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Local Discontinuous Galerkin Methods for the 2D Simulation of Quantum Transport Phenomena on Quantum Directional Coupler
Published online by Cambridge University Press: 03 June 2015
Abstract
In this paper, we present local discontinuous Galerkin methods (LDG) to simulate an important application of the 2D stationary Schrödinger 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 Schrödinger 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 Schrödinger equation to reduce the computational cost. The numerical results are shown to demonstrate the accuracy and capability of these methods.
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