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
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.
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