of-incommensurate-systems}
}