A NUMERICAL STUDY OF THE GAUSSIAN BEAM METHODS FOR SCHR(O|¨)DINGER-POISSON EQUATIONS

作     者：Shi Jin Hao Wu Xu Yang 

作者机构：Department of Mathematics University of Wisconsin Madison W1 53706 USA Department of Mathematical Sciences Tsinghua University Beijing 100084 China Department of Mathematics University of Wisconsin Madison WI 53706 USA Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544USA 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2010年第28卷第2期

页      面：261-272页

核心收录：

学科分类：070207[理学-光学] 07[理学] 08[工学] 070102[理学-计算数学] 0803[工学-光学工程] 0701[理学-数学] 0702[理学-物理学] 

基　　金：Research Program of China under the grant 2005CB321701 supported by a Van Vleck Distinguished Research Prize from University of Wisconsin-Madison 

主　　题：Schrodinger-Poisson equations Gaussian beam methods Vlasov-Poisson equations 

摘      要：As an important model in quantum semiconductor devices, the SchrSdinger-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 on our previous methods for the linear SchrSdinger equation, for the Schrodinger-Poisson equations, and then check their validity for this weakly-nonlinear system.