A spatial high-order hexahedral discontinuous Galerkin method to solve Maxwell's equations in time domain

Authors:
G. Cohen;X. Ferrieres;S. Pernet
Affiliations:
INRIA, Domaine ds Voluceau, Rocquencourt, Le Chesnay Cedex, France;ONERA DEMR, unité CDE, Toulouse, France;ONERA DEMR, unité CDE, Toulouse, France
Venue:
Journal of Computational Physics
Year:
2006

Citing 11
Cited 6

A new family of mixed finite elements in IR3

Numerische Mathematik
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
A perfectly matched layer for the absorption of electromagnetic waves

Journal of Computational Physics
Explicit Hybrid Time Domain Solver for the Maxwell Equations in 3D

Journal of Scientific Computing
A Vector Finite Element Time-Domain Method for Solving Maxwell's Equations on Unstructured Hexahedral Grids

SIAM Journal on Scientific Computing
A Nondiffusive Finite Volume Scheme for the Three-Dimensional Maxwell's Equations on Unstructured Meshes

SIAM Journal on Numerical Analysis
Nodal high-order methods on unstructured grids

Journal of Computational Physics
Mixed Discontinuous Galerkin Approximation of the Maxwell Operator

SIAM Journal on Numerical Analysis
A sequence of absorbing boundary conditions for Maxwell's equations

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

Journal of Computational Physics
A Discontinuous Galerkin Method for Linear Symmetric Hyperbolic Systems in Inhomogeneous Media

Journal of Scientific Computing

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
Locally implicit discontinuous Galerkin method for time domain electromagnetics

Journal of Computational Physics
Higher-order Finite Elements for Hybrid Meshes Using New Nodal Pyramidal Elements

Journal of Scientific Computing
A high-order non-conforming discontinuous Galerkin method for time-domain electromagnetics

Journal of Computational and Applied Mathematics
Efficient large scale electromagnetic simulations using dynamically adapted meshes with the discontinuous Galerkin method

Journal of Computational and Applied Mathematics
A hybrid finite-element/finite-difference method with an implicit–explicit time-stepping scheme for Maxwell's equations

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields

Quantified Score

Hi-index	31.46

Visualization

Abstract

In this paper, we present a non-dissipative spatial high-order discontinuous Galerkin method to solve the Maxwell equations in the time domain. The non-intuitive choice of the space of approximation and the basis functions induce an important gain for mass, stiffness and jump matrices in terms of memory. This spatial approximation, combined with a leapfrog scheme in time, leads also to a fast explicit and accurate method. A study of the dispersive error is carried out and a stability condition for the proposed scheme is established. Some comparisons with other schemes are presented to validate the new scheme and to point out its advantages. Finally, in order to improve the efficiency of the method in terms of CPU time on general unstructured meshes, a strategy of local time-stepping is proposed.