@Article{CiCP-16-3,
author = {},
title = {Exact Artificial Boundary Condition for the Poisson Equation in the Simulation of the 2D Schrödinger-Poisson System},
journal = {Communications in Computational Physics},
year = {2014},
volume = {16},
number = {3},
pages = {764--780},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.110813.140314a},
url = {https://global-sci.com/article/80457/exact-artificial-boundary-condition-for-the-poisson-equation-in-the-simulation-of-the-2d-schrodinger-poisson-system}
}