@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} }