Local Discontinuous Galerkin Methods for the 2D Simulation of Quantum Transport Phenomena on Quantum Directional Coupler (Communications in Computational Physics, 2020)
In this paper, we present local discontinuous Galerkin methods (LDG) tosimulate an important application of the 2D stationary Schrödinger equation calledquantum transport phenomena on a typical quantum directional coupler, which frequencychange mainly reflects in $y$-direction. We present the minimal dissipation LDG(MD-LDG) method with polynomial basis functions for the 2D stationary Schrödingerequation which can describe quantum transport phenomena. We also give the MD-LDGmethod with polynomial basis functions in $x$-direction and exponential basisfunctions in $y$-direction for the 2D stationary Schrödinger equation to reduce the computationalcost. The numerical results are shown to demonstrate the accuracy andcapability of these methods.