Free access
Issue
ESAIM: M2AN
Volume 40, Number 5, September-October 2006
Page(s) 815 - 841
DOI http://dx.doi.org/10.1051/m2an:2006035
Published online 16 January 2007
  1. E. Bécache, P. Joly and J. Rodríguez, Space-time mesh refinement for elastodynamics. Numerical results. Comput. Method. Appl. M. 194 (2005) 355–366. [CrossRef]
  2. N. Canouet, L. Fezoui and S. Piperno, A new Discontinuous Galerkin method for 3D Maxwell's equations on non-conforming grids, in Proc. Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation, G.C. Cohen et al. Ed., Springer, Jyväskylä, Finland (2003) 389–394.
  3. C. Chauviere, J.S. Hesthaven, A. Kanevsky and T. Warburton, High-order localized time integration for grid-induced stiffness, in Proc. Second M.I.T. Conference on Computational Fluid and Solid Mechanics, Cambridge, MA (2003).
  4. J.-P. Cioni, L. Fezoui, L. Anne and F. Poupaud, A parallel FVTD Maxwell solver using 3D unstructured meshes, in Proc. 13th annual review of progress in applied computational electromagnetics, Monterey, California (1997) 359–365.
  5. B. Cockburn, G.E. Karniadakis, C.-W. Shu Eds., Discontinuous Galerkin methods. Theory, computation and applications 11 Lect. Notes Comput. Sci. Engrg., Springer-Verlag, Berlin (2000).
  6. B. Cockburn and C.-W. Shu, Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 16 (2001) 173–261. [CrossRef] [MathSciNet]
  7. F. Collino, T. Fouquet and P. Joly, Conservative space-time mesh refinement methods for the FDTD solution of Maxwell's equations. J. Comput. Phys. 211 (2006) 9–35. [CrossRef] [MathSciNet]
  8. C. Dawson and R. Kirby, High resolution schemes for conservation laws with locally varying time steps. SIAM J. Sci. Comput. 22 (2001) 2256–2281. [CrossRef]
  9. 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.
  10. L. Fezoui, S. Lanteri, S. Lohrengel and S. Piperno, Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes. ESAIM: M2AN 39 (2005) 1149–1176. [CrossRef] [EDP Sciences]
  11. D.J. Hardy, D.I. Okunbor and R.D. Skeel, Symplectic variable step size integration for N-body problems. Appl. Numer. Math. 29 (1999) 19–30. [CrossRef] [MathSciNet]
  12. J. Hesthaven and C. Teng, Stable spectral methods on tetrahedral elements. SIAM J. Sci. Comput. 21 (2000) 2352–2380. [CrossRef] [MathSciNet]
  13. 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]
  14. 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]
  15. T. Hirono, W.W. Lui and K. Yokoyama, Time-domain simulation of electromagnetic field using a symplectic integrator. IEEE Microwave Guided Wave Lett. 7 (1997) 279–281. [CrossRef]
  16. T. Hirono, W.W. Lui, K. Yokoyama and S. Seki, Stability and numerical dispersion of symplectic fourth-order time-domain schemes for optical field simulation. J. Lightwave Tech. 16 (1998) 1915–1920. [CrossRef]
  17. T. Holder, B. Leimkuhler and S. Reich, Explicit variable step-size and time-reversible integration. Appl. Numer. Math. 39 (2001) 367–377. [CrossRef] [MathSciNet]
  18. W. Huang and B. Leimkuhler, The adaptive Verlet method. SIAM J. Sci. Comput. 18 (1997) 239–256. [CrossRef] [MathSciNet]
  19. J.M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations. J. Comput. Phys. 151 (1999) 881–909. [CrossRef] [MathSciNet]
  20. P. Joly and C. Poirier, A new second order 3D edge element on tetrahedra for time dependent Maxwell's equations, in Proc. 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.
  21. C.A. Kennedy and M.H. Carpenter, Additive Runge-Kutta schemes for convection-diffusion-reaction equations. Appl. Numer. Math. 44 (2003) 139–181. [CrossRef] [MathSciNet]
  22. 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 11 Lect. Notes Comput. Sci. Engrg. B. Cockburn, G.E. Karniadakis, C.-W. Shu Eds., Springer-Verlag, Berlin (2000) 355–362.
  23. B. Leimkuhler, Reversible adaptive regularization: perturbed Kepler motion and classical atomic trajectories. Philos. Trans. Roy. Soc. London Ser. A 357 (1999) 1101–1134. [CrossRef]
  24. X. Lu and R. Schmid, Symplectic discretization for Maxwell's equations. J. Math. Computing 25 (2001) 1–21.
  25. S. Piperno, Fully explicit DGTD methods for wave propagation on time-and-space locally refined grids, in Proc. Seventh International Conference on Mathematical and Numerical Aspects of Wave Propagation, Providence, RI (2005) 402–404.
  26. J.-F. Remacle, K. Pinchedez, J.E. Flaherty and M.S. Shephard, An efficient local time stepping-discontinuous Galerkin scheme for adaptive transient computations. Technical report 2001-13, Rensselaer Polytechnic Institute (2001).
  27. M. Remaki, A new finite volume scheme for solving Maxwell's system. COMPEL 19 (2000) 913–931.
  28. R. Rieben, D. White and G. Rodrigue, High-order symplectic integration methods for finite element solutions to time dependent Maxwell equations. IEEE Trans. Antennas Propagation 52 (2004) 2190–2195. [CrossRef]
  29. J.M. Sanz-Serna and M.P. Calvo, Numerical Hamiltonian Problems, Chapman and Hall, London, UK (1994).
  30. 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]
  31. 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 11 Lect. Notes Computat. Sci. Engrg., B. Cockburn, G.E. Karniadakis, C.-W. Shu Eds., Springer-Verlag, Berlin (2000) 451–458.
  32. T. Warburton, Spurious solutions and the Discontinuous Galerkin method on non-conforming meshes, in Proc. Seventh International Conference on Mathematical and Numerical Aspects of Wave Propagation, Providence, RI (2005) 405–407.
  33. K.S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Trans. Antennas Propagation 16 (1966) 302–307.

Recommended for you