Free Access
Issue |
ESAIM: M2AN
Volume 40, Number 5, September-October 2006
|
|
---|---|---|
Page(s) | 815 - 841 | |
DOI | https://doi.org/10.1051/m2an:2006035 | |
Published online | 16 January 2007 |
- E. Bécache, P. Joly and J. Rodríguez, Space-time mesh refinement for elastodynamics. Numerical results. Comput. Method. Appl. M. 194 (2005) 355–366. [CrossRef] [Google Scholar]
- 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. [Google Scholar]
- 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). [Google Scholar]
- 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. [Google Scholar]
- 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). [Google Scholar]
- B. Cockburn and C.-W. Shu, Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 16 (2001) 173–261. [CrossRef] [MathSciNet] [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
- 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. [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
- J. Hesthaven and C. Teng, Stable spectral methods on tetrahedral elements. SIAM J. Sci. Comput. 21 (2000) 2352–2380. [CrossRef] [MathSciNet] [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
- T. Holder, B. Leimkuhler and S. Reich, Explicit variable step-size and time-reversible integration. Appl. Numer. Math. 39 (2001) 367–377. [Google Scholar]
- W. Huang and B. Leimkuhler, The adaptive Verlet method. SIAM J. Sci. Comput. 18 (1997) 239–256. [CrossRef] [MathSciNet] [Google Scholar]
- J.M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations. J. Comput. Phys. 151 (1999) 881–909. [CrossRef] [MathSciNet] [Google Scholar]
- 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. [Google Scholar]
- 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] [Google Scholar]
- 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. [Google Scholar]
- B. Leimkuhler, Reversible adaptive regularization: perturbed Kepler motion and classical atomic trajectories. Philos. Trans. Roy. Soc. London Ser. A 357 (1999) 1101–1134. [CrossRef] [Google Scholar]
- X. Lu and R. Schmid, Symplectic discretization for Maxwell's equations. J. Math. Computing 25 (2001) 1–21. [Google Scholar]
- 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. [Google Scholar]
- 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). [Google Scholar]
- M. Remaki, A new finite volume scheme for solving Maxwell's system. COMPEL 19 (2000) 913–931. [Google Scholar]
- 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] [Google Scholar]
- J.M. Sanz-Serna and M.P. Calvo, Numerical Hamiltonian Problems, Chapman and Hall, London, UK (1994). [Google Scholar]
- 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] [Google Scholar]
- 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. [Google Scholar]
- 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. [Google Scholar]
- 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. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.