Volume 16, Issue 3
Exact Artificial Boundary Condition for the Poisson Equation in the Simulation of the 2d Schrödinger-poisson System

Norbert J. Mauser & Yong Zhang

Commun. Comput. Phys., 16 (2014), pp. 764-780.

Published online: 2014-12

Preview Full PDF 105 550
Export citation
  • 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 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.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • References
  • Hide All
    View All

@Article{CiCP-16-764, author = {Norbert J. Mauser and Yong Zhang}, 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 = {

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 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.110813.140314a}, url = {http://global-sci.org/intro/article_detail/cicp/7061.html} }
Copy to clipboard
The citation has been copied to your clipboard