Free Access
Volume 46, Number 5, September-October 2012
Page(s) 1225 - 1246
Published online 27 March 2012
  1. M.A. Botchev and J.G. Verwer, Numerical integration of damped maxwell equations. SIAM J. Sci. Comput. 31 (2009) 1322–1346. [CrossRef] [Google Scholar]
  2. A. Buffa and I. Perugia, Discontinuous Galerkin approximation of the Maxwell eigenproblem. SIAM J. Numer. Anal. 44 (2006) 2198–2226. [CrossRef] [MathSciNet] [Google Scholar]
  3. A. Catella, V. Dolean and S. Lanteri, An unconditionally stable discontinuous galerkin method for solving the 2-D time-domain Maxwell equations on unstructured triangular meshes. IEEE Trans. Magn. 44 (2008) 1250–1253. [CrossRef] [Google Scholar]
  4. B. Cockburn, G.E.G.E. Karniadakis and C.-W. Shu Eds., Discontinuous Galerkin methods. Theory, computation and applications. Springer-Verlag, Berlin (2000) [Google Scholar]
  5. G. Cohen, X. Ferrieres and S. Pernet, A spatial high order hexahedral discontinuous Galerkin method to solve Maxwell’s equations in time-domain. J. Comput. Phys. 217 (2006) 340–363. [CrossRef] [MathSciNet] [Google Scholar]
  6. J. Diaz and M.J. Grote, Energy conserving explicit local time-stepping for second-order wave equations. SIAM J. Sci. Comput. 31 (2009) 1985–2014. [CrossRef] [Google Scholar]
  7. V. Dolean, H. Fahs, L. Fezoui and S. Lanteri, Locally implicit discontinuous Galerkin method for time domain electromagnetics. J. Comput. Phys. 229 (2010) 512–526. [CrossRef] [MathSciNet] [Google Scholar]
  8. H. Fahs, Development of a hp-like discontinuous Galerkin time-domain method on non-conforming simplicial meshes for electromagnetic wave propagation. Int. J. Numer. Anal. Mod. 6 (2009) 193–216. [Google Scholar]
  9. I. Faragó, Á. Havasi and Z. Zlatev, Richardson-extrapolated sequential splitting and its application. J. Comput. Appl. Math. 234 (2010) 3283–3302. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  11. M.J. Grote and T. Mitkova, Explicit local time stepping methods for Maxwell’s equations. J. Comput. Appl. Math. 234 (2010) 3283–3302. [CrossRef] [MathSciNet] [Google Scholar]
  12. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II – Stiff and Differential-Algebraic problems, 2nd edition. Springer-Verlag, Berlin (1996). [Google Scholar]
  13. E. Hairer, C. Lubich and G. Wanner, Geometric Numerical Integration, 2nd edition. Springer-Verlag, Berlin (2002). [Google Scholar]
  14. 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]
  15. J. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods. Springer (2008). [Google Scholar]
  16. W. Hundsdorfer and J.G. Verwer, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations. Springer-Verlag, Berlin (2003). [Google Scholar]
  17. J. Jin, The Finite Element Method in Electromagnetics, 2nd edition. Wiley-IEEE Press (2002). [Google Scholar]
  18. G.Yu. Kulikov, Local theory of extrapolation methods. Numer. Algorithm 53 (2010) 321-342 [CrossRef] [Google Scholar]
  19. R.I. McLachlan, On the numerical integration of ordinary differential equations by symmetric composition methods. SIAM J. Sci. Comput. 16 (1995) 151–168. [CrossRef] [MathSciNet] [Google Scholar]
  20. E. Montseny, S. Pernet, X. Ferrires and G. Cohen, Dissipative terms and local time-stepping improvements in a spatial high order Discontinuous Galerkin scheme for the time-domain Maxwell’s equations. J. Comput. Phys. 227 (2008) 6795–6820. [CrossRef] [MathSciNet] [Google Scholar]
  21. J.C. Nédélec, Mixed finite elements in R3. Numer. Math. 35 (1980) 315–341. [CrossRef] [MathSciNet] [Google Scholar]
  22. J.C. Nédélec, A new dfamily of mixed finite elements in R3. Numer. Math. 50 (1986) 57–81. [CrossRef] [MathSciNet] [Google Scholar]
  23. S. Piperno, Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problem. ESAIM : M2AN 40 (2006) 815–841. [CrossRef] [EDP Sciences] [Google Scholar]
  24. M. Remaki, A new finite volume scheme for solving Maxwell’s system. Compel 19 (2000) 913-931. [Google Scholar]
  25. M. Suzuki, Fractal decomposition of exponential operators with applications to many-body theories and Monte-Carlo simulations. Phys. Lett. A 146 (1990) 319–323. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  26. A. Taube, M. Dumbser, C.D. Munz and R. Schneider, A high order discontinuous Galerkin method with local time stepping for the Maxwell equations. Int. J. Numer. Model. 22 (2009) 77–103. [CrossRef] [Google Scholar]
  27. J.G. Verwer, Component splitting for semi-discrete Maxwell equations. BIT Numer. Math. 51 (2011) 427–445. [Google Scholar]
  28. J.G Verwer, Composition methods, Maxwell’s and source term. CWI Technical report (2010); Available at [Google Scholar]
  29. J.G. Verwer and M.A. Botchev, Unconditionaly stable integration of Maxwell’s equations. Linear Algebra Appl. 431 (2009) 300–317. [CrossRef] [MathSciNet] [Google Scholar]
  30. J.G. Verwer and H.B. de Vries, Global extrapolation of a first order splitting method. SIAM J. Sci. Stat. Comput. 6 (1985) 771–780. [CrossRef] [Google Scholar]
  31. K.S. Yee, Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propag. 14 (1966) 302–307. [NASA ADS] [CrossRef] [Google Scholar]
  32. H. Yoshida, Construction of higher order symplectic integrators. Phys. Lett. A 150 (1990) 262–268. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]

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