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Volumn 40, Issue 5, 2006, Pages 815-841

Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems

Author keywords

Acoustics; Discontinuous Galerkin methods; Energy conservation; Maxwell's system; Second order accuracy; Symplectic schemes; Waves

Indexed keywords


EID: 33846453567     PISSN: 0764583X     EISSN: 12903841     Source Type: Journal    
DOI: 10.1051/m2an:2006035     Document Type: Article
Times cited : (88)

References (33)
  • 1
    • 10444271003 scopus 로고    scopus 로고
    • Space-time mesh refinement for elastodynamics. Numerical results
    • E. Bécache, P. Joly and J. Rodríguez, Space-time mesh refinement for elastodynamics. Numerical results. Comput. Method. Appl. M. 194 (2005) 355-366.
    • (2005) Comput. Method. Appl. M , vol.194 , pp. 355-366
    • Bécache, E.1    Joly, P.2    Rodríguez, J.3
  • 6
    • 0000076512 scopus 로고    scopus 로고
    • Runge-Kutta discontinuous Galerkin methods for convection-dominated problems
    • B. Cockburn and C.-W. Shu, Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 16 (2001) 173-261.
    • (2001) J. Sci. Comput , vol.16 , pp. 173-261
    • Cockburn, B.1    Shu, C.-W.2
  • 7
    • 25444469411 scopus 로고    scopus 로고
    • Conservative space-time mesh refinement methods for the FDTD solution of Maxwell's equations
    • 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.
    • (2006) J. Comput. Phys , vol.211 , pp. 9-35
    • Collino, F.1    Fouquet, T.2    Joly, P.3
  • 8
    • 0035683345 scopus 로고    scopus 로고
    • High resolution schemes for conservation laws with locally varying time steps
    • C. Dawson and R. Kirby, High resolution schemes for conservation laws with locally varying time steps. SIAM J. Sci. Comput. 22 (2001) 2256-2281.
    • (2001) SIAM J. Sci. Comput , vol.22 , pp. 2256-2281
    • Dawson, C.1    Kirby, R.2
  • 9
    • 0031539343 scopus 로고    scopus 로고
    • Éléments finis d'arête et condensation de masse pour les équations de Maxwell: Le cas de dimension 3
    • 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.
    • (1997) C. R. Acad. Sci. Paris Sér. I Math , vol.325 , pp. 1217-1222
    • Elmkies, A.1    Joly, P.2
  • 10
    • 30344457009 scopus 로고    scopus 로고
    • Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes
    • 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.
    • (2005) ESAIM: M2AN , vol.39 , pp. 1149-1176
    • Fezoui, L.1    Lanteri, S.2    Lohrengel, S.3    Piperno, S.4
  • 11
    • 0032737545 scopus 로고    scopus 로고
    • Symplectic variable step size integration for N-body problems
    • 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.
    • (1999) Appl. Numer. Math , vol.29 , pp. 19-30
    • Hardy, D.J.1    Okunbor, D.I.2    Skeel, R.D.3
  • 12
    • 0034503732 scopus 로고    scopus 로고
    • Stable spectral methods on tetrahedral elements
    • J. Hesthaven and C. Teng, Stable spectral methods on tetrahedral elements. SIAM J. Sci. Comput. 21 (2000) 2352-2380.
    • (2000) SIAM J. Sci. Comput , vol.21 , pp. 2352-2380
    • Hesthaven, J.1    Teng, C.2
  • 13
    • 0036740992 scopus 로고    scopus 로고
    • Nodal high-order methods on unstructured grids. I: Time-domain solution of Maxwell's equations
    • 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.
    • (2002) J. Comput. Phys , vol.181 , pp. 186-221
    • Hesthaven, J.1    Warburton, T.2
  • 14
    • 1642320193 scopus 로고    scopus 로고
    • High-order nodal discontinuous Galerkin methods for the maxwell eigenvalue problem
    • 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.
    • (2004) Philos. Trans. Roy. Soc. London Ser. A , vol.362 , pp. 493-524
    • Hesthaven, J.1    Warburton, T.2
  • 15
    • 0031234003 scopus 로고    scopus 로고
    • Time-domain simulation of electromagnetic field using a symplectic integrator
    • 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.
    • (1997) IEEE Microwave Guided Wave Lett , vol.7 , pp. 279-281
    • Hirono, T.1    Lui, W.W.2    Yokoyama, K.3
  • 16
    • 0032182706 scopus 로고    scopus 로고
    • Stability and numerical dispersion of symplectic fourth-order time-domain schemes for optical field simulation
    • 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.
    • (1998) J. Lightwave Tech , vol.16 , pp. 1915-1920
    • Hirono, T.1    Lui, W.W.2    Yokoyama, K.3    Seki, S.4
  • 17
    • 0035546021 scopus 로고    scopus 로고
    • Explicit variable step-size and time-reversible integration
    • T. Holder, B. Leimkuhler and S. Reich, Explicit variable step-size and time-reversible integration. Appl. Numer. Math. 39 (2001) 367-377.
    • (2001) Appl. Numer. Math , vol.39 , pp. 367-377
    • Holder, T.1    Leimkuhler, B.2    Reich, S.3
  • 19
    • 0000397429 scopus 로고    scopus 로고
    • Mimetic discretizations for Maxwell's equations
    • J.M. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations. J. Comput. Phys. 151 (1999) 881-909.
    • (1999) J. Comput. Phys , vol.151 , pp. 881-909
    • Hyman, J.M.1    Shashkov, M.2
  • 20
    • 0010732943 scopus 로고    scopus 로고
    • A new second order 3D edge element on tetrahedra for time dependent Maxwell's equations
    • A. Bermudez, D. Gomez, C. Hazard, P. Joly, J.-E. Roberts Eds, SIAM, Santiago de Compostella, Spain
    • 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.
    • (2000) Proc. Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation , pp. 842-847
    • Joly, P.1    Poirier, C.2
  • 21
    • 0037216570 scopus 로고    scopus 로고
    • Additive Runge-Kutta schemes for convection-diffusion-reaction equations
    • C.A. Kennedy and M.H. Carpenter, Additive Runge-Kutta schemes for convection-diffusion-reaction equations. Appl. Numer. Math. 44 (2003) 139-181.
    • (2003) Appl. Numer. Math , vol.44 , pp. 139-181
    • Kennedy, C.A.1    Carpenter, M.H.2
  • 22
    • 33846459217 scopus 로고    scopus 로고
    • 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.
    • 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
    • 0346968520 scopus 로고    scopus 로고
    • Reversible adaptive regularization: Perturbed Kepler motion and classical atomic trajectories
    • B. Leimkuhler, Reversible adaptive regularization: perturbed Kepler motion and classical atomic trajectories. Philos. Trans. Roy. Soc. London Ser. A 357 (1999) 1101-1134.
    • (1999) Philos. Trans. Roy. Soc. London Ser. A , vol.357 , pp. 1101-1134
    • Leimkuhler, B.1
  • 24
    • 33846417820 scopus 로고    scopus 로고
    • Symplectic discretization for Maxwell's equations
    • X. Lu and R. Schmid, Symplectic discretization for Maxwell's equations. J. Math. Computing 25 (2001) 1-21.
    • (2001) J. Math. Computing , vol.25 , pp. 1-21
    • Lu, X.1    Schmid, R.2
  • 26
    • 33846405087 scopus 로고    scopus 로고
    • An efficient local time stepping-discontinuous Galerkin scheme for adaptive transient computations
    • Technical report 2001-13, Rensselaer Polytechnic Institute
    • 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).
    • (2001)
    • Remacle, J.-F.1    Pinchedez, K.2    Flaherty, J.E.3    Shephard, M.S.4
  • 27
    • 0346425022 scopus 로고    scopus 로고
    • A new finite volume scheme for solving Maxwell's system
    • M. Remaki, A new finite volume scheme for solving Maxwell's system. COMPEL 19 (2000) 913-931.
    • (2000) COMPEL , vol.19 , pp. 913-931
    • Remaki, M.1
  • 28
    • 4344562945 scopus 로고    scopus 로고
    • High-order symplectic integration methods for finite element solutions to time dependent Maxwell equations
    • 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.
    • (2004) IEEE Trans. Antennas Propagation , vol.52 , pp. 2190-2195
    • Rieben, R.1    White, D.2    Rodrigue, G.3
  • 30
    • 0030138604 scopus 로고    scopus 로고
    • A comparative study of characteristic-based algorithms for the Maxwell equations
    • J. Shang and R. Fithen, A comparative study of characteristic-based algorithms for the Maxwell equations. J. Comput. Phys. 125 (1996) 378-394.
    • (1996) J. Comput. Phys , vol.125 , pp. 378-394
    • Shang, J.1    Fithen, R.2
  • 31
    • 0005683767 scopus 로고    scopus 로고
    • Application of the discontinuous Galerkin method to Maxwell's equations using unstructured polymorphic hp-finite elements
    • B. Cockburn, G.E. Karniadakis, C.-W. Shu Eds, Springer-Verlag, Berlin
    • 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.
    • (2000) Discontinuous Galerkin methods. Theory, computation and applications 11 Lect. Notes Computat. Sci. Engrg , pp. 451-458
    • Warburton, T.1
  • 33
    • 84894021661 scopus 로고
    • Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media
    • 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.
    • (1966) IEEE Trans. Antennas Propagation , vol.16 , pp. 302-307
    • Yee, K.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.