메뉴 건너뛰기




Volumn 16, Issue 4, 2008, Pages 507-530

Computational aspects of the Discontinuous Galerkin method for the wave equation

Author keywords

Discontinuous Galerkin method; Time integration methods; Wave propagation

Indexed keywords


EID: 58149263269     PISSN: 0218396X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218396X08003762     Document Type: Article
Times cited : (10)

References (31)
  • 1
    • 58149250017 scopus 로고    scopus 로고
    • W. Reed and T. Hill, Triangular mesh methods for the neutron transport equation, Technical Report LA-UR-73-479, Los Alamos National Laboratory, Los Alamos, New Mexico, USA, 1973.
    • W. Reed and T. Hill, Triangular mesh methods for the neutron transport equation, Technical Report LA-UR-73-479, Los Alamos National Laboratory, Los Alamos, New Mexico, USA, 1973.
  • 3
    • 84966238599 scopus 로고
    • An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation
    • C. Johnson and J. Pitkäranta, An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation, Math. Comput. 46 (1986) 285-312.
    • (1986) Math. Comput , vol.46 , pp. 285-312
    • Johnson, C.1    Pitkäranta, J.2
  • 4
    • 0039756618 scopus 로고    scopus 로고
    • A space-time finite element method for the nonlinear Schrödinger equation: The discontinuous Galerkin method
    • O. Karakashian and C. Makridakis, A space-time finite element method for the nonlinear Schrödinger equation: The discontinuous Galerkin method, Math. Comp. 67 (1998) 479-499.
    • (1998) Math. Comp , vol.67 , pp. 479-499
    • Karakashian, O.1    Makridakis, C.2
  • 5
    • 30344445666 scopus 로고    scopus 로고
    • Discontinuous Galerkin time domain (DGTD) methods for the study of 2-D waveguide-coupled microring resonators
    • X. Ji, T. Lu, W. Cai and P. Zhang, Discontinuous Galerkin time domain (DGTD) methods for the study of 2-D waveguide-coupled microring resonators, J. Light. Technol. 23 (2005) 3864-3874.
    • (2005) J. Light. Technol , vol.23 , pp. 3864-3874
    • Ji, X.1    Lu, T.2    Cai, W.3    Zhang, P.4
  • 6
    • 33645905751 scopus 로고    scopus 로고
    • Discontinuous Galerkin methods with plane waves for the displacement-based acoustic equation
    • G. Gabard, Discontinuous Galerkin methods with plane waves for the displacement-based acoustic equation, Int. J. Numer. Meth. Eng. 66 (2006) 549-569.
    • (2006) Int. J. Numer. Meth. Eng , vol.66 , pp. 549-569
    • Gabard, G.1
  • 8
    • 0036740992 scopus 로고    scopus 로고
    • Nodal high-order methods on unstructured grids I. Time-domain solution of Maxwell's equations
    • J. S. 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.S.1    Warburton, T.2
  • 9
    • 17444409296 scopus 로고    scopus 로고
    • A discontinuous Galerkin method for linear symmetric hyperbolic systems in inhomogeneous media
    • P. Monk and G. R. Richter, A discontinuous Galerkin method for linear symmetric hyperbolic systems in inhomogeneous media, J. Sci. Comput. 22-23 (2005) 443-477.
    • (2005) J. Sci. Comput , vol.22-23 , pp. 443-477
    • Monk, P.1    Richter, G.R.2
  • 10
    • 0000107216 scopus 로고    scopus 로고
    • Explicit finite element methods for symmetric hyperbolic equations
    • R. S. Falk and G. R. Richter, Explicit finite element methods for symmetric hyperbolic equations, Siam J. Numer. Anal. 36 (1999) 935-952.
    • (1999) Siam J. Numer. Anal , vol.36 , pp. 935-952
    • Falk, R.S.1    Richter, G.R.2
  • 11
    • 37849013422 scopus 로고    scopus 로고
    • Discontinuous Galerkin finite element method for the wave equation
    • M. J. Grote, A. Schneebeli and D. Schötzau, Discontinuous Galerkin finite element method for the wave equation, SIAM J. Numer. Anal. 44 (2005) 2408-2431.
    • (2005) SIAM J. Numer. Anal , vol.44 , pp. 2408-2431
    • Grote, M.J.1    Schneebeli, A.2    Schötzau, D.3
  • 12
    • 49049151571 scopus 로고
    • Flux vector splitting of the inviscid gas-dynamic equations with applications to the finite difference methods
    • J. Steger and R. F. Warming, Flux vector splitting of the inviscid gas-dynamic equations with applications to the finite difference methods, J. Comput. Phys. 40 (1981) 263-293.
    • (1981) J. Comput. Phys , vol.40 , pp. 263-293
    • Steger, J.1    Warming, R.F.2
  • 13
    • 17444410814 scopus 로고    scopus 로고
    • Selecting the numerical flux in discontinuous Galerkin methods for diffusion problems
    • R. M. Kirby and G. E. Karniadakis, Selecting the numerical flux in discontinuous Galerkin methods for diffusion problems, J. Sci. Comput. 22-23 (2005) 385-411.
    • (2005) J. Sci. Comput , vol.22-23 , pp. 385-411
    • Kirby, R.M.1    Karniadakis, G.E.2
  • 14
    • 85085773665 scopus 로고    scopus 로고
    • Two-dimensional wave analysis of the discontinuous Galerkin method with non-uniform grids and boundary conditions
    • AIAA-2002-2514, 17-19 June, Breckenridge, Colorado
    • F. Q. Hu and H. L. Atkins, Two-dimensional wave analysis of the discontinuous Galerkin method with non-uniform grids and boundary conditions, AIAA-2002-2514, 8th Aeroacoustics Conf., 17-19 June 2002, Breckenridge, Colorado.
    • (2002) 8th Aeroacoustics Conf
    • Hu, F.Q.1    Atkins, H.L.2
  • 15
    • 0000458188 scopus 로고    scopus 로고
    • An analysis of the discontinuous Galerkin method for wave propagation problems
    • F. Q. Hu, M. Y. Hussaini and P. Rasetarinera, An analysis of the discontinuous Galerkin method for wave propagation problems, J. Comput. Phys. 151 (1999) 921-946.
    • (1999) J. Comput. Phys , vol.151 , pp. 921-946
    • Hu, F.Q.1    Hussaini, M.Y.2    Rasetarinera, P.3
  • 16
    • 33645407168 scopus 로고    scopus 로고
    • Time-domain parallel simulation of heterogeneous wave propagation on unstructured grids using explicit, nondiffusive, discontinuous Galerkin methods
    • M. Bernacki, S. Lanteri and S. Piperno, Time-domain parallel simulation of heterogeneous wave propagation on unstructured grids using explicit, nondiffusive, discontinuous Galerkin methods, J. Comput. Acoust. 14 (2006) 57-81.
    • (2006) J. Comput. Acoust , vol.14 , pp. 57-81
    • Bernacki, M.1    Lanteri, S.2    Piperno, S.3
  • 17
    • 84980082640 scopus 로고
    • Symmetric positive linear differential equations
    • K. Friedrichs, Symmetric positive linear differential equations, Comm. Pure Appl. Math. 11 (1958) 333-418
    • (1958) Comm. Pure Appl. Math , vol.11 , pp. 333-418
    • Friedrichs, K.1
  • 18
    • 84966208271 scopus 로고
    • Absorbing boundary conditions for the numerical simulation of waves
    • B. Engquist and A. Majda, Absorbing boundary conditions for the numerical simulation of waves, Math. Comput. 31 (1977) 629-651.
    • (1977) Math. Comput , vol.31 , pp. 629-651
    • Engquist, B.1    Majda, A.2
  • 19
    • 0000185847 scopus 로고    scopus 로고
    • From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex
    • J. S. Hesthaven, From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex, SIAM J. Numer. Anal. 35 (1998) 655-676.
    • (1998) SIAM J. Numer. Anal , vol.35 , pp. 655-676
    • Hesthaven, J.S.1
  • 21
    • 0026371189 scopus 로고
    • Spectral methods on triangles and other domains
    • M. Dubiner, Spectral methods on triangles and other domains, J. Sci. Comp. 6 (1991) 345-390.
    • (1991) J. Sci. Comp , vol.6 , pp. 345-390
    • Dubiner, M.1
  • 23
    • 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 (2002) 139-181.
    • (2002) Appl. Numer. Math , vol.4 , Issue.4 , pp. 139-181
    • Kennedy, C.A.1    Carpenter, M.H.2
  • 25
    • 0001097696 scopus 로고
    • Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes
    • AIAA Paper 81-1259, Palo Alto, California
    • A. Jameson, W. Schmidt and E. Turkel, Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes, AIAA Paper 81-1259, AIAA 14th Fluid and Plasma Dynamics Conf., 1981, Palo Alto, California.
    • (1981) AIAA 14th Fluid and Plasma Dynamics Conf
    • Jameson, A.1    Schmidt, W.2    Turkel, E.3
  • 30
    • 0041909738 scopus 로고    scopus 로고
    • Higher order triangular finite elements with mass lumping for the wave equation
    • G. C. Cohen, P. Joly, J. E. Roberts and N. Tordjman, Higher order triangular finite elements with mass lumping for the wave equation, SLAM J. Numer. Anal. 38 (2001) 2047-2078.
    • (2001) SLAM J. Numer. Anal , vol.38 , pp. 2047-2078
    • Cohen, G.C.1    Joly, P.2    Roberts, J.E.3    Tordjman, N.4
  • 31
    • 84966227504 scopus 로고
    • An optimal-order estimate for the discontinuous Galerkin method
    • G. R. Richter, An optimal-order estimate for the discontinuous Galerkin method, Math. Comput. 50 (1988) 75-88.
    • (1988) Math. Comput , vol.50 , pp. 75-88
    • Richter, G.R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.