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Volumn 495, Issue , 2007, Pages 181-281

Numerical methods for elastic wave propagation

Author keywords

Elastic wave propagation; Finite difference time domain; Finite difference time domain method; Linear hyperbolic system; Seismic wave propagation

Indexed keywords


EID: 84919694628     PISSN: 02541971     EISSN: 23093706     Source Type: Book Series    
DOI: 10.1007/978-3-211-73572-5_6     Document Type: Chapter
Times cited : (13)

References (79)
  • 3
    • 0036018011 scopus 로고    scopus 로고
    • Approximation by quadrilateral finite elements
    • (electronic), ISSN 0025-5718
    • D. N. Arnold, D. Boffi, and R. S. Falk. Approximation by quadrilateral finite elements. Math. Comp., 71(239):909-922 (electronic), 2002. ISSN 0025-5718.
    • (2002) Math. Comp , vol.71 , Issue.239 , pp. 909-922
    • Arnold, D.N.1    Boffi, D.2    Falk, R.S.3
  • 5
    • 0016994507 scopus 로고
    • The effect of quadrature errors on finite element approximations for the second-order hyperbolic equations
    • G.A. Baker and V.A. Dougalis. The effect of quadrature errors on finite element approximations for the second-order hyperbolic equations. SIAM Journal on Numerical Analysis, 13:577-598, 1976.
    • (1976) SIAM Journal on Numerical Analysis , vol.13 , pp. 577-598
    • Baker, G.A.1    Dougalis, V.A.2
  • 8
    • 0038109871 scopus 로고    scopus 로고
    • Stability of perfectly matched layers, group velocities and anisotropic waves
    • E. Bécache, S. Fauqueux, and P. Joly. Stability of perfectly matched layers, group velocities and anisotropic waves. Journal of Computational Physics, 188:399-433, 2003.
    • (2003) Journal of Computational Physics , vol.188 , pp. 399-433
    • Bécache, E.1    Fauqueux, S.2    Joly, P.3
  • 9
    • 0036339907 scopus 로고    scopus 로고
    • On the analysis of Berengers perfectly matched layers for Maxwell equations
    • E. Bécache and P. Joly. On the analysis of Berengers perfectly matched layers for Maxwell equations. Mathematical Modelling and Numerical Analysis, 36:87-120, 2002.
    • (2002) Mathematical Modelling and Numerical Analysis , vol.36 , pp. 87-120
    • Bécache, E.1    Joly, P.2
  • 10
  • 11
    • 0036556456 scopus 로고    scopus 로고
    • A new family of mixed finite elements for the linear elastodynamic problem
    • E. Bécache, P. Joly, and C. Tsogka. A new family of mixed finite elements for the linear elastodynamic problem. SIAM Journal on Numerical Analysis, 39:2109-2132, 2002.
    • (2002) SIAM Journal on Numerical Analysis , vol.39 , pp. 2109-2132
    • Bécache, E.1    Joly, P.2    Tsogka, C.3
  • 13
    • 28044459877 scopus 로고
    • A perfectly matched layer for the absorption of electromagnetic waves
    • J.P. Bérenger. A perfectly matched layer for the absorption of electromagnetic waves. Journal Computational Physics, 114:185-200, 1994.
    • (1994) Journal Computational Physics , vol.114 , pp. 185-200
    • Bérenger, J.P.1
  • 14
    • 0030239565 scopus 로고    scopus 로고
    • Three-dimensional perfectly matched layer for the absorption of electromagnetic waves
    • J.P. Bérenger. Three-dimensional perfectly matched layer for the absorption of electromagnetic waves. Journal Computational Physics, 127:363-379, 1996.
    • (1996) Journal Computational Physics , vol.127 , pp. 363-379
    • Bérenger, J.P.1
  • 15
    • 0031098478 scopus 로고    scopus 로고
    • Improved PML for the FDTD solution of wave-structure interaction problems
    • J.P. Bérenger. Improved PML for the FDTD solution of wave-structure interaction problems. IEEE Transactions on Antennas and Propagation, 45:466-473, 1997.
    • (1997) IEEE Transactions on Antennas and Propagation , vol.45 , pp. 466-473
    • Bérenger, J.P.1
  • 17
    • 0032859104 scopus 로고    scopus 로고
    • Higher-order triangular and tetrahedral finite elements with mass lumping for solving the wave equation
    • M.J.S. Chin-Joe-Kong, W.A. Mulder, and M. Van Veldhuizen. Higher-order triangular and tetrahedral finite elements with mass lumping for solving the wave equation. Journal of Engineeting Mathematics, 35:405-426, 1999.
    • (1999) Journal of Engineeting Mathematics , vol.35 , pp. 405-426
    • Chin-Joe-Kong, M.J.S.1    Mulder, W.A.2    Van Veldhuizen, M.3
  • 22
    • 0000167493 scopus 로고    scopus 로고
    • Perfectly matched absorbing layers for the paraxial equations
    • F. Collino. Perfectly matched absorbing layers for the paraxial equations. Journal of Computational Physics, 131:164-180, 1996.
    • (1996) Journal of Computational Physics , vol.131 , pp. 164-180
    • Collino, F.1
  • 24
    • 0032475725 scopus 로고    scopus 로고
    • The Perfectly Matched Layer in curvilinear coordinates
    • F. Collino and P. Monk. The Perfectly Matched Layer in curvilinear coordinates. SIAM Journal on Scientific Computation, 164:157-171, 1998b.
    • (1998) SIAM Journal on Scientific Computation , vol.164 , pp. 157-171
    • Collino, F.1    Monk, P.2
  • 25
    • 0035071437 scopus 로고    scopus 로고
    • Application of the PML absorbing layer model to the linear elastodynamic problem in anisotropic heteregeneous media
    • F. Collino and C. Tsogka. Application of the PML absorbing layer model to the linear elastodynamic problem in anisotropic heteregeneous media. Geophysics, 66:294-305, 2001.
    • (2001) Geophysics , vol.66 , pp. 294-305
    • Collino, F.1    Tsogka, C.2
  • 29
    • 0000807980 scopus 로고
    • L 2-estimates for Galerkin methods for second order hyperbolic equations
    • T. Dupont. L 2-estimates for Galerkin methods for second order hyperbolic equations. SIAM Journal on Numerical Analysis, 10:880-889, 1973.
    • (1973) SIAM Journal on Numerical Analysis , vol.10 , pp. 880-889
    • Dupont, T.1
  • 32
    • 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. Mathematics of Computation, 31:629-651, 1977.
    • (1977) Mathematics of Computation , vol.31 , pp. 629-651
    • Engquist, B.1    Majda, A.2
  • 36
    • 0000606420 scopus 로고
    • On the boundary-value problems of the theory of elasticity and Korn’s inequality
    • K.O. Friedrichs. On the boundary-value problems of the theory of elasticity and Korn’s inequality. Annals of Mathematics, Second Series, 48:441-471, 1947.
    • (1947) Annals of Mathematics, Second Series , vol.48 , pp. 441-471
    • Friedrichs, K.O.1
  • 37
    • 14844339312 scopus 로고    scopus 로고
    • Orthogonal Polynomials: Computation and Approximation
    • Oxford University Press
    • W. Gautschi. Orthogonal Polynomials: Computation and Approximation. Numerical Mathematics and Scientific Computation. Oxford University Press, 2004.
    • (2004) Numerical Mathematics and Scientific Computation
    • Gautschi, W.1
  • 38
    • 0001790517 scopus 로고    scopus 로고
    • Contre-exemples à l’inégalité de Korn et au lemme de Lions dans des domaines irréguliers
    • Gauthier-Villars
    • G. Geymonat and G. Gilardi. Contre-exemples à l’inégalité de Korn et au lemme de Lions dans des domaines irréguliers. In Équations aux Dérivées Partielles et Applications, pages 541-548. Gauthier-Villars, 1998.
    • (1998) Équations Aux Dérivées Partielles Et Applications , pp. 541-548
    • Geymonat, G.1    Gilardi, G.2
  • 39
    • 1642325209 scopus 로고    scopus 로고
    • High-order local non-reflecting boundary conditions: A review
    • D. Givoli. High-order local non-reflecting boundary conditions: a review. Wave Motion, 39:319-326, 2004.
    • (2004) Wave Motion , vol.39 , pp. 319-326
    • Givoli, D.1
  • 41
    • 0029292813 scopus 로고
    • Exact nonreflecting boundary conditions for the time dependent wave equation
    • M. Grote and J. Keller. Exact nonreflecting boundary conditions for the time dependent wave equation. SIAM Journal on Applied Mathematics, 55:280-297, 1995.
    • (1995) SIAM Journal on Applied Mathematics , vol.55 , pp. 280-297
    • Grote, M.1    Keller, J.2
  • 42
    • 0030209904 scopus 로고    scopus 로고
    • Nonreflecting boundary conditions for time dependent scattering
    • M. Grote and J. Keller. Nonreflecting boundary conditions for time dependent scattering. Journal of Computational Physics, 127:52-81, 1996.
    • (1996) Journal of Computational Physics , vol.127 , pp. 52-81
    • Grote, M.1    Keller, J.2
  • 44
    • 85011457104 scopus 로고    scopus 로고
    • Radiation boundary conditions for the numerical simulation of waves
    • T. Hagstrom. Radiation boundary conditions for the numerical simulation of waves. Acta numerica, 8:47-106, 1999.
    • (1999) Acta Numerica , vol.8 , pp. 47-106
    • Hagstrom, T.1
  • 46
    • 0032141095 scopus 로고    scopus 로고
    • A formulation of asymptotic and exact boundary conditions using local operators
    • T. Hagstrom and S.I. Hariharan. A formulation of asymptotic and exact boundary conditions using local operators. Applied Numerical Mathematics, 27:403-416, 1998.
    • (1998) Applied Numerical Mathematics , vol.27 , pp. 403-416
    • Hagstrom, T.1    Hariharan, S.I.2
  • 48
    • 0029858582 scopus 로고    scopus 로고
    • Application of the perfectly matched layer (PML) absorbing boundary condition to elastic wave propagation
    • F. Hastings, J.B. Schneider, and S.L. Broschat. Application of the perfectly matched layer (PML) absorbing boundary condition to elastic wave propagation. Journal of the Acoustical Society of America, 100:3061-3069, 1996.
    • (1996) Journal of the Acoustical Society of America , vol.100 , pp. 3061-3069
    • Hastings, F.1    Schneider, J.B.2    Broschat, S.L.3
  • 49
    • 0022728049 scopus 로고
    • Initial-boundary value problems for linear hyperbolic systems
    • R.L. Higdon. Initial-boundary value problems for linear hyperbolic systems. SIAM Review, 28:177-217, 1986.
    • (1986) SIAM Review , vol.28 , pp. 177-217
    • Higdon, R.L.1
  • 50
    • 0025476463 scopus 로고
    • Radiation boundary conditions for elastic wave propagation
    • R.L. Higdon. Radiation boundary conditions for elastic wave propagation. SIAM Journal on Numerical Analysis, 27:831-870, 1990.
    • (1990) SIAM Journal on Numerical Analysis , vol.27 , pp. 831-870
    • Higdon, R.L.1
  • 51
    • 0025925925 scopus 로고
    • Absorbing boundary conditions for elastic waves
    • R.L. Higdon. Absorbing boundary conditions for elastic waves. Geophysics, 56:231-241, 1991.
    • (1991) Geophysics , vol.56 , pp. 231-241
    • Higdon, R.L.1
  • 52
    • 0000949380 scopus 로고
    • Absorbing boundary conditions for acoustic and elastic waves in stratified media
    • R.L. Higdon. Absorbing boundary conditions for acoustic and elastic waves in stratified media. Journal of Computational Physics, 101:386-418, 1992.
    • (1992) Journal of Computational Physics , vol.101 , pp. 386-418
    • Higdon, R.L.1
  • 57
    • 85053502674 scopus 로고
    • Initial-Boundary Value Problems and the Navier-Stokes Equations
    • H-O. Kreiss and J. Lorenz. Initial-Boundary Value Problems and the Navier-Stokes Equations. Academic Press, 1989.
    • (1989) Academic Press
    • Kreiss, H.-O.1    Lorenz, J.2
  • 58
    • 11744350396 scopus 로고
    • Free space boundary conditions for time dependant wave equation
    • E. Lindman. Free space boundary conditions for time dependant wave equation. Journal of Computational Physics, 18:66-78, 1975.
    • (1975) Journal of Computational Physics , vol.18 , pp. 66-78
    • Lindman, E.1
  • 61
    • 0035618464 scopus 로고    scopus 로고
    • Higher-order mass-lumped finite elements for the wave equation
    • W.A. Mulder. Higher-order mass-lumped finite elements for the wave equation. Journal of Computational Acoustics, 9:671-680, 2001.
    • (2001) Journal of Computational Acoustics , vol.9 , pp. 671-680
    • Mulder, W.A.1
  • 62
    • 0000667107 scopus 로고
    • On Korn’s second inequality
    • J.A. Nitsche. On Korn’s second inequality. RAIRO Analyse Numérique, 15:237-248, 1981.
    • (1981) RAIRO Analyse Numérique , vol.15 , pp. 237-248
    • Nitsche, J.A.1
  • 63
    • 0028852188 scopus 로고
    • An optimal absorbing boundary condition for elastic wave modeling
    • C. Peng and M.N. Toksoz. An optimal absorbing boundary condition for elastic wave modeling. Geophysics, 60:296-301, 1995.
    • (1995) Geophysics , vol.60 , pp. 296-301
    • Peng, C.1    Toksoz, M.N.2
  • 64
    • 0002210417 scopus 로고    scopus 로고
    • A reflectionless sponge layer absorbing boundary condition for the solution of Maxwell’s equations with high-order staggered finite difference schemes
    • P.G. Petropoulos, L. Zhao, and A.C. Cangellaris. A reflectionless sponge layer absorbing boundary condition for the solution of Maxwell’s equations with high-order staggered finite difference schemes. Journal of Computational Physics, 139:184-208, 1998.
    • (1998) Journal of Computational Physics , vol.139 , pp. 184-208
    • Petropoulos, P.G.1    Zhao, L.2    Cangellaris, A.C.3
  • 65
    • 0032075949 scopus 로고    scopus 로고
    • Instability in applying absorbing boundary conditions to high-order seismic modeling algorithms
    • A. Simone and S. Hestholm. Instability in applying absorbing boundary conditions to high-order seismic modeling algorithms. Geophysics, 63:1017-1023, 1998.
    • (1998) Geophysics , vol.63 , pp. 1017-1023
    • Simone, A.1    Hestholm, S.2
  • 68
    • 0000665373 scopus 로고    scopus 로고
    • Perfectly matched layer as an absorbing boundary condition for the linearized Euler equations in open and ducted domains
    • C.K.W. Tam, L. Auriault, and F. Cambuli. Perfectly matched layer as an absorbing boundary condition for the linearized Euler equations in open and ducted domains. Journal of Computational Physics, 144:213-234, 1998.
    • (1998) Journal of Computational Physics , vol.144 , pp. 213-234
    • Tam, C.K.W.1    Auriault, L.2    Cambuli, F.3
  • 70
    • 0032025544 scopus 로고    scopus 로고
    • Analytical derivation of a conformal perfectly matched absorber for electromagnetic waves
    • F.L. Teixeira and W.C. Chew. Analytical derivation of a conformal perfectly matched absorber for electromagnetic waves. Microwave and Optical Technology Letters, 17: 231-236, 1998.
    • (1998) Microwave and Optical Technology Letters , vol.17 , pp. 231-236
    • Teixeira, F.L.1    Chew, W.C.2
  • 71
    • 0032733386 scopus 로고    scopus 로고
    • Unified analysis of perfectly matched layers using differential forms
    • F.L. Teixeira and W.C. Chew. Unified analysis of perfectly matched layers using differential forms. Microwave and Optical Technology Letters, 20:124-126, 1999.
    • (1999) Microwave and Optical Technology Letters , vol.20 , pp. 124-126
    • Teixeira, F.L.1    Chew, W.C.2
  • 73
    • 84966217680 scopus 로고
    • Well posedness of one way equations and absorbing boundary conditions
    • L. Trefethen and L. Halpern. Well posedness of one way equations and absorbing boundary conditions. Mathematics of Computation, 47:421-435, 1986.
    • (1986) Mathematics of Computation , vol.47 , pp. 421-435
    • Trefethen, L.1    Halpern, L.2
  • 74
    • 0000125555 scopus 로고
    • Group velocity in finite difference schemes
    • L.N. Trefethen. Group velocity in finite difference schemes. SIAM Review, 24, 1982.
    • (1982) SIAM Review , pp. 24
    • Trefethen, L.N.1
  • 75
    • 0001185178 scopus 로고
    • Group velocity interpretation of the stability theory of Gustafsson, Kreiss and Sundström
    • L.N. Trefethen. Group velocity interpretation of the stability theory of Gustafsson, Kreiss and Sundström. Journal of Computational Physics, 49, 1983.
    • (1983) Journal of Computational Physics , pp. 49
    • Trefethen, L.N.1
  • 76
    • 84990553414 scopus 로고
    • Instability of difference models for hyperbolic initial boundary value problems
    • L.N. Trefethen. Instability of difference models for hyperbolic initial boundary value problems. Communications on Pure and Applied Mathematics, 37:329-367, 1984.
    • (1984) Communications on Pure and Applied Mathematics , vol.37 , pp. 329-367
    • Trefethen, L.N.1
  • 77
    • 0032137824 scopus 로고    scopus 로고
    • Absorbing PML boundary layers for wave-like equations. Absorbing boundary conditions
    • E. Turkel and A. Yefet. Absorbing PML boundary layers for wave-like equations. Absorbing boundary conditions. Applied Numerical Mathematics, 27:553-557, 1998.
    • (1998) Applied Numerical Mathematics , vol.27 , pp. 553-557
    • Turkel, E.1    Yefet, A.2
  • 78
    • 0030387909 scopus 로고    scopus 로고
    • A general approach to for developping unsplit-field time-domain implementations of perfectly matched layers for FDTD grid truncation
    • L. Zhao and A.C. Cangellaris. A general approach to for developping unsplit-field time-domain implementations of perfectly matched layers for FDTD grid truncation. IEEE Transactions on Microwave Theory and Technology, 44:2555-2563, 1996.
    • (1996) IEEE Transactions on Microwave Theory and Technology , vol.44 , pp. 2555-2563
    • Zhao, L.1    Cangellaris, A.C.2


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