Commun. Comput. Phys., 15 (2014), pp. 1012-1028.


Local Discontinuous Galerkin Methods for the 2D Simulation of Quantum Transport Phenomena on Quantum Directional Coupler

Li Guo 1, Yan Xu 1*

1 School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China.

Received 12 March 2013; Accepted (in revised version) 10 July 2013
Available online 21 January 2014
doi:10.4208/cicp.120313.100713s

Abstract

In this paper, we present local discontinuous Galerkin methods (LDG) to simulate an important application of the 2D stationary Schrodinger equation called quantum transport phenomena on a typical quantum directional coupler, which frequency change mainly reflects in y-direction. We present the minimal dissipation LDG (MD-LDG) method with polynomial basis functions for the 2D stationary Schrodinger equation which can describe quantum transport phenomena. We also give the MD-LDG method with polynomial basis functions in x-direction and exponential basis functions in y-direction for the 2D stationary Schrodinger equation to reduce the computational cost. The numerical results are shown to demonstrate the accuracy and capability of these methods.

AMS subject classifications: 65N30, 35Q40

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Key words: Local discontinuous Galerkin method, 2D stationary Schrodinger equation, quantum transport phenomena, quantum directional coupler.

*Corresponding author.
Email: lili2010@mail.ustc.edu.cn (L. Guo), yxu@ustc.edu.cn (Y. Xu)
 

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