메뉴 건너뛰기




Volumn 106, Issue 3, 2007, Pages 471-510

A hybrid numerical-asymptotic boundary integral method for high-frequency acoustic scattering

Author keywords

Acoustic scattering; Boundary integral method; High frequency; Hybrid numerical asymptotic; Wave number robust

Indexed keywords


EID: 34248169761     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-007-0071-4     Document Type: Article
Times cited : (96)

References (47)
  • 1
    • 0010633701 scopus 로고
    • Méthode des équations intégrales pour les hautes fréquencies
    • Série 1
    • Abboud, T., Nédélec, J.-C., Zhou B.: Méthode des équations intégrales pour les hautes fréquencies. C.R. Acad. Sci. Paris 318 Série 1, 165-170 (1994)
    • (1994) C.R. Acad. Sci. Paris , vol.318 , pp. 165-170
    • Abboud, T.1    Nédélec, J.-C.2    Zhou, B.3
  • 3
    • 0002749845 scopus 로고
    • On the choice of the coupling parameter in boundary integral formulations of the exterior acoustics problem
    • Amini, S.: On the choice of the coupling parameter in boundary integral formulations of the exterior acoustics problem. Appl. Anal. 35, 75-92 (1990)
    • (1990) Appl. Anal , vol.35 , pp. 75-92
    • Amini, S.1
  • 4
    • 34248219081 scopus 로고    scopus 로고
    • A collocation method for high frequency scattering by convex polygons. Reading University Numerical Analysis Report 7/05, Reading, UK
    • to appear
    • Arden, S., Chandler-Wilde, S.N., Langdon, S.: A collocation method for high frequency scattering by convex polygons. Reading University Numerical Analysis Report 7/05, Reading, UK. J. Comp. Appl. Math. (to appear)
    • J. Comp. Appl. Math
    • Arden, S.1    Chandler-Wilde, S.N.2    Langdon, S.3
  • 6
    • 0034566041 scopus 로고    scopus 로고
    • On evaluation of the diffraction coefficients for arbitrary "nonsingular" directions of a smooth convex cone
    • Babich, V.M., Dement'ev, D.B., Samokish, B.A., Smyshlyaev, V.P.: On evaluation of the diffraction coefficients for arbitrary "nonsingular" directions of a smooth convex cone. SIAM J. Appl. Math. 60, 536-573 (2000)
    • (2000) SIAM J. Appl. Math , vol.60 , pp. 536-573
    • Babich, V.M.1    Dement'ev, D.B.2    Samokish, B.A.3    Smyshlyaev, V.P.4
  • 8
    • 33745465893 scopus 로고    scopus 로고
    • The computation of conical diffraction coefficients in high-frequency acoustic wave scattering
    • Bonner, B.D., Graham, I.G., Smyshlyaev, V.P.: The computation of conical diffraction coefficients in high-frequency acoustic wave scattering. SIAM J. Numer. Anal. 43, 1202-1230 (2005)
    • (2005) SIAM J. Numer. Anal , vol.43 , pp. 1202-1230
    • Bonner, B.D.1    Graham, I.G.2    Smyshlyaev, V.P.3
  • 10
    • 0000204968 scopus 로고
    • Über das Dirichletsche Aussenraumproblem für die Helmholtzsche Schwingungsgleichung
    • Brakhage, H. Werner P.: Über das Dirichletsche Aussenraumproblem für die Helmholtzsche Schwingungsgleichung. Arch, der Math. 16, 325-329 (1965)
    • (1965) Arch, der Math , vol.16 , pp. 325-329
    • Brakhage, H.1    Werner, P.2
  • 11
    • 1642313920 scopus 로고    scopus 로고
    • Bruno, O.P., Geuzaine, C.A., Monro, J.A. Reitich F.: Prescribed error tolerances within fixed computational times for scattering problems of arbitrarily high frequency: the convex case. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 362, 629-645 (2004)
    • Bruno, O.P., Geuzaine, C.A., Monro, J.A. Reitich F.: Prescribed error tolerances within fixed computational times for scattering problems of arbitrarily high frequency: the convex case. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 362, 629-645 (2004)
  • 12
    • 22044435361 scopus 로고    scopus 로고
    • On the O(1) solution of multiple-scattering problems
    • Bruno, O.P., Geuzaine, C.A., Reitich, F.: On the O(1) solution of multiple-scattering problems. IEEE Trans. Magn. 41, 1488-1491 (2005)
    • (2005) IEEE Trans. Magn , vol.41 , pp. 1488-1491
    • Bruno, O.P.1    Geuzaine, C.A.2    Reitich, F.3
  • 13
    • 34248190752 scopus 로고    scopus 로고
    • Stabilisation of the acoustic single layer potential on non-smooth domains
    • Buffa, A., Sauter, S.A.: Stabilisation of the acoustic single layer potential on non-smooth domains. SIAM J. Sci. Comput. 28, 1974-1999 (2006)
    • (2006) SIAM J. Sci. Comput , vol.28 , pp. 1974-1999
    • Buffa, A.1    Sauter, S.A.2
  • 14
    • 0000181954 scopus 로고
    • The application of integral methods for the numerical solution of boundary value problems
    • Burton, A.J., Miller, G.F.: The application of integral methods for the numerical solution of boundary value problems. Proc. R. Soc. Lond. Ser. A 232, 201-210 (1971)
    • (1971) Proc. R. Soc. Lond. Ser. A , vol.232 , pp. 201-210
    • Burton, A.J.1    Miller, G.F.2
  • 15
    • 0010146357 scopus 로고
    • Short-wave asymptotic behaviour in the problem of diffraction by smooth convex contours(in Russian)
    • Buslaev, VS.: Short-wave asymptotic behaviour in the problem of diffraction by smooth convex contours(in Russian). Trudy Mat. Inst. Steklov. 73 14-117 (1964).
    • (1964) Trudy Mat. Inst. Steklov , vol.73 , pp. 14-117
    • Buslaev, V.S.1
  • 16
    • 0042888723 scopus 로고
    • Abbreviated English translation: On the shortwave asymptotic limit in the problem of diffraction by convex bodies
    • Abbreviated English translation: On the shortwave asymptotic limit in the problem of diffraction by convex bodies. Sov. Phys. Dokl. 7, 685-687 (1963)
    • (1963) Sov. Phys. Dokl , vol.7 , pp. 685-687
  • 17
    • 34248231785 scopus 로고    scopus 로고
    • Buslaev, VS.: Formulas for the short-wave asymptotic behavior in the diffraction problem by convex bodies, (in Russian) Vestnik Leningrad. University 17(13), 5-21 (1962)
    • Buslaev, VS.: Formulas for the short-wave asymptotic behavior in the diffraction problem by convex bodies, (in Russian) Vestnik Leningrad. University 17(13), 5-21 (1962)
  • 18
    • 34248175804 scopus 로고
    • The asymptotic behavior of the spectral characteristics of exterior problems for the Schrödinger operator (in Russian)
    • Buslaev, VS.: The asymptotic behavior of the spectral characteristics of exterior problems for the Schrödinger operator (in Russian). Izv. Akad. Nauk SSSR Ser. Mat. 39, 149-235 (1975);
    • (1975) Izv. Akad. Nauk SSSR Ser. Mat , vol.39 , pp. 149-235
    • Buslaev, V.S.1
  • 19
    • 34248158963 scopus 로고
    • English translation
    • English translation: Math. USSR-Izv. 9 139-223 (1975)
    • (1975) Math. USSR-Izv , vol.9 , pp. 139-223
  • 20
    • 0040183627 scopus 로고
    • Construction de la paramétrix du problème mixte hyperbolique pour l'equation des ondes
    • Chozarain, J.: Construction de la paramétrix du problème mixte hyperbolique pour l'equation des ondes. C. R. Acad. Sci. Paris 276, 1213-1215 (1973)
    • (1973) C. R. Acad. Sci. Paris , vol.276 , pp. 1213-1215
    • Chozarain, J.1
  • 23
    • 34248152697 scopus 로고
    • Rigorous justification of the shortwave asymptotic theory of diffraction in the shadow zone
    • Filippov, V.B.: Rigorous justification of the shortwave asymptotic theory of diffraction in the shadow zone. J. Sov. Math. 6, 577-626 (1976)
    • (1976) J. Sov. Math , vol.6 , pp. 577-626
    • Filippov, V.B.1
  • 25
    • 3042858769 scopus 로고    scopus 로고
    • A high-order algorithm for obstacle scattering in three dimensions
    • Ganesh, M., Graham, I.G.: A high-order algorithm for obstacle scattering in three dimensions. J. Comput. Phys. 198, 211-242 (2004)
    • (2004) J. Comput. Phys , vol.198 , pp. 211-242
    • Ganesh, M.1    Graham, I.G.2
  • 26
    • 34248168146 scopus 로고    scopus 로고
    • Efficient evaluation of highly oscillatory acoustic scattering surface integrals
    • 6/05, Reading, UK
    • Ganesh, M., Langdon, S., Sloan, I.H.: Efficient evaluation of highly oscillatory acoustic scattering surface integrals. Reading University Numerical Analysis Report 6/05, Reading, UK (2005)
    • (2005) Reading University Numerical Analysis Report
    • Ganesh, M.1    Langdon, S.2    Sloan, I.H.3
  • 28
    • 34248212764 scopus 로고    scopus 로고
    • Giladi, E., Keller, J.B.: An asymptotically derived boundary element method for the Helmholtz equation. In 20th Annual Review of Progress in Applied Computational Electromagnetics, Syracuse, New York (2004)
    • Giladi, E., Keller, J.B.: An asymptotically derived boundary element method for the Helmholtz equation. In 20th Annual Review of Progress in Applied Computational Electromagnetics, Syracuse, New York (2004)
  • 29
    • 0003284896 scopus 로고
    • The Analysis of Linear Differential Operators
    • Analysis. Springer, Berlin
    • Hörmander, L.: The Analysis of Linear Differential Operators. 1, Distribution Theory and Fourier Analysis. Springer, Berlin (1983)
    • (1983) Distribution Theory and Fourier , vol.1
    • Hörmander, L.1
  • 30
    • 0022059920 scopus 로고
    • Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering
    • Kress, R.: Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering. Q. J. Mech. Appl. Math. 38, 323-341 (1985)
    • (1985) Q. J. Mech. Appl. Math , vol.38 , pp. 323-341
    • Kress, R.1
  • 31
    • 0003376378 scopus 로고
    • On the condition number of boundary integral operators for the exterior Dirichlet problem for the Helmholtz equation
    • Kress, R., Spassov, W.T.: On the condition number of boundary integral operators for the exterior Dirichlet problem for the Helmholtz equation. Numer. Math. 42, 77-85 (1983)
    • (1983) Numer. Math , vol.42 , pp. 77-85
    • Kress, R.1    Spassov, W.T.2
  • 32
    • 0034134869 scopus 로고    scopus 로고
    • Bessel functions: Monotonicity and bounds
    • Landau, L.J.: Bessel functions: monotonicity and bounds. J. Lond. Math. Soc. 61, 197-215 (2000)
    • (2000) J. Lond. Math. Soc , vol.61 , pp. 197-215
    • Landau, L.J.1
  • 33
    • 33845517970 scopus 로고    scopus 로고
    • A wavenumber independent boundary element method for an acoustic scattering problem. Isaac Newton Institute for Mathematical Sciences Preprint N103049-1090 CPD, 2003
    • Langdon, S., Chandler-Wilde, S.N.: A wavenumber independent boundary element method for an acoustic scattering problem. Isaac Newton Institute for Mathematical Sciences Preprint N103049-1090 CPD, 2003, SIAM J. Numer. Anal. 43, 2450-2477 (2006)
    • (2006) SIAM J. Numer. Anal , vol.43 , pp. 2450-2477
    • Langdon, S.1    Chandler-Wilde, S.N.2
  • 34
    • 34248187096 scopus 로고    scopus 로고
    • Implementation of aboundary element method for high frequency scattering by convex polygons
    • Chen, K, ed, Liverpool, pp, University of Liverpool
    • Langdon, S., Chandler-Wilde, S. N.: Implementation of aboundary element method for high frequency scattering by convex polygons. In: Chen, K. (ed.) Proceedings of 5th UK Conference on Boundary Integral Methods, Liverpool, pp. 2-11. University of Liverpool (2005)
    • (2005) Proceedings of 5th UK Conference on Boundary Integral Methods , pp. 2-11
    • Langdon, S.1    Chandler-Wilde, S.N.2
  • 35
    • 0040310944 scopus 로고
    • Régularité Gevrey 3 pour la diffraction
    • Lebeau, G.: Régularité Gevrey 3 pour la diffraction. Comm. Partial Differ. Equ. 9, 1437-1494 (1984)
    • (1984) Comm. Partial Differ. Equ , vol.9 , pp. 1437-1494
    • Lebeau, G.1
  • 36
    • 0000804485 scopus 로고
    • Diffraction par un convexe
    • Hargé, T., Lebeau, G.: Diffraction par un convexe. Invent. Math. 118, 161-196 (1994)
    • (1994) Invent. Math , vol.118 , pp. 161-196
    • Hargé, T.1    Lebeau, G.2
  • 37
    • 84981757663 scopus 로고
    • Uniform asymptotic expansion of the field scattered by a convex onject at high frequencies
    • Ludwig, D.: Uniform asymptotic expansion of the field scattered by a convex onject at high frequencies. Comm. Pure Appl. Math. 20, 103-138 (1967)
    • (1967) Comm. Pure Appl. Math , vol.20 , pp. 103-138
    • Ludwig, D.1
  • 38
    • 84981760477 scopus 로고
    • An inequality for the reduced wave equation and the justification of geometrical optics
    • Morawetz, C.S., Ludwig, D.: An inequality for the reduced wave equation and the justification of geometrical optics. Comm. Pure Appl. Math. 21, 187-203 (1968)
    • (1968) Comm. Pure Appl. Math , vol.21 , pp. 187-203
    • Morawetz, C.S.1    Ludwig, D.2
  • 39
    • 0000498121 scopus 로고
    • Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle
    • Melrose, R.B., Taylor, M.E.: Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle. Adv. Math. 55, 242-315 (1985)
    • (1985) Adv. Math , vol.55 , pp. 242-315
    • Melrose, R.B.1    Taylor, M.E.2
  • 41
    • 84972575206 scopus 로고
    • Some estimates of Green's functions in the shadow
    • Popov, G.: Some estimates of Green's functions in the shadow. Osaka J. Math. 24, 1-12 (1987)
    • (1987) Osaka J. Math , vol.24 , pp. 1-12
    • Popov, G.1
  • 43
    • 84971184145 scopus 로고
    • Creeping modes in a shadow
    • Ursell, F.: Creeping modes in a shadow. Proc. Camb. Philos. Soc. 68, 171-191 (1968)
    • (1968) Proc. Camb. Philos. Soc , vol.68 , pp. 171-191
    • Ursell, F.1
  • 45
    • 0040310946 scopus 로고
    • Rigorous justification of the asymptotic solutions of "sliding-wave" type
    • Zayaev, A.B., Filippov, V.P.: Rigorous justification of the asymptotic solutions of "sliding-wave" type. J. Sov. Math. 30, 2395-2406 (1985)
    • (1985) J. Sov. Math , vol.30 , pp. 2395-2406
    • Zayaev, A.B.1    Filippov, V.P.2
  • 46
    • 34248203665 scopus 로고
    • Rigorous justification of the Friedlander-Keller formulas
    • Zayaev, A.B., Filippov, V.P. : Rigorous justification of the Friedlander-Keller formulas. J. Sov. Math. 32, 134-143 (1986)
    • (1986) J. Sov. Math , vol.32 , pp. 134-143
    • Zayaev, A.B.1    Filippov, V.P.2
  • 47
    • 84974003600 scopus 로고
    • High frequency scatering by a convex obstacle
    • Zworski, M.: High frequency scatering by a convex obstacle. Duke Math. J. 61, 545-634 (1990)
    • (1990) Duke Math. J , vol.61 , pp. 545-634
    • Zworski, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.