A high-order multiscale discontinuous Galerkin method for two-dimensional Schrödinger equation in quantum transport
DOI10.1016/j.cam.2022.114701zbMath1502.65196OpenAlexW4293065564WikidataQ113878679 ScholiaQ113878679MaRDI QIDQ2088817
Publication date: 6 October 2022
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2022.114701
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) NLS equations (nonlinear Schrödinger equations) (35Q55) Schrödinger operator, Schrödinger equation (35J10) Statistical mechanics of semiconductors (82D37) Statistical mechanics of nanostructures and nanoparticles (82D80)
Cites Work
- Unnamed Item
- A new multiscale discontinuous Galerkin method for the one-dimensional stationary Schrödinger equation
- Multi-scale discontinuous Galerkin method for solving elliptic problems with curvilinear unidirectional rough coefficients
- The WKB local discontinuous Galerkin method for the simulation of Schrödinger equation in a resonant tunneling diode
- Subband decomposition approach for the simulation of quantum electron transport in nanostructures
- Discontinuous Galerkin method based on non-polynomial approximation spaces
- An accelerated algorithm for 2D simulations of the quantum ballistic transport in nanoscale MOSFETs
- High-order multiscale discontinuous Galerkin methods for the one-dimensional stationary Schrödinger equation
- Discontinuous Galerkin methods with plane waves for time-harmonic problems
- An analysis of the minimal dissipation local discontinuous Galerkin method for convection-diffusion problems
- Numerical analysis of a multiscale finite element scheme for the resolution of the stationary Schrödinger equation
- Multiscale simulation of transport in an open quantum system: Resonances and WKB interpolation
- WKB-Based Schemes for the Oscillatory 1D Schrödinger Equation in the Semiclassical Limit
- Error estimates for the Ultra Weak Variational Formulation of the Helmholtz equation
- Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
- Plane wave discontinuous Galerkin methods: Analysis of theh-version
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- A Generalized Stationary Algorithm for Resonant Tunneling: Multi-Mode Approximation and High Dimension
- Local Discontinuous Galerkin Methods for the 2D Simulation of Quantum Transport Phenomena on Quantum Directional Coupler
- Discontinuous Galerkin method for a class of elliptic multi‐scale problems
- Multiscale Discontinuous Galerkin Methods for Elliptic Problems with Multiple Scales
