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Volumn 6, Issue 2, 2009, Pages 193-216

Development of a hp-like discontinuous Galerkin time-domain method on non-conforming simplical meshes for electromagnetic wave propagation

(1)  Fahs, Hassan a  

a INRIA   (France)

Author keywords

Computational electromagnetism; Discontinuous Galerkin method; hp like method; Maxwell's equations; Non conforming triangular mesh

Indexed keywords


EID: 62749143547     PISSN: 17055105     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (19)

References (36)
  • 1
    • 32944481626 scopus 로고    scopus 로고
    • Bounded error schemes for the wave equation on complex domains
    • S. Abarbanel, A. Ditkowski and A. Yefet, Bounded error schemes for the wave equation on complex domains, J. Sci. Comput., 26(2006), 67-81.
    • (2006) J. Sci. Comput , vol.26 , pp. 67-81
    • Abarbanel, S.1    Ditkowski, A.2    Yefet, A.3
  • 2
    • 33646377393 scopus 로고    scopus 로고
    • Parallel unstructured mesh solvers for heterogeneous wave propagation problems
    • M. Bernacki, L. Fezoui, S. Lanteri and S. Piperno, Parallel unstructured mesh solvers for heterogeneous wave propagation problems, Appl. Math. Model., 30(2006), 744-763.
    • (2006) Appl. Math. Model , vol.30 , pp. 744-763
    • Bernacki, M.1    Fezoui, L.2    Lanteri, S.3    Piperno, S.4
  • 3
    • 0025399769 scopus 로고
    • Solving Maxwell equations in a closed cavity, and the question of spurious modes
    • A. Bossavit, Solving Maxwell equations in a closed cavity, and the question of spurious modes, IEEE Trans. Magnetics, 26(1990), 702-705.
    • (1990) IEEE Trans. Magnetics , vol.26 , pp. 702-705
    • Bossavit, A.1
  • 4
    • 0042858321 scopus 로고    scopus 로고
    • 2D case
    • An upwinding embedded boundary method for Maxwell's equations in media with material interfaces
    • W. Cai and S. Deng, An upwinding embedded boundary method for Maxwell's equations in media with material interfaces: 2D case, J. Comput. Phys., 190(2003), 159-183.
    • (2003) J. Comput. Phys , vol.190 , pp. 159-183
    • Cai, W.1    Deng, S.2
  • 5
    • 25444433326 scopus 로고    scopus 로고
    • Discontinuous Galerkin time-domain solution of Maxwell's equations on locally-refined nonconforming cartesian grids
    • N. Canouet, L. Fezoui and S. Piperno, Discontinuous Galerkin time-domain solution of Maxwell's equations on locally-refined nonconforming cartesian grids, COMPEL, 24(2005), 1381-1401.
    • (2005) COMPEL , vol.24 , pp. 1381-1401
    • Canouet, N.1    Fezoui, L.2    Piperno, S.3
  • 6
    • 0003979117 scopus 로고    scopus 로고
    • Discontinuous Galerkin methods
    • B. Cockburn, G. E. Karniadakis and C. W. Shu, editors, Theory, computation and applications, of, Springer-Verlag
    • B. Cockburn, G. E. Karniadakis and C. W. Shu, editors, Discontinuous Galerkin methods. Theory, computation and applications, vol. 11 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2000.
    • (2000) Lecture Notes in Computational Science and Engineering , vol.11
  • 7
    • 34147102272 scopus 로고    scopus 로고
    • Robust a posteriori error estimation for the heterogeneous Maxwell equations
    • S. Cochez-Dhondt and S. Nicaise, Robust a posteriori error estimation for the heterogeneous Maxwell equations, Comput. Methods Appl. Mech. Engrg., 196(2007), 2583-2595.
    • (2007) Comput. Methods Appl. Mech. Engrg , vol.196 , pp. 2583-2595
    • Cochez-Dhondt, S.1    Nicaise, S.2
  • 8
    • 33748559096 scopus 로고    scopus 로고
    • A spatial high-order hexahedral discontinuous Galerkin method to solve Maxwell's equations in time domain
    • 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.
    • (2006) J. Comput. Phys , vol.217 , pp. 340-363
    • Cohen, G.1    Ferrieres, X.2    Pernet, S.3
  • 9
    • 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
  • 10
    • 0038054072 scopus 로고    scopus 로고
    • An encyclopedia of cubature formulas
    • R. Cools, An encyclopedia of cubature formulas, J. Complexity, 19(2003), 445-453.
    • (2003) J. Complexity , vol.19 , pp. 445-453
    • Cools, R.1
  • 11
    • 0002258004 scopus 로고    scopus 로고
    • Convergent cartesian grid methods for Maxwell's equations in complex geometries
    • A. Ditkowski, K. Dridi and J. S. Hesthaven, Convergent cartesian grid methods for Maxwell's equations in complex geometries, J. Comput. Phys., 170(2001), 39-80.
    • (2001) J. Comput. Phys , vol.170 , pp. 39-80
    • Ditkowski, A.1    Dridi, K.2    Hesthaven, J.S.3
  • 12
    • 0035329254 scopus 로고    scopus 로고
    • Staircase-free finite-difference time-domain formulation for general materials in complex geometries
    • K. Dridi, J. S. Hesthaven and A. Ditkowski, Staircase-free finite-difference time-domain formulation for general materials in complex geometries, IEEE Trans. Antennas and Propagat., 49(2001), 749-755.
    • (2001) IEEE Trans. Antennas and Propagat , vol.49 , pp. 749-755
    • Dridi, K.1    Hesthaven, J.S.2    Ditkowski, A.3
  • 13
    • 44049089843 scopus 로고    scopus 로고
    • Preliminary investigation of a non-conforming discontinuous Galerkin method for solving the time domain Maxwell equations
    • H. Fahs, L. Fezoui, S. Lanteri and F. Rapetti, Preliminary investigation of a non-conforming discontinuous Galerkin method for solving the time domain Maxwell equations, IEEE Trans. on Magnet., 44(2008), 1254-1257.
    • (2008) IEEE Trans. on Magnet , vol.44 , pp. 1254-1257
    • Fahs, H.1    Fezoui, L.2    Lanteri, S.3    Rapetti, F.4
  • 14
    • 30344457009 scopus 로고    scopus 로고
    • L. Fezoui, S. Lanteri, S. Lohrengel and S. Piperno, Convergence and stability of a discontinuous Galerkin time-domain method for the heterogeneous Maxwell equations on unstructured meshes, ESAIM: Math. Model. and Numer. Anal., 39(2005), 1149-1176.
    • L. Fezoui, S. Lanteri, S. Lohrengel and S. Piperno, Convergence and stability of a discontinuous Galerkin time-domain method for the heterogeneous Maxwell equations on unstructured meshes, ESAIM: Math. Model. and Numer. Anal., 39(2005), 1149-1176.
  • 15
    • 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
  • 16
    • 1642294072 scopus 로고    scopus 로고
    • High-order accurate methods in time-domain computational electromagnetics
    • J. S. Hesthaven, High-order accurate methods in time-domain computational electromagnetics, Adv. Imaging Electron Phys., 127(2003), 59-123.
    • (2003) Adv. Imaging Electron Phys , vol.127 , pp. 59-123
    • Hesthaven, J.S.1
  • 17
    • 0001374260 scopus 로고    scopus 로고
    • Spectral collocation time-domain modeling of diffractive optical elements
    • J. S. Hesthaven, P. G. Dinesen and J. P. Lynov, Spectral collocation time-domain modeling of diffractive optical elements, J. Comput. Phys., 155(1999), 287-306.
    • (1999) J. Comput. Phys , vol.155 , pp. 287-306
    • Hesthaven, J.S.1    Dinesen, P.G.2    Lynov, J.P.3
  • 18
    • 33748798020 scopus 로고    scopus 로고
    • High-order accurate modeling of electromagnetic wave propagation across media: Grid conforming bodies
    • E. Kashdan and E. Turkel, High-order accurate modeling of electromagnetic wave propagation across media: Grid conforming bodies, J. Comput. Phys., 218(2006), 816-835.
    • (2006) J. Comput. Phys , vol.218 , pp. 816-835
    • Kashdan, E.1    Turkel, E.2
  • 21
    • 14844295419 scopus 로고    scopus 로고
    • An hp-adaptive finite element method for scattering problems in computational electromagnetics
    • W. Rachowicz and A. Zdunek, An hp-adaptive finite element method for scattering problems in computational electromagnetics, Internat. J. Numer. Methods Engrg., 62(2005), 1226-1249.
    • (2005) Internat. J. Numer. Methods Engrg , vol.62 , pp. 1226-1249
    • Rachowicz, W.1    Zdunek, A.2
  • 22
    • 5144220422 scopus 로고    scopus 로고
    • State-of-the-art, trends and directions in computational electromagnetics
    • F. Reitich and K. K. Tamma, State-of-the-art, trends and directions in computational electromagnetics, Comput. Meth. Eng. Sci., 5(2004), 287-294.
    • (2004) Comput. Meth. Eng. Sci , vol.5 , pp. 287-294
    • Reitich, F.1    Tamma, K.K.2
  • 23
    • 0037356074 scopus 로고    scopus 로고
    • An adaptive discontinuous Galerkin technique with an orthogonal basis applied to compressible flow problems
    • J.-F. Remacle, J. Flaherty and M. Shephard, An adaptive discontinuous Galerkin technique with an orthogonal basis applied to compressible flow problems, SIAM Review, 45(2003), 53-72.
    • (2003) SIAM Review , vol.45 , pp. 53-72
    • Remacle, J.-F.1    Flaherty, J.2    Shephard, M.3
  • 25
    • 33645713474 scopus 로고    scopus 로고
    • Two dimensional multidomain pseudospectral time-domain algorithm based on alternating-direction implicit method
    • Y. Shi, L. Li and C.-H. Liang, Two dimensional multidomain pseudospectral time-domain algorithm based on alternating-direction implicit method, IEEE Trans. Antennas and Propagat., 54(2006), 1207-1214.
    • (2006) IEEE Trans. Antennas and Propagat , vol.54 , pp. 1207-1214
    • Shi, Y.1    Li, L.2    Liang, C.-H.3
  • 27
    • 0036748422 scopus 로고    scopus 로고
    • High order explicit time integration schemes for Maxwell's equations
    • H. Spachmann, R. Schuhmann and T. Weiland, High order explicit time integration schemes for Maxwell's equations, Int. J. Numer. Model., 15(2002), 419-437.
    • (2002) Int. J. Numer. Model , vol.15 , pp. 419-437
    • Spachmann, H.1    Schuhmann, R.2    Weiland, T.3
  • 29
    • 0034190308 scopus 로고    scopus 로고
    • Fourth order compact implicit method for the Maxwell equations with discontinuous coefficients
    • E. Turkel and A. Yefet, Fourth order compact implicit method for the Maxwell equations with discontinuous coefficients, Appl. Numer. Math., 33(2000), 125-134.
    • (2000) Appl. Numer. Math , vol.33 , pp. 125-134
    • Turkel, E.1    Yefet, A.2
  • 30
    • 0034190411 scopus 로고    scopus 로고
    • On the construction of a high order difference scheme for complex domains in a cartesian grid
    • E. Turkel and A. Yefet, On the construction of a high order difference scheme for complex domains in a cartesian grid, Appl. Numer. Math., 33(2000), 113-124.
    • (2000) Appl. Numer. Math , vol.33 , pp. 113-124
    • Turkel, E.1    Yefet, A.2
  • 31
    • 2442543283 scopus 로고    scopus 로고
    • A staggered upwind embedded boundary (SUEB) method to eliminate the FDTD staircasing error
    • T. Xiao and Q. H. Liu, A staggered upwind embedded boundary (SUEB) method to eliminate the FDTD staircasing error, IEEE Trans. Antennas and Propagat., 52(2004), 730-741.
    • (2004) IEEE Trans. Antennas and Propagat , vol.52 , pp. 730-741
    • Xiao, T.1    Liu, Q.H.2
  • 32
    • 0037138010 scopus 로고    scopus 로고
    • An explicit fourth-order orthogonal curvilinear staggered-grid FDTD method for Maxwell's equations
    • Z. Xie, C.-H. Chan and B. Zhang, An explicit fourth-order orthogonal curvilinear staggered-grid FDTD method for Maxwell's equations, J. Comput. Phys., 175(2002), 739-763.
    • (2002) J. Comput. Phys , vol.175 , pp. 739-763
    • Xie, Z.1    Chan, C.-H.2    Zhang, B.3
  • 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 and Propagat., 14(1966), 302-307.
    • (1966) IEEE Trans. Antennas and Propagat , vol.14 , pp. 302-307
    • Yee, K.S.1
  • 34
    • 0000522244 scopus 로고    scopus 로고
    • A staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations
    • A. Yefet and P. G. Petropoulos, A staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations, J. Comput. Phys., 168(2001), 286-315.
    • (2001) J. Comput. Phys , vol.168 , pp. 286-315
    • Yefet, A.1    Petropoulos, P.G.2
  • 35
    • 0035069046 scopus 로고    scopus 로고
    • High-order, leapfrog methodology for the temporally dependent Maxwell's equations
    • J. L. Young, High-order, leapfrog methodology for the temporally dependent Maxwell's equations, Radio Sci., 36(2001), 9-17.
    • (2001) Radio Sci , vol.36 , pp. 9-17
    • Young, J.L.1
  • 36
    • 4544354197 scopus 로고    scopus 로고
    • High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces
    • S. Zhao and G. W. Wei, High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces, J. Comput. Phys., 200(2004), 60-103.
    • (2004) J. Comput. Phys , vol.200 , pp. 60-103
    • Zhao, S.1    Wei, G.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.