2021/03/27 by Ting Wang, Huajie Chen, Wang, Ting +5
Engineering · Mathematics · #Computational Physics (physics.comp-ph) #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2103.14897
openalex publication_date 2021/03/27 · openalex created_date 2021/04/13 · openalex updated_date 2026/07/28
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.