메뉴 건너뛰기




Volumn 145, Issue 2, 1998, Pages 611-638

Discrete Transparent Boundary Conditions for Wide Angle Parabolic Equations in Underwater Acoustics

Author keywords

Discrete transparent boundary conditions; Finite differences; Transparent boundary conditions; Underwater acoustics; Wide angle parabolic equation

Indexed keywords

ACOUSTIC FIELDS; BOUNDARY CONDITIONS; FINITE DIFFERENCE METHOD; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0011217467     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.6043     Document Type: Article
Times cited : (79)

References (49)
  • 2
    • 0002444258 scopus 로고
    • Exact and asymptotic representations of the sound field in a stratified ocean
    • Ahluwalia D. S., Keller J. B. Exact and asymptotic representations of the sound field in a stratified ocean. Wave Propagation and Underwater Acoustics. 70:1977;14.
    • (1977) Wave Propagation and Underwater Acoustics , vol.70 , pp. 14
    • Ahluwalia, D.S.1    Keller, J.B.2
  • 3
    • 0040580194 scopus 로고    scopus 로고
    • Error estimates for finite difference methods for a wide-angle "parabolic" equation
    • Akrivis G. D., Dougalis V. A., Zouraris G. E. Error estimates for finite difference methods for a wide-angle "parabolic" equation. SIAM J. Num. Anal. 33:1996;2488.
    • (1996) SIAM J. Num. Anal. , vol.33 , pp. 2488
    • Akrivis, G.D.1    Dougalis, V.A.2    Zouraris, G.E.3
  • 4
    • 0022786406 scopus 로고
    • Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order
    • Amos D. E. Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order. ACM Trans. Math. Software. 12:1986;265.
    • (1986) ACM Trans. Math. Software , vol.12 , pp. 265
    • Amos, D.E.1
  • 9
    • 0001262382 scopus 로고
    • Implementation of transparent boundaries for numerical solution of the Schrödinger equation
    • Baskakov V. A., Popov A. V. Implementation of transparent boundaries for numerical solution of the Schrödinger equation. Wave Motion. 14:1991;123.
    • (1991) Wave Motion , vol.14 , pp. 123
    • Baskakov, V.A.1    Popov, A.V.2
  • 11
    • 0010156915 scopus 로고
    • Conditions aux limites transparentes et artificielles pour l'équation de Schrödinger en dimension 1 d'espace
    • Bruneau C. H., Di Menza L. Conditions aux limites transparentes et artificielles pour l'équation de Schrödinger en dimension 1 d'espace. C.R. Acad. Sci. Paris Ser. I. 320:1995;89.
    • (1995) C.R. Acad. Sci. Paris Ser. I , vol.320 , pp. 89
    • Bruneau, C.H.1    Di Menza, L.2
  • 12
    • 0001095190 scopus 로고
    • Coarse grid calculation of waves in inhomogeneous media with application to delineation of complicated seismic structure
    • Claerbout J. F. Coarse grid calculation of waves in inhomogeneous media with application to delineation of complicated seismic structure. Geophysics. 35:1970;407.
    • (1970) Geophysics , vol.35 , pp. 407
    • Claerbout, J.F.1
  • 14
    • 0001418867 scopus 로고
    • Applications and time-domain solution of higher-order parabolic equations in underwater acoustics
    • Collins M. D. Applications and time-domain solution of higher-order parabolic equations in underwater acoustics. J. Acoust. Soc. Am. 86:1989;1097.
    • (1989) J. Acoust. Soc. Am. , vol.86 , pp. 1097
    • Collins, M.D.1
  • 15
    • 0000821904 scopus 로고
    • A higher-order parabolic equation for wave propagation in an ocean overlying an elastic bottom
    • Collins M. D. A higher-order parabolic equation for wave propagation in an ocean overlying an elastic bottom. J. Acoust. Soc. Am. 86:1989;1459.
    • (1989) J. Acoust. Soc. Am. , vol.86 , pp. 1459
    • Collins, M.D.1
  • 16
    • 0013500098 scopus 로고
    • Higher-order and elastic parabolic equations for wave propagation in the ocean
    • D. LeeA. CakmakR. Vichnevetsky, IMACS, New Brunswick, NJ
    • M. D. Collins, Higher-order and elastic parabolic equations for wave propagation in the ocean, Computational Acoustics, Vol. 3, D. LeeA. CakmakR. Vichnevetsky, IMACS, New Brunswick, NJ, 1990, 167.
    • (1990) Computational Acoustics , vol.3 , pp. 167
    • Collins, M.D.1
  • 17
    • 0027341189 scopus 로고
    • A split-step Padé solution for the parabolic equation method
    • Collins M. D. A split-step Padé solution for the parabolic equation method. J. Acoust. Soc. Am. 93:1993;1736.
    • (1993) J. Acoust. Soc. Am. , vol.93 , pp. 1736
    • Collins, M.D.1
  • 21
    • 33644684976 scopus 로고    scopus 로고
    • Discrete transparent boundary conditions for parabolic equations
    • Ehrhardt M. Discrete transparent boundary conditions for parabolic equations. Proceedings of the GAMM 96 Conference. 77:1997.
    • (1997) Proceedings of the GAMM 96 Conference , vol.77
    • Ehrhardt, M.1
  • 22
    • 0000733481 scopus 로고
    • Exact and operator rational approximate solutions of the Helmholtz, Weyl composition equation in underwater acoustics - The quadratic profile
    • Fishman L. Exact and operator rational approximate solutions of the Helmholtz, Weyl composition equation in underwater acoustics - The quadratic profile. J. Math. Phys. 33:1992;1887.
    • (1992) J. Math. Phys. , vol.33 , pp. 1887
    • Fishman, L.1
  • 23
    • 0021638831 scopus 로고
    • The rational approximation to the acoustic wave equation with bottom interaction
    • Greene R. R. The rational approximation to the acoustic wave equation with bottom interaction. J. Acoust. Soc. Am. 76:1984;1764.
    • (1984) J. Acoust. Soc. Am. , vol.76 , pp. 1764
    • Greene, R.R.1
  • 24
    • 0000182001 scopus 로고
    • A high-angle one-way wave equation for seismic wave propagation along rough and sloping interfaces
    • Greene R. R. A high-angle one-way wave equation for seismic wave propagation along rough and sloping interfaces. J. Acoust. Soc. Am. 77:1985;1991.
    • (1985) J. Acoust. Soc. Am. , vol.77 , pp. 1991
    • Greene, R.R.1
  • 26
    • 0001315174 scopus 로고
    • Non-Markovian open-system boundary conditions for the time-dependent Schrödinger equation
    • Hellums J. R., Frensley W. R. Non-Markovian open-system boundary conditions for the time-dependent Schrödinger equation. Phys. Rev. B. 49:1994;2904.
    • (1994) Phys. Rev. B , vol.49 , pp. 2904
    • Hellums, J.R.1    Frensley, W.R.2
  • 29
    • 0039987120 scopus 로고
    • General boundary value problems for differential equations of Sobolev type
    • Lagnese J. E. General boundary value problems for differential equations of Sobolev type. SIAM J. Math. Anal. 3:1972;105.
    • (1972) SIAM J. Math. Anal. , vol.3 , pp. 105
    • Lagnese, J.E.1
  • 30
    • 0023533509 scopus 로고
    • Ocean acoustic propagation by finite difference methods
    • Lee D., McDaniel S. T. Ocean acoustic propagation by finite difference methods. Comput. Math. Appl. 14:1987;305.
    • (1987) Comput. Math. Appl. , vol.14 , pp. 305
    • Lee, D.1    McDaniel, S.T.2
  • 31
    • 0019614104 scopus 로고
    • Finite-difference solution to the parabolic wave equation
    • Lee D., Botseas G., Papadakis J. S. Finite-difference solution to the parabolic wave equation. J. Acoust. Soc. Am. 70:1981;795.
    • (1981) J. Acoust. Soc. Am. , vol.70 , pp. 795
    • Lee, D.1    Botseas, G.2    Papadakis, J.S.3
  • 32
    • 84976706602 scopus 로고
    • Algorithm 413: ENTCAF and ENTCRE: Evaluation of normalized Taylor coefficients of an analytic function
    • Lyness J. N. Algorithm 413: ENTCAF and ENTCRE: Evaluation of normalized Taylor coefficients of an analytic function. Comm. ACM. 14:1971;669.
    • (1971) Comm. ACM , vol.14 , pp. 669
    • Lyness, J.N.1
  • 33
    • 0039987122 scopus 로고    scopus 로고
    • Weak limits of finite difference schemes for Schrödinger-type equations
    • Markowich P. A., Pietra P., Pohl C. Weak limits of finite difference schemes for Schrödinger-type equations. Numer. Math. 1997.
    • (1997) Numer. Math.
    • Markowich, P.A.1    Pietra, P.2    Pohl, C.3
  • 34
    • 84966240649 scopus 로고
    • The numerical solution of second order boundary value problems on nonuniform meshes
    • Manteuffel T. A., White A. B. Jr. The numerical solution of second order boundary value problems on nonuniform meshes. Math. Comput. 47:1986;511.
    • (1986) Math. Comput. , vol.47 , pp. 511
    • Manteuffel, T.A.1    White A.B., Jr.2
  • 36
    • 0020116515 scopus 로고
    • A finite-difference treatment of interface conditions for the parabolic wave equation: The horizontal interface
    • McDaniel S. T., Lee D. A finite-difference treatment of interface conditions for the parabolic wave equation: The horizontal interface. J. Acoust. Soc. Am. 71:1982;855.
    • (1982) J. Acoust. Soc. Am. , vol.71 , pp. 855
    • McDaniel, S.T.1    Lee, D.2
  • 37
    • 0002145516 scopus 로고
    • Impedance formulation of the bottom boundary condition for the parabolic equation model in underwater acoustics
    • J. S. Papadakis, Impedance Formulation of the Bottom Boundary Condition for the Parabolic Equation Model in Underwater Acoustics, NORDA Parabolic Equation Workshop, 1982.
    • (1982) NORDA Parabolic Equation Workshop
    • Papadakis, J.S.1
  • 38
    • 0026616466 scopus 로고
    • A new method for a realistic treatment of the sea bottom in the parabolic approximation
    • Papadakis J. S., Taroudakis M. I., Papadakis P. J., Mayfield B. A new method for a realistic treatment of the sea bottom in the parabolic approximation. J. Acoust. Soc. Am. 92:1992;2030.
    • (1992) J. Acoust. Soc. Am. , vol.92 , pp. 2030
    • Papadakis, J.S.1    Taroudakis, M.I.2    Papadakis, P.J.3    Mayfield, B.4
  • 39
    • 0011188824 scopus 로고
    • Impedance bottom boundary conditions for the parabolic-type approximations in underwater acoustics
    • R. VichnevetskyD. KnightG. Richter, IMACS, New Brunswick, NJ
    • J. S. Papadakis, Impedance bottom boundary conditions for the parabolic-type approximations in underwater acoustics, Advances in Computer Methods for Partial Differential Equations VII, R. VichnevetskyD. KnightG. Richter, IMACS, New Brunswick, NJ, 1992, 585.
    • (1992) Advances in Computer Methods for Partial Differential Equations VII , pp. 585
    • Papadakis, J.S.1
  • 41
    • 0010945360 scopus 로고
    • Discrete transparent boundary conditions for the numerical solution of Fresnel's equation
    • Schmidt F., Deuflhard P. Discrete transparent boundary conditions for the numerical solution of Fresnel's equation. Comput. Math. Appl. 29:1995;53.
    • (1995) Comput. Math. Appl. , vol.29 , pp. 53
    • Schmidt, F.1    Deuflhard, P.2
  • 42
    • 0031161655 scopus 로고    scopus 로고
    • Discrete transparent boundary conditions for Schrödinger-type equations
    • Schmidt F., Yevick D. Discrete transparent boundary conditions for Schrödinger-type equations. J. Comput. Phys. 134:1997;96.
    • (1997) J. Comput. Phys. , vol.134 , pp. 96
    • Schmidt, F.1    Yevick, D.2
  • 45
    • 0000978807 scopus 로고
    • The parabolic approximation method
    • J. B. KellerJ. S. Papadakis, Springer, New York
    • F. D. Tappert, The parabolic approximation method, Wave Propagation and Underwater Acoustics, 70, J. B. KellerJ. S. Papadakis, Springer, New York, 1977, 224.
    • (1977) Wave Propagation and Underwater Acoustics , vol.70 , pp. 224
    • Tappert, F.D.1
  • 46
    • 0025039829 scopus 로고
    • Wide-angle parabolic equation solutions to two range-dependent benchmark problems
    • Thomson D. J. Wide-angle parabolic equation solutions to two range-dependent benchmark problems. J. Acoust. Soc. Am. 87:1990;1514.
    • (1990) J. Acoust. Soc. Am. , vol.87 , pp. 1514
    • Thomson, D.J.1
  • 47
    • 0001347206 scopus 로고
    • An exact radiation condition for use with the a posteriori PE method
    • Thomson D. J., Mayfield M. E. An exact radiation condition for use with the a posteriori PE method. J. Comput. Acoust. 2:1994;113.
    • (1994) J. Comput. Acoust. , vol.2 , pp. 113
    • Thomson, D.J.1    Mayfield, M.E.2
  • 48
    • 38249037558 scopus 로고
    • Wave propagation and reflection in irregular grids for hyperbolic equations
    • Vichnevetsky R. Wave propagation and reflection in irregular grids for hyperbolic equations. Appl. Numer. Math. 3:1987;133.
    • (1987) Appl. Numer. Math. , vol.3 , pp. 133
    • Vichnevetsky, R.1
  • 49
    • 0025307734 scopus 로고
    • One-way wave equations for seismoacoustic propagation in elastic waveguides
    • Wetton B. T., Brooke G. H. One-way wave equations for seismoacoustic propagation in elastic waveguides. J. Acoust. Soc. Am. 87:1990;624.
    • (1990) J. Acoust. Soc. Am. , vol.87 , pp. 624
    • Wetton, B.T.1    Brooke, G.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.