메뉴 건너뛰기




Volumn 186, Issue 1, 2003, Pages 24-46

High-order non-reflecting boundary scheme for time-dependent waves

Author keywords

Artificial boundary; Auxiliary variables; Finite difference; Higdon; High order; Non reflecting boundary condition; Waves

Indexed keywords

BOUNDARY CONDITIONS; ELECTRIC CONDUCTORS; NUMERICAL METHODS; WAVE EQUATIONS; WAVEGUIDES;

EID: 0037456944     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(03)00005-6     Document Type: Article
Times cited : (212)

References (61)
  • 2
    • 2142739347 scopus 로고
    • Non-reflecting boundary conditions: A review
    • D. Givoli, Non-reflecting boundary conditions: a review, J. Comput. Phys. 94 (1991) 1-29.
    • (1991) J. Comput. Phys. , vol.94 , pp. 1-29
    • Givoli, D.1
  • 3
    • 0032137784 scopus 로고    scopus 로고
    • Numerical solution of problems on unbounded domains, a review
    • S.V. Tsynkov, Numerical solution of problems on unbounded domains, a review, Appl. Numer. Math. 27 (1998) 465-532.
    • (1998) Appl. Numer. Math. , vol.27 , pp. 465-532
    • Tsynkov, S.V.1
  • 4
    • 0033221790 scopus 로고    scopus 로고
    • Exact representations on artificial interfaces and applications in mechanics
    • D. Givoli, Exact representations on artificial interfaces and applications in mechanics, Appl. Mech. Rev. 52 (1999) 333-349.
    • (1999) Appl. Mech. Rev. , vol.52 , pp. 333-349
    • Givoli, D.1
  • 5
    • 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 Numer. 8 (1999) 47-106.
    • (1999) Acta Numer. , vol.8 , pp. 47-106
    • Hagstrom, T.1
  • 6
    • 84980151986 scopus 로고
    • Radiation boundary conditions for acoustic and elastic calculations
    • B. Engquist, A. Majda, Radiation boundary conditions for acoustic and elastic calculations, Commun. Pure Appl. Math. 32 (1979) 313-357.
    • (1979) Commun. Pure Appl. Math. , vol.32 , pp. 313-357
    • Engquist, B.1    Majda, A.2
  • 7
    • 84980167404 scopus 로고
    • Radiation boundary conditions for wave-like equations
    • A. Bayliss, E. Turkel, Radiation boundary conditions for wave-like equations, Commun. Pure Appl. Math. 33 (1980) 707-725.
    • (1980) Commun. Pure Appl. Math. , vol.33 , pp. 707-725
    • Bayliss, A.1    Turkel, E.2
  • 8
    • 0000271460 scopus 로고
    • Exact non-reflecting boundary conditions
    • J.B. Keller, D. Givoli, Exact non-reflecting boundary conditions, J. Comput. Phys. 82 (1989) 172-192.
    • (1989) J. Comput. Phys. , vol.82 , pp. 172-192
    • Keller, J.B.1    Givoli, D.2
  • 9
    • 0025421673 scopus 로고
    • Non-reflecting boundary conditions for elastic waves
    • D. Givoli, J.B. Keller, Non-reflecting boundary conditions for elastic waves, Wave Motion 12 (1990) 261-279.
    • (1990) Wave Motion , vol.12 , pp. 261-279
    • Givoli, D.1    Keller, J.B.2
  • 10
    • 0001406966 scopus 로고
    • Artificial boundary conditions for the numerical solution of external viscous flow problems
    • V.S. Ryaben'kii, S.V. Tsynkov, Artificial boundary conditions for the numerical solution of external viscous flow problems, SIAM J. Numer. Anal. 32 (1995) 1355-1389.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1355-1389
    • Ryaben'kii, V.S.1    Tsynkov, S.V.2
  • 11
    • 0041397301 scopus 로고    scopus 로고
    • External flow computations using global boundary conditions
    • S.V. Tsynkov, E. Turkel, S. Abarbanel, External flow computations using global boundary conditions, AIAA J. 34 (1996) 700-706.
    • (1996) AIAA J. , vol.34 , pp. 700-706
    • Tsynkov, S.V.1    Turkel, E.2    Abarbanel, S.3
  • 12
    • 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, J. Comput. Phys. 114 (1994) 185-200.
    • (1994) J. Comput. Phys. , vol.114 , pp. 185-200
    • Bérenger, J.P.1
  • 13
    • 0000766738 scopus 로고
    • High order absorbing boundary conditions for wave propagation models. Straight line boundary and corner cases
    • R. Kleinman, et al. (Eds.), Proceedings of the 2nd International Conference on Mathematical and Numerical Aspects of Wave Propagation SIAM, Delaware
    • F. Collino, High order absorbing boundary conditions for wave propagation models. Straight line boundary and corner cases, in: R. Kleinman, et al. (Eds.), Proceedings of the 2nd International Conference on Mathematical and Numerical Aspects of Wave Propagation, SIAM, Delaware, 1993, pp. 161-171.
    • (1993) , pp. 161-171
    • Collino, F.1
  • 14
    • 0029292813 scopus 로고
    • Exact nonreflecting boundary conditions for the time dependent wave equation
    • M.J. Grote, J.B. Keller, Exact nonreflecting boundary conditions for the time dependent wave equation, SIAM J. Appl. Math. 55 (1995) 280-297.
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 280-297
    • Grote, M.J.1    Keller, J.B.2
  • 15
    • 0030209904 scopus 로고    scopus 로고
    • Nonreflecting boundary conditions for time dependent scattering
    • M.J. Grote, J.B. Keller, Nonreflecting boundary conditions for time dependent scattering, J. Comput. Phys. 127 (1996) 52-65.
    • (1996) J. Comput. Phys. , vol.127 , pp. 52-65
    • Grote, M.J.1    Keller, J.B.2
  • 16
    • 0033708024 scopus 로고    scopus 로고
    • Nonreflecting boundary conditions for elastic waves
    • M.J. Grote, J.B. Keller, Nonreflecting boundary conditions for elastic waves, SIAM J. Appl. Math. 60 (2000) 803-819.
    • (2000) SIAM J. Appl. Math. , vol.60 , pp. 803-819
    • Grote, M.J.1    Keller, J.B.2
  • 17
    • 0001025850 scopus 로고
    • Conditions for complete transparency on the sphere for the three-dimensional wave equation
    • I.L. Sofronov, Conditions for complete transparency on the sphere for the three-dimensional wave equation, Russian Acad. Dci. Dokl. Math. 46 (1993) 397-401.
    • (1993) Russian Acad. Dci. Dokl. Math. , vol.46 , pp. 397-401
    • Sofronov, I.L.1
  • 18
    • 0001886048 scopus 로고    scopus 로고
    • Progressive wave expansions and open boundary problems, in computational wave propagation
    • B. Engquist, G.A. Kriegsmann (Eds.), Springer, New York
    • T. Hagstrom, S.I. Hariharan, Progressive wave expansions and open boundary problems, in computational wave propagation, in: B. Engquist, G.A. Kriegsmann (Eds.), IMA Volumes in Mathematics and Its Applications, vol. 86, Springer, New York, 1997, pp. 23-43.
    • (1997) IMA Volumes in Mathematics and Its Applications , vol.86 , pp. 23-43
    • Hagstrom, T.1    Hariharan, S.I.2
  • 19
    • 0032141095 scopus 로고    scopus 로고
    • A formulation of asymptotic and exact boundary conditions using local operators
    • T. Hagstrom, S.I. Hariharan, A formulation of asymptotic and exact boundary conditions using local operators, Appl. Numer. Math. 27 (1998) 403-416.
    • (1998) Appl. Numer. Math. , vol.27 , pp. 403-416
    • Hagstrom, T.1    Hariharan, S.I.2
  • 20
    • 0034345543 scopus 로고    scopus 로고
    • Continued-fraction absorbing boundary conditions for the wave equation
    • M.N. Guddati, J.L. Tassoulas, Continued-fraction absorbing boundary conditions for the wave equation, J. Comput. Acoust. 8 (2000) 139-156.
    • (2000) J. Comput. Acoust. , vol.8 , pp. 139-156
    • Guddati, M.N.1    Tassoulas, J.L.2
  • 21
    • 0000797694 scopus 로고    scopus 로고
    • High-order non-reflecting boundary conditions without high-order derivatives
    • D. Givoli, High-order non-reflecting boundary conditions without high-order derivatives, J. Comput. Phys. 170 (2001) 849-870.
    • (2001) J. Comput. Phys. , vol.170 , pp. 849-870
    • Givoli, D.1
  • 22
    • 0037051758 scopus 로고    scopus 로고
    • An optimal high-order non-reflecting finite element scheme for wave scattering problems
    • D. Givoli, I. Patlashenko, An optimal high-order non-reflecting finite element scheme for wave scattering problems, Int. J. Numer. Meth. Eng. 53 (2002) 2389-2411.
    • (2002) Int. J. Numer. Meth. Eng. , vol.53 , pp. 2389-2411
    • Givoli, D.1    Patlashenko, I.2
  • 23
    • 0032137824 scopus 로고    scopus 로고
    • Absorbing PML boundary layers for wave-like equations
    • E. Turkel, A. Yefet, Absorbing PML boundary layers for wave-like equations, Appl. Numer. Math. 27 (1998) 533-557.
    • (1998) Appl. Numer. Math. , vol.27 , pp. 533-557
    • Turkel, E.1    Yefet, A.2
  • 24
    • 0032203675 scopus 로고    scopus 로고
    • The perfectly matched layer in curvilinear coordinates
    • F. Collino, P. Monk, The perfectly matched layer in curvilinear coordinates, SIAM J. Sci. Comp. 19 (1998) 2061-2090.
    • (1998) SIAM J. Sci. Comp. , vol.19 , pp. 2061-2090
    • Collino, F.1    Monk, P.2
  • 25
    • 0001700219 scopus 로고
    • Exact boundary conditions for scattering, problems
    • L. Ting, M.J. Miksis, Exact boundary conditions for scattering problems, J. Acoust. Soc. Am. 80 (1986) 1825-1827.
    • (1986) J. Acoust. Soc. Am. , vol.80 , pp. 1825-1827
    • Ting, L.1    Miksis, M.J.2
  • 26
    • 0000778752 scopus 로고
    • Non-reflecting boundary conditions based on Kirchhoff-type formulae
    • D. Givoli, D. Cohen, Non-reflecting boundary conditions based on Kirchhoff-type formulae, J. Comput. Phys. 117 (1995) 102-113.
    • (1995) J. Comput. Phys. , vol.117 , pp. 102-113
    • Givoli, D.1    Cohen, D.2
  • 27
    • 0031696423 scopus 로고    scopus 로고
    • Highly accurate non-reflecting boundary conditions for finite element simulations of transient acoustics problems
    • A.J. Safjan, Highly accurate non-reflecting boundary conditions for finite element simulations of transient acoustics problems, Comput. Meth. Appl. Mech. Eng. 152 (1998) 175-193.
    • (1998) Comput. Meth. Appl. Mech. Eng. , vol.152 , pp. 175-193
    • Safjan, A.J.1
  • 28
    • 0026815499 scopus 로고
    • A spatially exact non-reflecting boundary condition for time dependent problems
    • D. Givoli, A spatially exact non-reflecting boundary condition for time dependent problems, Comput. Meth. Appl. Mech. Eng. 95 (1992) 97-113.
    • (1992) Comput. Meth. Appl. Mech. Eng. , vol.95 , pp. 97-113
    • Givoli, D.1
  • 29
    • 0035902807 scopus 로고    scopus 로고
    • Time-stepping schemes for systems of volterra integra-differential equations
    • I. Patlashenko, D. Givoli, P. Barbone, Time-stepping schemes for systems of volterra integra-differential equations, Comput. Meth. Appl. Mech. Eng. 190 (2001) 5691-5718.
    • (2001) Comput. Meth. Appl. Mech. Eng. , vol.190 , pp. 5691-5718
    • Patlashenko, I.1    Givoli, D.2    Barbone, P.3
  • 30
    • 0030171759 scopus 로고    scopus 로고
    • Space-time finite element method for structural acoustics in infinite domains. Part 2: Exact time-dependent non-reflecting boundary conditions
    • L.L. Thompson, P.M. Pinsky, Space-time finite element method for structural acoustics in infinite domains. Part 2: Exact time-dependent non-reflecting boundary conditions, Comput. Meth. Appl. Mech. Eng. 132 (1996) 229-258.
    • (1996) Comput. Meth. Appl. Mech. Eng. , vol.132 , pp. 229-258
    • Thompson, L.L.1    Pinsky, P.M.2
  • 31
    • 0000985886 scopus 로고    scopus 로고
    • Rapid evaluation of nonreflecting boundary kernels for time-domain wave propagation
    • B. Alpert, L. Greengard, T. Hagstrom, Rapid evaluation of nonreflecting boundary kernels for time-domain wave propagation, SIAM J. Numer. Anal. 37 (2000) 1138-1164.
    • (2000) SIAM J. Numer. Anal. , vol.37 , pp. 1138-1164
    • Alpert, B.1    Greengard, L.2    Hagstrom, T.3
  • 32
    • 0000479160 scopus 로고    scopus 로고
    • An integral evolution formula for the wave equation
    • B. Alpert, L. Greengard, T. Hagstrom, An integral evolution formula for the wave equation, J. Comput. Phys. 162 (2000) 536-543.
    • (2000) J. Comput. Phys. , vol.162 , pp. 536-543
    • Alpert, B.1    Greengard, L.2    Hagstrom, T.3
  • 33
    • 0033588430 scopus 로고    scopus 로고
    • Finite element formulation of exact nonreflecting boundary conditions for the time-dependent wave equation
    • L.L. Thompson, R. Huan, Finite element formulation of exact nonreflecting boundary conditions for the time-dependent wave equation, Int. J. Numer. Meth. Eng. 45 (1999) 1607-1630.
    • (1999) Int. J. Numer. Meth. Eng. , vol.45 , pp. 1607-1630
    • Thompson, L.L.1    Huan, R.2
  • 34
    • 0033872244 scopus 로고    scopus 로고
    • Accurate radiation boundary conditions for the time-dependent wave equation on unbounded domains
    • R. Huan, L.L. Thompson, Accurate radiation boundary conditions for the time-dependent wave equation on unbounded domains, Int. J. Numer. Meth. Eng. 47 (2000) 1569-1603.
    • (2000) Int. J. Numer. Meth. Eng. , vol.47 , pp. 1569-1603
    • Huan, R.1    Thompson, L.L.2
  • 35
    • 0037137834 scopus 로고    scopus 로고
    • Unified formulation of radiation conditions for the wave equation
    • S. Krenk, Unified formulation of radiation conditions for the wave equation, Int. J. Numer. Meth. Eng. 53 (2002) 275-295.
    • (2002) Int. J. Numer. Meth. Eng. , vol.53 , pp. 275-295
    • Krenk, S.1
  • 36
    • 0342316328 scopus 로고    scopus 로고
    • High order implementations of accurate boundary conditions
    • Proceedings of the 5th AIAA/CEAS Aeroacoustics; Conference, Seattle, WA, AIAA
    • J. Goodrich, T. Hagstrom, High order implementations of accurate boundary conditions, in: Proceedings of the 5th AIAA/CEAS Aeroacoustics; Conference, Seattle, WA, AIAA, 1999.
    • (1999)
    • Goodrich, J.1    Hagstrom, T.2
  • 37
    • 0242617669 scopus 로고    scopus 로고
    • A perfectly matched layer formulation for the nonlinear shallow water equations models: The split equation approach
    • (to appear)
    • I.M. Navon, B. Neta, M.Y. Hussaini, A perfectly matched layer formulation for the nonlinear shallow water equations models: the split equation approach (to appear).
    • Navon, I.M.1    Neta, B.2    Hussaini, M.Y.3
  • 38
    • 0033417375 scopus 로고    scopus 로고
    • Recent Advances in the DtN finite element method for unbounded domains
    • D. Givoli, Recent Advances in the DtN finite element method for unbounded domains, Arch. Comput. Meth. Eng. 6 (1999) 71-116.
    • (1999) Arch. Comput. Meth. Eng. , vol.6 , pp. 71-116
    • Givoli, D.1
  • 40
    • 0028374972 scopus 로고
    • Radiation boundary conditions for dispersive waves
    • R.L. Higdon, Radiation boundary conditions for dispersive waves, SIAM J. Numer. Anal. 31 (1994) 64-100.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 64-100
    • Higdon, R.L.1
  • 41
    • 84966222177 scopus 로고
    • Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation
    • R.L. Higdon, Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation, Math. Comput. 47 (1986) 437-459.
    • (1986) Math. Comput. , vol.47 , pp. 437-459
    • Higdon, R.L.1
  • 42
    • 0002618740 scopus 로고
    • Numerical absorbing boundary conditions for the wave equation
    • R.L. Higdon, Numerical absorbing boundary conditions for the wave equation, Math. Comput. 49 (1987) 65-90.
    • (1987) Math. Comput. , vol.49 , pp. 65-90
    • Higdon, R.L.1
  • 43
    • 0025476463 scopus 로고
    • Radiation boundary conditions for elastic wave propagation
    • R.L. Higdon, Radiation boundary conditions for elastic wave propagation, SIAM J. Numer. Anal. 27 (1990) 831-870.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 831-870
    • Higdon, R.L.1
  • 44
    • 0025925925 scopus 로고
    • Absorbing boundary conditions for elastic waves
    • R.L. Higdon, Absorbing boundary conditions for elastic waves, Geophysics 56 (1991) 231-241.
    • (1991) Geophysics , vol.56 , pp. 231-241
    • Higdon, R.L.1
  • 45
    • 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, J. Comput. Phys. 101 (1992) 386-418.
    • (1992) J. Comput. Phys. , vol.101 , pp. 386-418
    • Higdon, R.L.1
  • 46
    • 84903489561 scopus 로고    scopus 로고
    • High-order non-reflecting boundary conditions for dispersive waves
    • (in press)
    • D. Givoli, B. Neta, High-order non-reflecting boundary conditions for dispersive waves, Wave Motion (in press).
    • Wave Motion
    • Givoli, D.1    Neta, B.2
  • 47
    • 85190090173 scopus 로고    scopus 로고
    • Mathematical analysis of absorbing boundary conditions for the wave equation: The corner problem
    • preprint
    • O. Vacus, Mathematical analysis of absorbing boundary conditions for the wave equation: the corner problem, preprint.
    • Vacus, O.1
  • 48
    • 0000851502 scopus 로고
    • Consistent boundary conditions for the numerical models of systems that admit dispersive waves
    • R.A. Pearson, Consistent boundary conditions for the numerical models of systems that admit dispersive waves, J. Atmos. Sci. 31 (1974) 1418-1489.
    • (1974) J. Atmos. Sci. , vol.31 , pp. 1418-1489
    • Pearson, R.A.1
  • 49
    • 0016870918 scopus 로고
    • A simple boundary condition for unbounded hyperbolic flows
    • I. Orlanski, A simple boundary condition for unbounded hyperbolic flows, J. Comput. Phys. 21 (1976) 251-269.
    • (1976) J. Comput. Phys. , vol.21 , pp. 251-269
    • Orlanski, I.1
  • 50
    • 0021638932 scopus 로고
    • A radiation boundary condition for multi-dimensional flows
    • W.H. Raymond, H.L. Kuo, A radiation boundary condition for multi-dimensional flows, Q. J. R. Meteorol. Soc. 110 (1984) 535-551.
    • (1984) Q. J. R. Meteorol. Soc. , vol.110 , pp. 535-551
    • Raymond, W.H.1    Kuo, H.L.2
  • 51
    • 0019655459 scopus 로고
    • Radiation conditions for the lateral boundaries of limited-area numerical models
    • M.J. Miller, A.J. Thorpe, Radiation conditions for the lateral boundaries of limited-area numerical models, Q. J. R. Meteorol. Soc. 107 (1981) 615-628.
    • (1981) Q. J. R. Meteorol. Soc. , vol.107 , pp. 615-628
    • Miller, M.J.1    Thorpe, A.J.2
  • 52
    • 0017824625 scopus 로고
    • Numerical simulation of hydrostatic mountain waves
    • J.B. Klemp, D.K. Lilly, Numerical simulation of hydrostatic mountain waves, J. Atmos. Sci. 35 (1978) 78-107.
    • (1978) J. Atmos. Sci. , vol.35 , pp. 78-107
    • Klemp, J.B.1    Lilly, D.K.2
  • 53
    • 0000823772 scopus 로고
    • The use of open boundary conditions with the Storm-Surge equations
    • M. Wurtele, J. Paegle, A. Sielecki, The use of open boundary conditions with the Storm-Surge equations, Mon. Weather Rev. 99 (1971) 537-544.
    • (1971) Mon. Weather Rev. , vol.99 , pp. 537-544
    • Wurtele, M.1    Paegle, J.2    Sielecki, A.3
  • 54
    • 0001115236 scopus 로고    scopus 로고
    • The naval research laboratory's coupled ocean/atmosphere mesoscale prediction system (COAMPS)
    • R.M. Hodur, The naval research laboratory's coupled ocean/atmosphere mesoscale prediction system (COAMPS), Mon. Weather Rev. 125 (1997) 1414-1430.
    • (1997) Mon. Weather Rev. , vol.125 , pp. 1414-1430
    • Hodur, R.M.1
  • 55
    • 0031105169 scopus 로고    scopus 로고
    • Open boundary conditions for obliquely propagating nonlinear shallow-water waves in a wave channel
    • X. Ren, K.H. Wang, K.R. Jin, Open boundary conditions for obliquely propagating nonlinear shallow-water waves in a wave channel, Comput. Fluids 26 (1997) 269-278.
    • (1997) Comput. Fluids , vol.26 , pp. 269-278
    • Ren, X.1    Wang, K.H.2    Jin, K.R.3
  • 56
    • 0031773212 scopus 로고    scopus 로고
    • Open boundary conditions in stratified ocean models
    • T.G. Jensen, Open boundary conditions in stratified ocean models, J. Marine Syst. 16 (1998) 297-322.
    • (1998) J. Marine Syst. , vol.16 , pp. 297-322
    • Jensen, T.G.1
  • 57
    • 0035238994 scopus 로고    scopus 로고
    • Improvement on open boundaries on a time dependent numerical model of wave propagation in the nearshore region
    • F.S.B.F. Oliveira, Improvement on open boundaries on a time dependent numerical model of wave propagation in the nearshore region, Ocean Eng. 28 (2000) 95-115.
    • (2000) Ocean Eng. , vol.28 , pp. 95-115
    • Oliveira, F.S.B.F.1
  • 59
    • 0001818026 scopus 로고
    • Symmetric linear multistep methods for second order differential equations with periodic solutions
    • B.P. Sommeijer, P.J. van der Houwen, B. Neta, Symmetric linear multistep methods for second order differential equations with periodic solutions, Appl. Numer. Math. 2 (1986) 69-77.
    • (1986) Appl. Numer. Math. , vol.2 , pp. 69-77
    • Sommeijer, B.P.1    van der Houwen, P.J.2    Neta, B.3
  • 60
    • 0012745051 scopus 로고    scopus 로고
    • High-order Higdon non-reflecting boundary conditions for the shallow water equations
    • Report NPS-MA-02-001, Naval Postgraduate School, Monterey, CA
    • D. Givoli, B. Neta, High-order Higdon non-reflecting boundary conditions for the shallow water equations, Report NPS-MA-02-001, Naval Postgraduate School, Monterey, CA, 2002.
    • (2002)
    • Givoli, D.1    Neta, B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.