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Volumn 82, Issue 282, 2013, Pages 919-952

Error estimates for Gaussian beam superpositions

Author keywords

Error estimates; Gaussian beams; High frequency wave propagation

Indexed keywords


EID: 84873266486     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-2012-02656-1     Document Type: Article
Times cited : (49)

References (36)
  • 1
    • 78751701178 scopus 로고    scopus 로고
    • Gaussian beam decomposition of high frequency wave fields using expectation-maximization
    • G. Ariel, B. Engquist, N. M. Tanushev, and R. Tsai. Gaussian beam decomposition of high frequency wave fields using expectation-maximization. J. Comput. Phys., 230(6):2303-2321, 2011.
    • (2011) J. Comput. Phys. , vol.230 , Issue.6 , pp. 2303-2321
    • Ariel, G.1    Engquist, B.2    Tanushev, N.M.3    Tsai, R.4
  • 3
    • 0012495013 scopus 로고
    • On discontinuities of Green's function of the wave equation with variable coefficient
    • Leningrad University, Saint-Petersburg
    • V. M. Babič and T. F. Pankratova. On discontinuities of Green's function of the wave equation with variable coefficient. Problemy Matem. Fiziki, 6, 1973. Leningrad University, Saint-Petersburg.
    • (1973) Problemy Matem. Fiziki , vol.6
    • Babič, V.M.1    Pankratova, T.F.2
  • 5
    • 77953933814 scopus 로고    scopus 로고
    • Gaussian beams summation for the wave equation in a convex domain
    • S. Bougacha, J.L. Akian, and R. Alexandre. Gaussian beams summation for the wave equation in a convex domain. Commun. Math. Sci., 7(4):973-1008, 2009.
    • (2009) Commun. Math. Sci. , vol.7 , Issue.4 , pp. 973-1008
    • Bougacha, S.1    Akian, J.L.2    Alexandre, R.3
  • 6
    • 84984525506 scopus 로고
    • Computation of wave fields in inhomogeneous media - Gaussian beam approach
    • V. Červený, M. M. Popov, and I. Pšenčík. Computation of wave fields in inhomogeneous media - Gaussian beam approach. Geophys. J. R. Astr. Soc., 70:109-128, 1982.
    • (1982) Geophys. J. R. Astr. Soc. , vol.70 , pp. 109-128
    • Červený, V.1    Popov, M.M.2    Pšenčík, I.3
  • 7
    • 24644487123 scopus 로고    scopus 로고
    • Computational high frequency wave propagation
    • B. Engquist and O. Runborg. Computational high frequency wave propagation. Acta Numerica, 12:181-266, 2003.
    • (2003) Acta Numerica , vol.12 , pp. 181-266
    • Engquist, B.1    Runborg, O.2
  • 8
    • 0025626799 scopus 로고
    • Gaussian beam migration
    • N. R. Hill. Gaussian beam migration. Geophysics, 55(11):1416-1428, 1990.
    • (1990) Geophysics , vol.55 , Issue.11 , pp. 1416-1428
    • Hill, N.R.1
  • 9
    • 0035387609 scopus 로고    scopus 로고
    • Prestack Gaussian beam depth migration
    • N. R. Hill. Prestack Gaussian beam depth migration. Geophysics, 66(4):1240-1250, 2001.
    • (2001) Geophysics , vol.66 , Issue.4 , pp. 1240-1250
    • Hill, N.R.1
  • 10
    • 0002820858 scopus 로고
    • Fourier integral operators
    • L. Hörmander. Fourier integral operators. I. Acta Math., 127(1-2):79-183, 1971.
    • (1971) I. Acta Math. , vol.127 , Issue.1-2 , pp. 79-183
    • Hörmander, L.1
  • 11
    • 0002709344 scopus 로고
    • On the existence and the regularity of solutions of linear pseudo-differential equations
    • L. Hörmander. On the existence and the regularity of solutions of linear pseudo-differential equations. L'Enseignement Math́ematique, XVII:99-163, 1971.
    • (1971) L'Enseignement Math́ematique , vol.17 , pp. 99-163
    • Hörmander, L.1
  • 12
    • 0003668851 scopus 로고    scopus 로고
    • I. Classics in Mathematics. Springer, Berlin, Distribution theory and Fourier analysis, Reprint of the 1990 edition
    • L. Hörmander. The analysis of linear partial differential operators. I. Classics in Mathematics. Springer, Berlin, 2003. Distribution theory and Fourier analysis, Reprint of the 1990 edition.
    • (2003) The analysis of linear partial differential operators
    • Hörmander, L.1
  • 14
    • 77950364040 scopus 로고    scopus 로고
    • Gaussian beam methods for the Schrödinger equation in the semiclassical regime: Lagrangian and Eulerian formulations
    • S. Jin, H.Wu, and X. Yang. Gaussian beam methods for the Schrödinger equation in the semiclassical regime: Lagrangian and Eulerian formulations. Commun. Math. Sci., 6:995-1020, 2008.
    • (2008) Commun. Math. Sci. , vol.6 , pp. 995-1020
    • Jin, S.1    Wu, H.2    Yang, X.3
  • 15
    • 12244269802 scopus 로고
    • Application of the method of summation of Gaussian beams for calculation of high-frequency wave fields
    • A. P. Katchalov and M. M. Popov. Application of the method of summation of Gaussian beams for calculation of high-frequency wave fields. Sov. Phys. Dokl., 26:604-606, 1981.
    • (1981) Sov. Phys. Dokl. , vol.26 , pp. 604-606
    • Katchalov, A.P.1    Popov, M.M.2
  • 16
    • 0000724502 scopus 로고
    • Corrected Bohr-Sommerfeld quantum conditions for nonseparable systems
    • J. B. Keller. Corrected Bohr-Sommerfeld quantum conditions for nonseparable systems. Ann. Physics, 4:180-188, 1958.
    • (1958) Ann. Physics , vol.4 , pp. 180-188
    • Keller, J.B.1
  • 17
    • 84986357083 scopus 로고
    • Expansion of a high-frequency time-harmonic wavefield given on an initial surface into Gaussian beams
    • L. Klimeš. Expansion of a high-frequency time-harmonic wavefield given on an initial surface into Gaussian beams. Geophys. J. R. Astr. Soc., 79:105-118, 1984.
    • (1984) Geophys. J. R. Astr. Soc. , vol.79 , pp. 105-118
    • Klimeš, L.1
  • 18
    • 0022841585 scopus 로고
    • Discretization error for the superposition of Gaussian beams
    • L. Klimeš. Discretization error for the superposition of Gaussian beams. Geophys. J. R. Astr. Soc., 86:531-551, 1986.
    • (1986) Geophys. J. R. Astr. Soc. , vol.86 , pp. 531-551
    • Klimeš, L.1
  • 19
    • 0012179999 scopus 로고
    • On a modification of the geometrical optics method
    • Yu. A. Kravtsov. On a modification of the geometrical optics method. Izv. VUZ Radiofiz., 7(4):664-673, 1964.
    • (1964) Izv. VUZ Radiofiz. , vol.7 , Issue.4 , pp. 664-673
    • Kravtsov, Y.A.1
  • 20
    • 61349126449 scopus 로고    scopus 로고
    • Eulerian Gaussian beams for Schrödinger equations in the semi-classical regime
    • S. Leung and J. Qian. Eulerian Gaussian beams for Schrödinger equations in the semi-classical regime. J. Comput. Phys., 228:2951-2977, 2009.
    • (2009) J. Comput. Phys. , vol.228 , pp. 2951-2977
    • Leung, S.1    Qian, J.2
  • 21
    • 34548534954 scopus 로고    scopus 로고
    • Eulerian Gaussian beams for high frequency wave propagation
    • S. Leung, J. Qian, and R. Burridge. Eulerian Gaussian beams for high frequency wave propagation. Geophysics, 72:SM61-SM76, 2007.
    • (2007) Geophysics , vol.72
    • Leung, S.1    Qian, J.2    Burridge, R.3
  • 22
    • 77956014068 scopus 로고    scopus 로고
    • Recovery of high frequency wave fields for the acoustic wave equation
    • H. Liu and J. Ralston. Recovery of high frequency wave fields for the acoustic wave equation. Multiscale Model. Sim., 8(2):428-444, 2009.
    • (2009) Multiscale Model. Sim. , vol.8 , Issue.2 , pp. 428-444
    • Liu, H.1    Ralston, J.2
  • 23
    • 77955846856 scopus 로고    scopus 로고
    • Recovery of high frequency wave fields from phase space-based measurements
    • H. Liu and J. Ralston. Recovery of high frequency wave fields from phase space-based measurements. Multiscale Model. Sim., 8(2):622-644, 2010.
    • (2010) Multiscale Model. Sim. , vol.8 , Issue.2 , pp. 622-644
    • Liu, H.1    Ralston, J.2
  • 24
    • 84981755544 scopus 로고
    • Uniform asymptotic expansions at a caustic
    • D. Ludwig. Uniform asymptotic expansions at a caustic. Comm. Pure Appl. Math., 19:215-250, 1966.
    • (1966) Comm. Pure Appl. Math. , vol.19 , pp. 215-250
    • Ludwig, D.1
  • 25
    • 1842557759 scopus 로고    scopus 로고
    • Semiclassical approximation in quantum mechanics
    • D. Reidel Publishing Co., Dordrecht, 1981. Translated from the Russian by J. Niederle and J. Tolar, Contemporary Mathematics
    • V. P. Maslov and M. V. Fedoriuk. Semiclassical approximation in quantum mechanics, volume 7 of Mathematical Physics and Applied Mathematics. D. Reidel Publishing Co., Dordrecht, 1981. Translated from the Russian by J. Niederle and J. Tolar, Contemporary Mathematics, 5.
    • Mathematical Physics and Applied Mathematics , vol.7 , pp. 5
    • Maslov, V.P.1    Fedoriuk, M.V.2
  • 26
    • 84873277812 scopus 로고    scopus 로고
    • A wave front Gaussian beam method for high-frequency wave propagation
    • University of Reading, UK
    • M. Motamed and O. Runborg. A wave front Gaussian beam method for high-frequency wave propagation. In Proceedings of WAVES 2007, University of Reading, UK, 2007.
    • (2007) Proceedings of WAVES 2007
    • Motamed, M.1    Runborg, O.2
  • 27
    • 77955843316 scopus 로고    scopus 로고
    • Taylor expansion and discretization errors in Gaussian beam superposition
    • M. Motamed and O. Runborg. Taylor expansion and discretization errors in Gaussian beam superposition. Wave Motion, 2010.
    • (2010) Wave Motion
    • Motamed, M.1    Runborg, O.2
  • 28
    • 0019899451 scopus 로고
    • A new method of computation of wave fields using Gaussian beams
    • M. M. Popov. A new method of computation of wave fields using Gaussian beams. Wave Motion, 4:85-97, 1982.
    • (1982) Wave Motion , vol.4 , pp. 85-97
    • Popov, M.M.1
  • 29
    • 77955512346 scopus 로고    scopus 로고
    • Fast Gaussian wavepacket transforms and Gaussian beams for the Schrödinger equation
    • J. Qian and L. Ying. Fast Gaussian wavepacket transforms and Gaussian beams for the Schrödinger equation. Journal of Computational Physics, 229:7848-7873, 2010.
    • (2010) Journal of Computational Physics , vol.229 , pp. 7848-7873
    • Qian, J.1    Ying, L.2
  • 30
    • 0000952462 scopus 로고
    • Gaussian beams and the propagation of singularities
    • Math. Assoc. America, Washington, DC, MAA Stud. Math.
    • J. Ralston. Gaussian beams and the propagation of singularities. In Studies in partial differential equations, volume 23 of MAA Stud. Math., pages 206-248. Math. Assoc. America, Washington, DC, 1982.
    • (1982) Studies in partial differential equations , vol.23 , pp. 206-248
    • Ralston, J.1
  • 31
    • 58849130742 scopus 로고    scopus 로고
    • 2-boundedness theorems for semiclassical Fourier integral operators with complex phase
    • arxiv:0710.4200v3
    • 2-boundedness theorems for semiclassical Fourier integral operators with complex phase. arxiv:0710.4200v3, 2007.
    • (2007) , vol.710
    • Rousse, V.1    Swart, T.2
  • 32
    • 58849104349 scopus 로고    scopus 로고
    • A mathematical justification for the Herman-Kluk propagator
    • V. Rousse and T. Swart. A mathematical justification for the Herman-Kluk propagator. Comm. Math. Phys., 286(2):725-750, 2009.
    • (2009) Comm. Math. Phys. , vol.286 , Issue.2 , pp. 725-750
    • Rousse, V.1    Swart, T.2
  • 33
    • 35349007284 scopus 로고    scopus 로고
    • Mathematical models and numerical methods for high frequency waves
    • O. Runborg. Mathematical models and numerical methods for high frequency waves. Commun. Comput. Phys., 2:827-880, 2007.
    • (2007) Commun. Comput. Phys. , vol.2 , pp. 827-880
    • Runborg, O.1
  • 34
    • 49349099865 scopus 로고    scopus 로고
    • Superpositions and higher order Gaussian beams
    • N. M. Tanushev. Superpositions and higher order Gaussian beams. Commun. Math. Sci., 6(2):449-475, 2008.
    • (2008) Commun. Math. Sci. , vol.6 , Issue.2 , pp. 449-475
    • Tanushev, N.M.1
  • 35
    • 70349733388 scopus 로고    scopus 로고
    • Gaussian beam decomposition of high frequency wave fields
    • N. M. Tanushev, B. Engquist, and R. Tsai. Gaussian beam decomposition of high frequency wave fields. J. Comput. Phys., 228(23):8856-8871, 2009.
    • (2009) J. Comput. Phys. , vol.228 , Issue.23 , pp. 8856-8871
    • Tanushev, N.M.1    Engquist, B.2    Tsai, R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.