메뉴 건너뛰기




Volumn 234, Issue 12, 2010, Pages 3283-3302

Explicit local time-stepping methods for Maxwell's equations

Author keywords

Discontinuous Galerkin methods; Electromagnetic waves; Explicit time integration; Finite element methods; Local time stepping; Maxwell's equations

Indexed keywords

CONDUCTING MEDIA; DISCONTINUOUS GALERKIN; DISCONTINUOUS GALERKIN METHODS; DISCRETE ENERGIES; DISCRETE TIME; DISCRETISATION; EXPLICIT TIME INTEGRATION; FINITE ELEMENT DISCRETISATIONS; LOCAL MESH REFINEMENT; LOCAL TIME; MASS MATRICES; MAXWELL'S EQUATIONS; NUMERICAL EXPERIMENTS; TIME DEPENDENT; TIME STEP; TIME-INTEGRATION SCHEME;

EID: 77955272191     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2010.04.028     Document Type: Article
Times cited : (63)

References (35)
  • 1
    • 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 Propag. 14 1966 302 307
    • (1966) IEEE Trans. Antennas Propag. , vol.14 , pp. 302-307
    • Yee, K.S.1
  • 3
  • 4
    • 34250103285 scopus 로고
    • 3
    • J.C. Ndlec A new family of mixed finite elements in R 3 Numer. Math. 50 1986 57 81
    • (1986) Numer. Math. , vol.50 , pp. 57-81
    • Nédélec, J.C.1
  • 5
    • 0036298745 scopus 로고    scopus 로고
    • A vector finite element time-domain method for solving Maxwell's Equations on unstructured hexahedral grids
    • G. Rodrigue, and D. White A vector finite element time-domain method for solving Maxwell's Equations on unstructured hexahedral grids SIAM J. Sci. Comput. 23 2001 683 701
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 683-701
    • Rodrigue, G.1    White, D.2
  • 6
    • 0001602221 scopus 로고
    • A mixed finite element formulation for Maxwell's equations in the time domain
    • R.L. Lee, and N.K. Madsen A mixed finite element formulation for Maxwell's equations in the time domain J. Comput. Phys. 88 1990 284 304
    • (1990) J. Comput. Phys. , vol.88 , pp. 284-304
    • Lee, R.L.1    Madsen, N.K.2
  • 7
    • 0026121692 scopus 로고
    • Elimination of vector parasites in finite element Maxwell solutions
    • K.D. Paulsen, and D.R. Lynch Elimination of vector parasites in finite element Maxwell solutions IEEE Trans. Microwave Theory Tech. 39 1991 395 404
    • (1991) IEEE Trans. Microwave Theory Tech. , vol.39 , pp. 395-404
    • Paulsen, K.D.1    Lynch, D.R.2
  • 10
    • 84966246413 scopus 로고
    • TVB RungeKutta local projection discontinuous Galerkin method for conservation laws II: General framework
    • B. Cockburn, and C.-W. Shu TVB RungeKutta local projection discontinuous Galerkin method for conservation laws II: general framework Math. Comp. 52 1989 411 435
    • (1989) Math. Comp. , vol.52 , pp. 411-435
    • Cockburn, B.1    Shu, C.-W.2
  • 11
    • 17444409297 scopus 로고    scopus 로고
    • High-order RKDG methods for computational electromagnetics
    • M.-H. Chen, B. Cockburn, and F. Reitich High-order RKDG methods for computational electromagnetics J. Sci. Comput. 22 2005 205 226
    • (2005) J. Sci. Comput. , vol.22 , pp. 205-226
    • Chen, M.-H.1    Cockburn, B.2    Reitich, F.3
  • 12
    • 0005683767 scopus 로고    scopus 로고
    • Application of the discontinuous Galerkin method to Maxwell's equations using unstructured polymorphic hp-finite elements
    • in: B. Cockburn, G.E. Karniadakis, C.-W. Shu (Eds.)
    • T. Warburton Application of the discontinuous Galerkin method to Maxwell's equations using unstructured polymorphic h p -finite elements B. Cockburn, G.E. Karniadakis, C.-W. Shu, Discontinuous Galerkin Methods: Theory, Computation and Applications Lecture Notes in Computer Science Engineering vol. 11 2000 Springer Berlin 451 458
    • (2000) Discontinuous Galerkin Methods: Theory, Computation and Applications, Lecture Notes in Computer Science Engineering , vol.11 , pp. 451-458
    • Warburton, T.1
  • 13
    • 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. Comp. Phys. 181 2002 186 221
    • (2002) J. Comp. Phys. , vol.181 , pp. 186-221
    • Hesthaven, J.S.1    Warburton, T.2
  • 14
    • 34548425646 scopus 로고    scopus 로고
    • Dispersion and dissipation error in high-order RungeKutta discontinuous Galerkin discretisations of the Maxwell equations
    • D. Srmny, M.A. Botchev, and J.J.W. van der Vegt Dispersion and dissipation error in high-order RungeKutta discontinuous Galerkin discretisations of the Maxwell equations J. Sci. Comput. 33 2007 47 74
    • (2007) J. Sci. Comput. , vol.33 , pp. 47-74
    • Sármány, D.1    Botchev, M.A.2    Van Der Vegt, J.J.W.3
  • 15
    • 34247214527 scopus 로고    scopus 로고
    • Interior penalty discontinuous Galerkin method for Maxwell's equations: Energy norm error estimates
    • M.J. Grote, A. Schneebeli, and D. Schtzau Interior penalty discontinuous Galerkin method for Maxwell's equations: energy norm error estimates J. Comput. Appl. Math. 204 2007 375 386
    • (2007) J. Comput. Appl. Math. , vol.204 , pp. 375-386
    • Grote, M.J.1    Schneebeli, A.2    Schötzau, D.3
  • 16
    • 46349083775 scopus 로고    scopus 로고
    • 2-norm error estimates
    • M.J. Grote, A. Schneebeli, and D. Schtzau Interior penalty discontinuous Galerkin method for Maxwell's equations: optimal l 2 -norm error estimates IMA J. Numer. Anal. 28 2008 440 468
    • (2008) IMA J. Numer. Anal. , vol.28 , pp. 440-468
    • Grote, M.J.1    Schneebeli, A.2    Söchtzau, D.3
  • 17
    • 67349191482 scopus 로고    scopus 로고
    • Optimal error estimates for the fully discrete interior penalty DG method for the wave equation
    • M.J. Grote, and D. Schtzau Optimal error estimates for the fully discrete interior penalty DG method for the wave equation J. Sci. Comput. 40 2009 257 272
    • (2009) J. Sci. Comput. , vol.40 , pp. 257-272
    • Grote, M.J.1    Schtzau, D.2
  • 18
    • 0042763514 scopus 로고    scopus 로고
    • A conservative spacetime mesh refinement method for the 1-D wave equation
    • F. Collino, T. Fouquet, and P. Joly A conservative spacetime mesh refinement method for the 1-D wave equation. I. construction Numer. Math. 95 2003 197 221
    • (2003) I. construction, Numer. Math. , vol.95 , pp. 197-221
    • Collino, F.1    Fouquet, T.2    Joly, P.3
  • 19
    • 77955282049 scopus 로고    scopus 로고
    • Convergence and component splitting for the Crank-Nicolson-Leap-Frog integration method
    • J.G. Verwer, Convergence and component splitting for the CrankNicolsonLeapFrog integration method, CWI Tech. Report MAS-E0902, 2009.
    • (2009) CWI Tech. Report MAS-E0902
    • J.G. Verwer1
  • 20
    • 25444469411 scopus 로고    scopus 로고
    • Conservative spacetime mesh refinement method for the FDTD solution of Maxwell's equations
    • F. Collino, T. Fouquet, and P. Joly Conservative spacetime mesh refinement method 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
  • 22
    • 33846453567 scopus 로고    scopus 로고
    • Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems
    • S. Piperno Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems M2AN Math. Model. Numer. Anal. 40 2006 815 841
    • (2006) M2AN Math. Model. Numer. Anal. , vol.40 , pp. 815-841
    • Piperno, S.1
  • 23
    • 44649127306 scopus 로고    scopus 로고
    • Dissipative terms and local time-stepping improvements in a spatial high order discontinuous Galerkin scheme for the time-domain Maxwell's equations
    • 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
    • (2008) J. Comput. Phys. , vol.227 , pp. 6795-6820
    • Montseny, E.1    Pernet, S.2    Ferrires, X.3    Cohen, G.4
  • 24
    • 35548982113 scopus 로고    scopus 로고
    • Discontinuous Galerkin approximation of the Maxwell eigenproblem
    • A. Buffa, and I. Perugia Discontinuous Galerkin approximation of the Maxwell eigenproblem SIAM J. Numer. Anal. 44 2006 2198 2226
    • (2006) SIAM J. Numer. Anal. , vol.44 , pp. 2198-2226
    • Buffa, A.1    Perugia, I.2
  • 25
    • 76449110893 scopus 로고    scopus 로고
    • Energy conserving explicit local time-stepping for second-order wave equations
    • 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
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 1985-2014
    • Diaz, J.1    Grote, M.J.2
  • 26
    • 59349096512 scopus 로고    scopus 로고
    • A high-order discontinuous Galerkin method with time-accurate local time stepping for the Maxwell equations
    • A. Taube, M. Dumbser, C.-D. Munz, and R. Schneider A high-order discontinuous Galerkin method with time-accurate local time stepping for the Maxwell equations Int. J. Numer. Model. 22 2009 77 103
    • (2009) Int. J. Numer. Model. , vol.22 , pp. 77-103
    • Taube, A.1    Dumbser, M.2    Munz, C.-D.3    Schneider, R.4
  • 28
    • 67349198438 scopus 로고    scopus 로고
    • The mortar-discontinuous galerkin method for the 2D Maxwell eigenproblem
    • A. Buffa, I. Perugia, and T. Warburton The mortar-discontinuous galerkin method for the 2D Maxwell eigenproblem J. Sci. Comp. 40 2009 86 114
    • (2009) J. Sci. Comp. , vol.40 , pp. 86-114
    • Buffa, A.1    Perugia, I.2    Warburton, T.3
  • 29
    • 0036410391 scopus 로고    scopus 로고
    • Unified analysis of discontinuous Galerkin methods for elliptic problems
    • D.N. Arnold, F. Brezzi, B. Cockburn, and L.D. Marini Unified analysis of discontinuous Galerkin methods for elliptic problems SIAM J. Numer. Anal. 39 2001 1749 1779
    • (2001) SIAM J. Numer. Anal. , vol.39 , pp. 1749-1779
    • Arnold, D.N.1    Brezzi, F.2    Cockburn, B.3    Marini, L.D.4
  • 30
    • 20144385612 scopus 로고    scopus 로고
    • Mixed discontinuous Galerkin approximation of the Maxwell operator
    • P. Houston, I. Perugia, and D. Schtzau Mixed discontinuous Galerkin approximation of the Maxwell operator SIAM J. Numer. Anal. 42 2004 434 459
    • (2004) SIAM J. Numer. Anal. , vol.42 , pp. 434-459
    • Houston, P.1    Perugia, I.2    Schötzau, D.3
  • 32
    • 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 Propagat. 52 2004 2190 2195
    • (2004) IEEE Trans. Antennas Propagat. , vol.52 , pp. 2190-2195
    • Rieben, R.1    White, D.2    Rodrigue, G.3
  • 33
    • 0000611937 scopus 로고
    • A modified equation approach to constructing fourth order methods for acoustic wave propagation
    • G.R. Shubin, and J.B. Bell A modified equation approach to constructing fourth order methods for acoustic wave propagation SIAM J. Sci. Stat. Comput. 8 1987 135 151
    • (1987) SIAM J. Sci. Stat. Comput. , vol.8 , pp. 135-151
    • Shubin, G.R.1    Bell, J.B.2
  • 34
    • 67349247633 scopus 로고    scopus 로고
    • Numerical integration of damped Maxwell equations
    • M.A. Botchev, and J.G. Verwer Numerical integration of damped Maxwell equations SIAM J. Sci. Comput. 31 2009 1322 1346
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 1322-1346
    • Botchev, M.A.1    Verwer, J.G.2
  • 35
    • 0041909738 scopus 로고    scopus 로고
    • Higher order triangular finite elements with mass lumping for the wave equation
    • G. Cohen, P. Joly, J.E. Roberts, and N. Tordjman Higher order triangular finite elements with mass lumping for the wave equation SIAM J. Numer. Anal. 38 2001 2047 2078
    • (2001) SIAM J. Numer. Anal. , vol.38 , pp. 2047-2078
    • Cohen, G.1    Joly, P.2    Roberts, J.E.3    Tordjman, N.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.