Layer-Splitting Methods for Time-Dependent Schrödinger Equations of Incommensurate Systems

Layer-Splitting Methods for Time-Dependent Schrödinger Equations of Incommensurate Systems

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.

Author Details

Ting Wang

Huajie Chen

Aihui Zhou

Yuzhi Zhou