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Artificial boundary conditions for the semi-discretized one-dimensional nonlocal Schrödinger equation
Journal of Computational Physics ( IF 4.1 ) Pub Date : 2021-07-27 , DOI: 10.1016/j.jcp.2021.110575
Songsong Ji , Gang Pang , Xavier Antoine , Jiwei Zhang

A general method is proposed to build exact artificial boundary conditions for the one-dimensional nonlocal Schrödinger equation. To this end, we first consider the spatial semi-discretization of the nonlocal equation, and then develop an accurate numerical method for computing the Green's function of the semi-discrete nonlocal Schrödinger equation. These Green's functions are next used to build the exact boundary conditions corresponding to the semi-discrete model. Numerical results illustrate the accuracy of the boundary conditions. The methodology can also be applied to other nonlocal models and could be extended to higher dimensions.



中文翻译:

半离散化一维非局部薛定谔方程的人工边界条件

提出了一种通用方法来为一维非局部薛定谔方程建立精确的人工边界条件。为此,我们首先考虑非局部方程的空间半离散化,然后开发一种精确的数值方法来计算半离散非局部薛定谔方程的格林函数。这些格林函数接下来用于构建对应于半离散模型的精确边界条件。数值结果说明了边界条件的准确性。该方法也可以应用于其他非局部模型,并可以扩展到更高的维度。

更新日期:2021-08-03
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