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

Volumn 227, Issue 14, 2008, Pages 6795-6820

  Montseny, E ^a   Pernet, S ^b   Ferrieres X ^c   Cohen, G ^d  

^a UNIVERSITÉ DE TOULOUSE   (France)

^b CERFACS   (France)

^c ONERA   (France)

^d INRIA ROCQUENCOURT   (France)

Author keywords

Discontinuous Galerkin method; Local time stepping; Maxwell's equations

Indexed keywords

GALERKIN METHODS; TIME DOMAIN ANALYSIS;

DISCONTINOUS GALERKIN METHODS; DISCONTINUOUS GALERKIN SCHEMES; HIGH-ORDER; HIGHER-ORDER; LOCAL TIME STEPPING; NUMERICAL SCHEME; PENALISATION; SPEED UP; SPURIOUS MODES; TIME-DOMAIN MAXWELL EQUATIONS;

MAXWELL EQUATIONS;

EID: 44649127306     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.03.032     Document Type: Article

References (21)

1. Cangellaris A.C., and Wright D.B. Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena. IEEE Trans. Antennas Prop. AP-39 10 (1991) 1518-1525
2. Yee K.S. Numerical solution of initial boundary value problems involving Maxwell's equation in isotropic media. IEEE Trans. Antennas Prop. 14 3 (1966) 302-307
3. A. Taflove, S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, second ed., Artech, Norwood, MA.
4. Bonnet P., and Ferrieres X. Numerical modeling of scattering problems using a time domain finite volume method. JEMWA 11 (1997) 1165-1189
5. Piperno S., Remaki M., and Fezoui L. A non-diffusive finite volume scheme for the 3D Maxwell equations on unstructured meshes. SIAM J. Numer. Anal. 39 6 (2002) 2089-2108
6. Edelvik F., and Ledfelt G. Explicit hybrid time domain solver for the Maxwell equations in 3D. J. Sci. Comput. 15 1 (2000)
7. Hesthavens J.S., and Warburton T. High-order Nodal methods on unstructured grids. I. Time-domain solution of Maxwell's equations. J. Comput. Phys. 181 (2002) 1-34
8. Cohen G., Ferriéres X., and Pernet S. A spatial high order hexahedral Discontinuous Galerkin method to solve Maxwell's equations in time domain. J. Comput. Phys. 217 (2006) 340-363
9. Cohen G., and Duruflé M. Nonspurious spectral-like element methods for Maxwell's equations. J. Comp. Math. 25 (2007) 282-304
10. Pernet S., and Ferrieres X. HP - a priori error estimates for a non-dissipative spectral Discontinuous Galerkin method to solve the Maxwell equations in the time domain. Math. Comp. 76 (2007) 1801-1832
11. Berenger J.-P. A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114 (1994) 185-200
12. 3. Numer. Math. 35 3 (1980) 315-341
13. S. Pernet, Etude de méthodes d'ordre élevé pour résoudre les équations de Maxwell dans le domaine temporel. application à la détection et à la compatibilité électromagnétique, Doctorat de mathématiques appliquées de l'Université Dauphine-Paris IX, 2004.
14. Collino F., Fouquet T., and Joly P. Conservative space-time mesh refinement methods for the FDTD solution of Maxwell's equation. J. Comput. Phys. 211 (2006) 9-35
15. Piperno S. Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems. M2AN 40 5 (2006) 815-841
16. Nettesheim P., and Reich S. Symplectic multiple-time-stepping integrators for quantum-classical molecular dynamics. Lect. Notes Comput. Sci. Eng. 4 (1998) 412-420
17. M. Remaki, Méthodes numériques pour les equations de Maxwell instationnaires en milieu hétérogène, Doctorat de mathématiques appliquées de l'Ecole Nationale des Ponts et Chaussées, 1999.
18. Ern A., and Guermond J.-L. Discontinuous Galerkin methods for Friedrichs' systems. I. General theory. SIAM J. Numer. Anal. 44 2 (2006) 753-778
19. Dumbser M., Kaser M., and Toro E.F. An arbitrary high order Discontinuous Galerkin method for elastic waves on unstructured meshes V: Local time stepping and p-adaptivity. Geophys. J. Int. (2000) 142
20. Hesthaven J.S., and Warburton T. High order Nodal Discontinuous Galerkin methods for the Maxwell eigenvalue problem. R. Soc. Lond. Ser. A 362 (2004) 493-524
21. Ainsworth M. Dispersive and dissipative behaviour of high order Discontinuous Galerkin finite element methods. J. Comp. Phys. 198 (2004) 106-130