Exact Artificial Boundary Condition for the Poisson Equation in the Simulation of the 2D Schrödinger-Poisson System

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.

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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

Keywords:   

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