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

作　　者：Norbert J.Mauser Yong Zhang 

机构地区：[1]Wolfgang Pauli Institute c/o Fak.Mathematik,University Wien,Oskar-Morgenstern-Platz 1,1090 Vienna,Austria.

出　　处：《Communications in Computational Physics》2014年第8期764-780,共17页计算物理通讯（英文）

基　　金：Singapore A*STAR SERC PSF-Grant No.1321202067;National Natural Science Foundation of China Grant NSFC41390452;the Doctoral Programme Foundation of Institution of Higher Education of China as well as by the Austrian Science Foundation(FWF)under grant No.F41(project VICOM)and grant No.I830(project LODIQUAS)and grant No.W1245 and the Austrian Ministry of Science and Research via its grant for the WPI.

摘　　要：We study the computation of ground states and time dependent solutions of the Schr¨odinger-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 inθ,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.

关 键 词：2D Schrodinger-Poisson system exact artificial boundary condition backward Euler scheme semi-implicit/leap-frog scheme backward Euler sine pseudospectral method. 

分 类 号：O17[理学—数学]