TY - JOUR
T1 - Layer-Splitting Methods for Time-Dependent Schrödinger Equations of Incommensurate Systems
AU - Wang , Ting
AU - Chen , Huajie
AU - Zhou , Aihui
AU - Zhou , Yuzhi
JO - Communications in Computational Physics
VL - 5
SP - 1474
EP - 1498
PY - 2021
DA - 2021/10
SN - 30
DO - http://doi.org/10.4208/cicp.OA-2021-0070
UR - https://global-sci.org/intro/article_detail/cicp/19937.html
KW - Incommensurate system, time-dependent Schrödinger equation, time stepping scheme.
AB - <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>