Pang Gang, Bian Lei, Tang Shaoqiang
HEDPS, CAPT, LTCS, and C-IFSA, College of Engineering, Peking University, Beijing 100871, People's Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 2):066709. doi: 10.1103/PhysRevE.86.066709. Epub 2012 Dec 26.
An explicit local boundary condition is proposed for finite-domain simulations of the linear Schrödinger equation on an unbounded domain. Based on an exact boundary condition in terms of the Bessel functions, it takes a simple form with 16 neighboring grid points, and it involves no empirical parameter. While the computing load is rather low, the proposed boundary condition is effective in reflection suppression, comparable to the exact convolution treatments. An extension to nonlinear Schrödinger equations is also proposed. Numerical comparisons clearly demonstrate the effectiveness of this ALmost EXact (ALEX) boundary condition for both the linear and the cubic nonlinear Schrödinger equations.
针对无界域上线性薛定谔方程的有限域模拟，提出了一种显式局部边界条件。基于贝塞尔函数的精确边界条件，它采用了一种包含16个相邻网格点的简单形式，且不涉及经验参数。虽然计算量相当低，但所提出的边界条件在反射抑制方面是有效的，可与精确卷积处理相媲美。还提出了对非线性薛定谔方程的扩展。数值比较清楚地证明了这种几乎精确（ALEX）边界条件对线性和三次非线性薛定谔方程的有效性。
