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Volume 15, Issue 4
Local Discontinuous Galerkin Methods for the 2D Simulation of Quantum Transport Phenomena on Quantum Directional Coupler

Li Guo & Yan Xu

DOI: 10.4208/cicp.120313.100713s

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

Published online: 2014-04

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  • 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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@Article{CiCP-15-1012, author = {}, title = {Local Discontinuous Galerkin Methods for the 2D Simulation of Quantum Transport Phenomena on Quantum Directional Coupler}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {4}, pages = {1012--1028}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.120313.100713s}, url = {http://global-sci.org/intro/article_detail/cicp/7125.html} }
TY - JOUR T1 - Local Discontinuous Galerkin Methods for the 2D Simulation of Quantum Transport Phenomena on Quantum Directional Coupler JO - Communications in Computational Physics VL - 4 SP - 1012 EP - 1028 PY - 2014 DA - 2014/04 SN - 15 DO - http://doi.org/10.4208/cicp.120313.100713s UR - https://global-sci.org/intro/article_detail/cicp/7125.html KW - AB -

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.

Li Guo & Yan Xu. (2020). Local Discontinuous Galerkin Methods for the 2D Simulation of Quantum Transport Phenomena on Quantum Directional Coupler. Communications in Computational Physics. 15 (4). 1012-1028. doi:10.4208/cicp.120313.100713s
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