A generalized discontinuous Galerkin (GDG) method for Schrödinger equations with nonsmooth solutions

DOI10.1016/j.jcp.2007.10.023zbMath1135.65374OpenAlexW2003175826MaRDI QIDQ2478522

Wei Cai, Xia Ji, Kai Fan

Publication date: 28 March 2008

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2007.10.023

zbMATH Keywords

numerical resultsdiscontinuous Galerkin methodSchrödinger equationoptical waveguidessplit distributionstime-harmonic Maxwell eqution

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) 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 initial value and initial-boundary value problems involving PDEs (65M60) Antennas, waveguides in optics and electromagnetic theory (78A50)

Related Items (5)

Interior penalty bilinear IFE discontinuous Galerkin methods for elliptic equations with discontinuous coefficient ⋮ A linearized energy-conservative finite element method for the nonlinear Schrödinger equation with wave operator ⋮ Energy conserving local discontinuous Galerkin methods for the nonlinear Schrödinger equation with wave operator ⋮ A full vectorial generalized discontinuous Galerkin beam propagation method (GDG-BPM) for nonsmooth electromagnetic fields in waveguides ⋮ Uniform in time error analysis of HDG approximation for Schrödinger equation based on HDG projection

Cites Work

• Local discontinuous Galerkin methods for nonlinear Schrödinger equations
• Discontinuous Galerkin methods for dispersive and lossy Maxwell's equations and PML boundary conditions
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• A New Method of Imposing Boundary Conditions in Pseudospectral Approximations of Hyperbolic Equations
• An Interior Penalty Finite Element Method with Discontinuous Elements
• Finite Element Methods for Elliptic Equations Using Nonconforming Elements
• An Elliptic Collocation-Finite Element Method with Interior Penalties
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• A Stable Penalty Method for the Compressible Navier–Stokes Equations: I. Open Boundary Conditions

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