A new multiscale discontinuous Galerkin method for the one-dimensional stationary Schrödinger equation

DOI10.1007/s10915-015-0022-7zbMath1342.65169OpenAlexW2061489048MaRDI QIDQ283315

Wei Wang, Chi-Wang Shu, Bo Dong

Publication date: 13 May 2016

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-015-0022-7

zbMATH Keywords

numerical exampleerror analysisdiscontinuous Galerkin methodSchrödinger equationmultiscale methodwave function

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (7)

High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments ⋮ Time-splitting Galerkin method for spin-orbit-coupled Bose-Einstein condensates ⋮ High-order multiscale discontinuous Galerkin methods for the one-dimensional stationary Schrödinger equation ⋮ Efficient approximation algorithm for the Schrödinger–Possion system ⋮ Conservative super-convergent and hybrid discontinuous Galerkin methods applied to nonlinear Schrödinger equations ⋮ Uniform in time error analysis of HDG approximation for Schrödinger equation based on HDG projection ⋮ A high-order multiscale discontinuous Galerkin method for two-dimensional Schrödinger equation in quantum transport

Cites Work

• 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
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• 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
• Discontinuous Galerkin method for a class of elliptic multi‐scale problems
• Multiscale Discontinuous Galerkin Methods for Elliptic Problems with Multiple Scales
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