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

Published online by Cambridge University Press:  03 June 2015

Norbert J. Mauser*
Affiliation:
Wolfgang Pauli Institute c/o Fak. Mathematik, University Wien, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
Yong Zhang*
Affiliation:
Wolfgang Pauli Institute c/o Fak. Mathematik, University Wien, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
*
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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 (MNlogN) 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.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2014

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