Exact Artificial Boundary Condition for the Poisson Equation in the Simulation of the 2D Schrödinger-Poisson System
Year: 2014
Communications in Computational Physics, Vol. 16 (2014), Iss. 3 : pp. 764–780
Abstract
We study the computation of ground states and time dependent solutions of the Schrödinger-Poisson system (SPS) on a bounded domain in 2D (i.e. in two space dimensions). On a disc-shaped domain, we derive exact artificial boundary conditions for the Poisson potential based on truncated Fourier series expansion in θ, and propose a second order finite difference scheme to solve the $r$-variable ODEs of the Fourier coefficients. The Poisson potential can be solved within $\mathcal{O}$($M NlogN$) arithmetic operations where $M,N$ are the number of grid points in $r$-direction and the Fourier bases. Combined with the Poisson solver, a backward Euler and a semi-implicit/leap-frog method are proposed to compute the ground state and dynamics respectively. Numerical results are shown to confirm the accuracy and efficiency. Also we make it clear that backward Euler sine pseudospectral (BESP) method in [33] can not be applied to 2D SPS simulation.
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.110813.140314a
Communications in Computational Physics, Vol. 16 (2014), Iss. 3 : pp. 764–780
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
-
Accurate and efficient computation of nonlocal potentials based on Gaussian-sum approximation
Exl, Lukas | Mauser, Norbert J. | Zhang, YongJournal of Computational Physics, Vol. 327 (2016), Iss. P.629
https://doi.org/10.1016/j.jcp.2016.09.045 [Citations: 16] -
Efficiency of using adaptive artificial boundary conditions at computer simulation of contrast spatio‐temporal laser‐induced structures in a semiconductor
Trofimov, Vyacheslav | Loginova, Maria | Egorenkov, VladimirComputational and Mathematical Methods, Vol. 3 (2021), Iss. 6
https://doi.org/10.1002/cmm4.1165 [Citations: 2] -
Accurate and Efficient Numerical Methods for Computing Ground States and Dynamics of Dipolar Bose-Einstein Condensates via the Nonuniform FFT
Bao, Weizhu | Tang, Qinglin | Zhang, YongCommunications in Computational Physics, Vol. 19 (2016), Iss. 5 P.1141
https://doi.org/10.4208/cicp.scpde14.37s [Citations: 22] -
On Optimal Zero-Padding of Kernel Truncation Method
Liu, Xin | Tang, Qinglin | Zhang, Shaobo | Zhang, YongSIAM Journal on Scientific Computing, Vol. 46 (2024), Iss. 1 P.A23
https://doi.org/10.1137/23M1550803 [Citations: 0] -
On the Rotating Nonlinear Klein--Gordon Equation: NonRelativistic Limit and Numerical Methods
Mauser, Norbert J. | Zhang, Yong | Zhao, XiaofeiMultiscale Modeling & Simulation, Vol. 18 (2020), Iss. 2 P.999
https://doi.org/10.1137/18M1233509 [Citations: 6] -
A time splitting Chebyshev-Fourier spectral method for the time-dependent rotating nonlocal Schrödinger equation in polar coordinates
Wang, Hanquan | Wang, Jing | Zhang, Shaobo | Zhang, YongJournal of Computational Physics, Vol. 498 (2024), Iss. P.112680
https://doi.org/10.1016/j.jcp.2023.112680 [Citations: 1] -
A splitting Chebyshev collocation method for Schrödinger–Poisson system
Wang, Hanquan | Liang, Zhenguo | Liu, RonghuaComputational and Applied Mathematics, Vol. 37 (2018), Iss. 4 P.5034
https://doi.org/10.1007/s40314-018-0616-4 [Citations: 2] -
Computing the ground state and dynamics of the nonlinear Schrödinger equation with nonlocal interactions via the nonuniform FFT
Bao, Weizhu | Jiang, Shidong | Tang, Qinglin | Zhang, YongJournal of Computational Physics, Vol. 296 (2015), Iss. P.72
https://doi.org/10.1016/j.jcp.2015.04.045 [Citations: 26] -
Time-Splitting Compact Difference Scheme for Solving Schrodinger-Poisson Equations
姜, 珊
Advances in Applied Mathematics, Vol. 08 (2019), Iss. 01 P.7
https://doi.org/10.12677/AAM.2019.81002 [Citations: 0] -
Central vortex steady states and dynamics of Bose–Einstein condensates interacting with a microwave field
Wang, Di | Cai, Yongyong | Wang, QiPhysica D: Nonlinear Phenomena, Vol. 419 (2021), Iss. P.132852
https://doi.org/10.1016/j.physd.2021.132852 [Citations: 0]