Analysis and application of the nodal discontinuous Galerkin method for wave propagation in metamaterials

Authors:
Jichun Li;Jan S. Hesthaven
Affiliations:
Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, Nevada 89154-4020, USA;EPFL-SB-MATHICSE-MCSS, Ecole Polytechnique Fédale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
Venue:
Journal of Computational Physics
Year:
2014

Citing 18
Cited 0

Absorbing PML boundary layers for wave-like equations

Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

SIAM Journal on Numerical Analysis
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations

Journal of Computational Physics
Nodal high-order methods on unstructured grids

Journal of Computational Physics
Locally divergence-free discontinuous Galerkin methods for the Maxwell equations

Journal of Computational Physics
Discontinuous Galerkin methods for dispersive and lossy Maxwell's equations and PML boundary conditions

Journal of Computational Physics
Interior penalty method for the indefinite time-harmonic Maxwell equations

Numerische Mathematik
A numerical study for the performance of the Runge-Kutta discontinuous Galerkin method based on different numerical fluxes

Journal of Computational Physics
Interior penalty discontinuous Galerkin method for Maxwell's equations: Energy norm error estimates

Journal of Computational and Applied Mathematics
Dissipative terms and local time-stepping improvements in a spatial high order Discontinuous Galerkin scheme for the time-domain Maxwell's equations

Journal of Computational Physics
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications

Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
The Direct Discontinuous Galerkin (DDG) Methods for Diffusion Problems

SIAM Journal on Numerical Analysis
Locally implicit discontinuous Galerkin method for time domain electromagnetics

Journal of Computational Physics
Error analysis of a discontinuous Galerkin method for Maxwell equations in dispersive media

Journal of Computational Physics
Development of discontinuous Galerkin methods for Maxwell's equations in metamaterials and perfectly matched layers

Journal of Computational and Applied Mathematics
Discontinuous Galerkin Methods: Theory, Computation and Applications

Discontinuous Galerkin Methods: Theory, Computation and Applications
Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials

Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials
Convergence and superconvergence of staggered discontinuous Galerkin methods for the three-dimensional Maxwell's equations on Cartesian grids

Journal of Computational Physics

Quantified Score

Hi-index	31.45

Visualization

Abstract

In this paper, we develop a nodal discontinuous Galerkin method for solving the time-dependent Maxwell@?s equations when metamaterials are involved. Both semi- and fully-discrete schemes are constructed. Numerical stability and error estimate are proved for both schemes. Numerical results are presented to demonstrate that the method is not only efficient but also very effective in solving metamaterial Maxwell@?s equations.