A Comparative Study of Characteristic-Based Algorithms for the Maxwell Equations

Shang, J. S.; Fithen, Robert M.

doi:10.1006/jcph.1996.0100

Cited by 46 publications

(14 citation statements)

References 21 publications

(85 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…FVTD methods (i.e. piecewise constant, discontinuous, Galerkin-type finite element approximation) have been developed on body-fitted coordinates [23], on unstructured finite element triangulations [4] or on totally destructured meshes [1]. First-order conservative upwind schemes, for which stability [19], convergence [8] and L 1 error estimates of h 1/2 [25] were proven, are too dissipative to be used for the Keywords and phrases.…”

Section: Introductionmentioning

confidence: 99%

Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes

et al. 2005

View full text Add to dashboard Cite

Abstract. A Discontinuous Galerkin method is used for to the numerical solution of the time-domainMaxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy is conserved for metallic cavities. Convergence is proved for P k Discontinuous elements on tetrahedral meshes, as well as a discrete divergence preservation property. Promising numerical examples with low-order elements show the potential of the method.

show abstract

Section: Introductionmentioning

confidence: 99%

Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes

et al. 2005

View full text Add to dashboard Cite

show abstract

“…One can mention Finite Element Time-Domain (FETD) methods, which have been accelerated using accurate mass lumping [9,20], mimetic methods [19], or Finite Volume Time-Domain (FVTD) methods [4,27,30], which all fail in being at the same time efficient, easily extendible to high orders of accuracy, stable, and energy-conserving. The global conservation of the electromagnetic energy, which is one particular aspect of Yee's original method, is also achieved for FETD methods or for FVTD methods based on totally centered numerical fluxes [27], coupled with a centered implicit time-scheme or an explicit leapfrog time-scheme.…”

Section: Introductionmentioning

confidence: 99%

Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems

Piperno

2006

ESAIM: M2AN

View full text Add to dashboard Cite

Abstract. The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution of wave propagation problems. Able to deal with unstructured, possibly locally-refined meshes, they handle easily complex geometries and remain fully explicit with easy parallelization and extension to high orders of accuracy. Non-dissipative versions exist, where some discrete electromagnetic energy is exactly conserved. However, the stability limit of the methods, related to the smallest elements in the mesh, calls for the construction of local-time stepping algorithms. These schemes have already been developed for N -body mechanical problems and are known as symplectic schemes. They are applied here to DGTD methods on wave propagation problems.Mathematics Subject Classification. 65L05, 65L20, 65M12, 65M60, 78M10.

show abstract

“…Many different types of methods have been proposed in order to handle complex geometries and heterogeneous configurations by dealing with unstructured tetrahedral meshes, including, for example, mass lumped Finite Element Time-Domain (FETD) methods [5,17], mimetic methods [16], or Finite Volume Time-Domain (FVTD) methods [26,3,23], which all fail in being at the same time as efficient as explicit methods, easily extendible to high orders of accuracy, and provably stable. The global conservation of the electromagnetic energy and the preservation of divergence, which are two desirable properties of Yee's original method, have been also obtained for FETD methods or for FVTD methods based on totally centered numerical fluxes [23], coupled with a centered implicit time-scheme or an explicit leap-frog time-scheme.…”

Section: Introductionmentioning

confidence: 99%

DGTD methods using modal basis functions and symplectic local time-stepping

Piperno

2006

European Journal of Computational Mechanics

View full text Add to dashboard Cite

The Discontinuous Galerkin Time Domain (DGTD) methods are now widely used for the solution of wave propagation problems. Able to deal with unstructured meshes past complex geometries, they remain fully explicit with easy parallelization and extension to high orders of accuracy. Still, modal or nodal local basis functions have to be chosen carefully to obtain actual numerical accuracy. Concerning time discretization, explicit nondissipative energy-preserving time-schemes exist, but their stability limit remains linked to the smallest element size in the mesh. Symplectic algorithms, based on local-time stepping or local implicit scheme formulations, can lead to dramatic reductions of computational time, which is shown here on two-dimensional acoustics problems.Key-words: waves, acoustics, Maxwell's system, Discontinuous Galerkin methods, mass matrix condition number, symplectic schemes, energy conservation, local time-stepping.Méthodes DGTD avec fonctions de base modales et schémas en temps symplectiques : applications en propagation d'ondes.Résumé : Les méthodes de Galerkine discontinu sont maintenant largement utilisées pour la résolution numérique de problèmes de propagation d'ondes. S'appuyant sur des maillages non-structurés autour des géométries les plus générales, elles restent quasiment complète-ment explicites, facilement parallélisables et d'ordre élevé. Il convient néanmoins d'optimiser le choix des fonctions de base discontinues (modales ou nodales). Pour ce qui est de la discrét-isation en temps, des schémas explicites non-dissipatifs existent, mais leur limite de stabilité reste liée aux plus petits éléments du maillage. Des algorithmes symplectiques, avec pas de temps local ou schéma localement implicite, conduisent à des diminutions considérables du temps de calcul.

show abstract

A Comparative Study of Characteristic-Based Algorithms for the Maxwell Equations

Cited by 46 publications

References 21 publications

Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes

Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes

Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems

DGTD methods using modal basis functions and symplectic local time-stepping

Contact Info

Product

Resources

About