A NUMERICAL STUDY OF THE GAUSSIAN BEAM METHODS FOR SCHRODINGER-POISSON EQUATIONS

被引：19

作者：

Jin, Shi ^{[1
]}

Wu, Hao ^{[2
]}

Yang, Xu ^{[1
,3
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

[3] Princeton Univ, Program Appl & Computat Math, Princeton, NJ 08544 USA

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2010年 / 28卷 / 02期

基金：

美国国家科学基金会;

关键词：

Schrodinger-Poisson equations; Gaussian beam methods; Vlasov-Poisson equations; VLASOV-POISSON; SEMICLASSICAL LIMIT; LEVEL SET; WEAK SOLUTIONS; APPROXIMATION; OBSERVABLES; DIMENSION; SYSTEMS;

D O I：

10.4208/jcm.2009.10-m1005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

As an important model in quantum semiconductor devices, the Schrodinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gaussian beam methods for the numerical simulation of the one-dimensional Schrodinger-Poisson equations. The Gaussian beam methods for high frequency waves outperform the geometrical optics method in that the former are accurate even around caustics. The purposes of the paper are first to develop the Gaussian beam methods, based oil our previous methods for the linear Schrodinger equation, for the Schrodinger-Poisson equations, and then check their validity for this weakly-nonlinear system.

引用

页码：261 / 272

页数：12

共 50 条

[1]

Abdallah N.B., 1997, ZAMP, V48, P135

[2] On a multidimensional Schrodinger-Poisson scattering model for semiconductors [J].