Free access
Issue
ESAIM: M2AN
Volume 39, Number 6, November-December 2005
Page(s) 1149 - 1176
DOI http://dx.doi.org/10.1051/m2an:2005049
Published online 15 November 2005
  1. F. Bourdel, P.-A. Mazet and P. Helluy, Resolution of the non-stationary or harmonic Maxwell equations by a discontinuous finite element method. Application to an E.M.I. (electromagnetic impulse) case. Comput. Method Appl. Sci. Engrg. (1991) 405–422.
  2. N. Canouet, L. Fezoui and S. Piperno, A discontinuous galerkin method for 3d maxwell's equation on non-conforming grids, in Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation. G.C. Cohen Ed., Springer, Jyvskyl, Finland (2003) 389–394.
  3. P. Ciarlet, The Finite Element Method for Elliptic Problems. North Holland-Elsevier Science Publishers, Amsterdam, New York, Oxford (1978).
  4. J.-P. Cioni, L. Fezoui, L. Anne and F. Poupaud, A parallel FVTD Maxwell solver using 3D unstructured meshes, in 13th annual review of progress in applied computational electromagnetics, Monterey, California (1997) 359–365.
  5. B. Cockburn, G.E. Karniadakis and C.-W. Shu, Eds., Discontinuous Galerkin methods. Theory, computation and applications. Lect. Notes Comput. Sci. Eng. 11 (2000).
  6. B. Cockburn, F. Li and C.-W. Shu, Locally divergence-free discontinuous galerkin methods for the maxwell equations. J. Comput. Phys. 194 (2004) 588–610. [CrossRef] [MathSciNet]
  7. A. Elmkies and P. Joly, Éléments finis d'arête et condensation de masse pour les équations de Maxwell: le cas de dimension 3. C. R. Acad. Sci. Paris Sér. I Math. 325 (1997) 1217–1222.
  8. R. Eymard, T. Gallouët and R. Herbin, The finite volume method, Handbook Numer. Anal., North Holland-Elsevier Science Publishers, Amsterdam, New York, Oxford 7-3 (2000).
  9. R.S. Falk and G.R. Richter, Explicit finite element methods for symmetric hyperbolic equations. SIAM J. Numer. Anal. 36 (1998) 935–952. [CrossRef]
  10. J. Hesthaven and C. Teng, Stable spectral methods on tetrahedral elements. SIAM J. Sci. Comput. 21 (2000) 2352–2380. [CrossRef] [MathSciNet]
  11. J. Hesthaven and T. Warburton, Nodal high-order methods on unstructured grids. I: Time-domain solution of Maxwell's equations. J. Comput. Phys. 181 (2002) 186–221. [CrossRef] [MathSciNet]
  12. J. Hesthaven and T. Warburton, High-order nodal discontinuous galerkin methods for the maxwell eigenvalue problem. Philos. Trans. Roy. Soc. London Ser. A 362 (2004) 493–524. [CrossRef]
  13. J.M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations. J. Comput. Phys. 151 (1999) 881–909. [CrossRef] [MathSciNet]
  14. P. Joly and C. Poirier, A new second order 3D edge element on tetrahedra for time dependent Maxwell's equations, in Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation, A. Bermudez, D. Gomez, C. Hazard, P. Joly, J.-E. Roberts, Eds., SIAM, Santiago de Compostella, Spain (2000) 842–847.
  15. D.A. Kopriva, S.L. Woodruff and M.Y. Hussaini, Discontinuous spectral element approximation of Maxwell's equations, in Discontinuous Galerkin methods. Theory, computation and applications., B. Cockburn and G.E. Karniadakis, C.-W. Shu, Eds. Lect. Notes Comput. Sci. Eng. 11 (2000) 355–362.
  16. D. Kröner, M. Rokyta and M. Wierse, A Lax-Wendroff type theorem for upwind finite volume schemes in 2-D. J. Numer. Math. 4 (1996) 279–292.
  17. S. Lohrengel and M. Remaki, A FV scheme for Maxwell's equations: Convergence analysis on unstructured meshes, in Finite Volumes for Complex Applications III, R. Herbin, D. Kröner, Eds., Hermes Penton Science, London, Porquerolles, France (2002) 219–226.
  18. F. Poupaud and M. Remaki, Existence and uniqueness of the Maxwell's system solutions in heterogeneous and irregular media. C. R. Acad. Sci. Paris Sér. I Math. 330 (2000) 99–103.
  19. S. Piperno, L2-stability of the upwind first order finite volume scheme for the Maxwell equation in two and three dimensions on arbitrary unstructured meshes. ESAIM: M2AN 34 (2000) 139–158. [CrossRef] [EDP Sciences]
  20. S. Piperno, Schémas en éléments finis discontinus localement raffinés en espace et en temps pour les équations de Maxwell 1D. INRIA Research report 4986 (2003).
  21. S. Piperno, M. Remaki and L. Fezoui, A non-diffusive finite volume scheme for the 3D Maxwell equations on unstructured meshes. SIAM J. Numer. Anal. 39 (2002) 2089–2108. [CrossRef] [MathSciNet]
  22. M. Remaki, A new finite volume scheme for solving Maxwell's system. COMPEL 19 (2000) 913–931.
  23. J. Shang and R. Fithen, A comparative study of characteristic-based algorithms for the Maxwell equations. J. Comput. Phys. 125 (1996) 378–394. [CrossRef] [MathSciNet]
  24. A. Taflove, Re-inventing electromagnetics: supercomputing solution of Maxwell's equations via direct time integration on space grids. AIAA paper 92–0333 (1992).
  25. J.-P. Vila, Convergence and error estimates in finite volume schemes for general multidimensional scalar conservation laws. I. Explicit monotone schemes. RAIRO Modél. Math. Anal. Numér. 28 (1994) 267–295. [MathSciNet]
  26. T. Warburton, Application of the discontinuous Galerkin method to Maxwell's equations using unstructured polymorphic hp-finite elements, in Discontinuous Galerkin methods. Theory, computation and applications, B. Cockburn, G.E. Karniadakis, C.-W. Shu, Eds. Lect. Notes Comput. Sci. Eng. 11 (2000) 451–458.
  27. K.S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE T. Antenn. Prop. AP-16 (1966) 302–307.

Recommended for you