메뉴 건너뛰기




Volumn 69, Issue 9, 2015, Pages 949-963

A wavefront-based Gaussian beam method for computing high frequency wave propagation problems

Author keywords

Asymptotic approximation; High frequency; Summation of Gaussian beams; Wave propagation; Wavefront methods

Indexed keywords

GAUSSIAN DISTRIBUTION; GEOMETRICAL OPTICS; NUMERICAL METHODS; WAVE PROPAGATION; WAVEFRONTS;

EID: 84926422117     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2015.02.021     Document Type: Article
Times cited : (9)

References (43)
  • 1
    • 24644487123 scopus 로고    scopus 로고
    • Computational high frequency wave propagation
    • B. Engquist, and O. Runborg Computational high frequency wave propagation Acta Numer. 12 2003 181 266
    • (2003) Acta Numer. , vol.12 , pp. 181-266
    • Engquist, B.1    Runborg, O.2
  • 2
    • 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 2007 827 880
    • (2007) Commun. Comput. Phys. , vol.2 , pp. 827-880
    • Runborg, O.1
  • 3
    • 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 1982 85 97
    • (1982) Wave Motion , vol.4 , pp. 85-97
    • Popov, M.M.1
  • 4
    • 0012495013 scopus 로고
    • On discontinuities of Green's function of the wave equation with variable coefficient
    • (in Russian) Leningrad University Press
    • V.M. Babič, and T.F. Pankratova On discontinuities of Green's function of the wave equation with variable coefficient Probl. Math. Phys. 6 1973 9 27 (in Russian) Leningrad University Press
    • (1973) Probl. Math. Phys. , vol.6 , pp. 9-27
    • Babič, V.M.1    Pankratova, T.F.2
  • 5
    • 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 1981 604 606
    • (1981) Sov. Phys. Dokl. , vol.26 , pp. 604-606
    • Katchalov, A.P.1    Popov, M.M.2
  • 6
    • 84984525506 scopus 로고
    • Computation of wave fields in inhomogeneous media - Gaussian beam approach
    • V.C. Červený, M.M. Popov, and I. Pšenčík Computation of wave fields in inhomogeneous media - Gaussian beam approach Geophys. J. R. Astron. Soc. 70 1982 109 128
    • (1982) Geophys. J. R. Astron. Soc. , vol.70 , pp. 109-128
    • Červený, V.C.1    Popov, M.M.2    Pšenčík, I.3
  • 7
    • 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. Astron. Soc. 79 1984 105 118
    • (1984) Geophys. J. R. Astron. Soc. , vol.79 , pp. 105-118
    • Klimeš, L.1
  • 8
    • 36749113388 scopus 로고
    • Frozen Gaussians: A very simple semiclassical approximation
    • E.J. Heller Frozen Gaussians: a very simple semiclassical approximation J. Chem. Phys. 76 1981 2923 2931
    • (1981) J. Chem. Phys. , vol.76 , pp. 2923-2931
    • Heller, E.J.1
  • 9
    • 4243938937 scopus 로고
    • A semiclassical justification for the use of non-spreading wavepackets in dynamics calculations
    • M.F. Herman, and E. Kluk A semiclassical justification for the use of non-spreading wavepackets in dynamics calculations Chem. Phys. 91 1984 27 34
    • (1984) Chem. Phys. , vol.91 , pp. 27-34
    • Herman, M.F.1    Kluk, E.2
  • 10
    • 0025626799 scopus 로고
    • Gaussian beam migration
    • N.R. Hill Gaussian beam migration Geophysics 55 1990 1416 1428
    • (1990) Geophysics , vol.55 , pp. 1416-1428
    • Hill, N.R.1
  • 11
    • 0035387609 scopus 로고    scopus 로고
    • Prestack Gaussian beam depth migration
    • N.R. Hill Prestack Gaussian beam depth migration Geophysics 66 2001 1240 1250
    • (2001) Geophysics , vol.66 , pp. 1240-1250
    • Hill, N.R.1
  • 12
    • 0000952462 scopus 로고
    • Gaussian beams and the propagation of singularities
    • W. Littman, MAA Stud. Math. Math. Assoc. America Washington, DC
    • J. Ralston Gaussian beams and the propagation of singularities W. Littman, Studies in Partial Differential Equations MAA Stud. Math. vol. 23 1982 Math. Assoc. America Washington, DC 206 248
    • (1982) Studies in Partial Differential Equations , vol.23 , pp. 206-248
    • Ralston, J.1
  • 13
    • 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. Simul. 8 2010 622 644
    • (2010) Multiscale Model. Simul. , vol.8 , pp. 622-644
    • Liu, H.1    Ralston, J.2
  • 14
    • 84873266486 scopus 로고    scopus 로고
    • Error estimates for Gaussian beam superpositions
    • H. Liu, O. Runborg, and N.M. Tanushev Error estimates for Gaussian beam superpositions Math. Comp. 82 2013 919 952
    • (2013) Math. Comp. , vol.82 , pp. 919-952
    • Liu, H.1    Runborg, O.2    Tanushev, N.M.3
  • 15
    • 84858792565 scopus 로고    scopus 로고
    • Convergence of frozen Gaussian approximation for high frequency wave propagation
    • J. Lu, and X. Yang Convergence of frozen Gaussian approximation for high frequency wave propagation Comm. Pure Appl. Math. 65 2012 759 789
    • (2012) Comm. Pure Appl. Math. , vol.65 , pp. 759-789
    • Lu, J.1    Yang, X.2
  • 16
    • 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 2009 973 1008
    • (2009) Commun. Math. Sci. , vol.7 , pp. 973-1008
    • Bougacha, S.1    Akian, J.-L.2    Alexandre, R.3
  • 17
    • 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 47 2010 421 439
    • (2010) Wave Motion , vol.47 , pp. 421-439
    • Motamed, M.1    Runborg, O.2
  • 18
  • 20
    • 33746060863 scopus 로고    scopus 로고
    • A Poisson integrator for Gaussian wavepacket dynamics
    • E. Faou, and C. Lubich A Poisson integrator for Gaussian wavepacket dynamics Comput. Vis. Sci. 9 2006 45 55
    • (2006) Comput. Vis. Sci. , vol.9 , pp. 45-55
    • Faou, E.1    Lubich, C.2
  • 21
    • 49349099865 scopus 로고    scopus 로고
    • Superpositions and higher order Gaussian beams
    • N.M. Tanushev Superpositions and higher order Gaussian beams Commun. Math. Sci. 6 2008 449 475
    • (2008) Commun. Math. Sci. , vol.6 , pp. 449-475
    • Tanushev, N.M.1
  • 22
    • 84878989671 scopus 로고    scopus 로고
    • Gaussian beam methods for the Dirac equation in the semi-classical regime
    • H. Wu, Z. Huang, S. Jin, and D. Yin Gaussian beam methods for the Dirac equation in the semi-classical regime Commun. Math. Sci. 10 2012 1301 1315
    • (2012) Commun. Math. Sci. , vol.10 , pp. 1301-1315
    • Wu, H.1    Huang, Z.2    Jin, S.3    Yin, D.4
  • 23
    • 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 2007 SM61 SM76
    • (2007) Geophysics , vol.72 , pp. SM61-SM76
    • Leung, S.1    Qian, J.2    Burridge, R.3
  • 24
    • 77950364040 scopus 로고    scopus 로고
    • Gaussian beam methods for the Schrödinger equation in the semi-classical regime: Lagrangian and Eulerian formulations
    • S. Jin, H. Wu, and X. Yang Gaussian beam methods for the Schrödinger equation in the semi-classical regime: Lagrangian and Eulerian formulations Commun. Math. Sci. 6 2008 995 1020
    • (2008) Commun. Math. Sci. , vol.6 , pp. 995-1020
    • Jin, S.1    Wu, H.2    Yang, X.3
  • 25
    • 77952425757 scopus 로고    scopus 로고
    • Bloch decomposition-based Gaussian beam method for the Schrödinger equation with periodic potentials
    • S. Jin, H. Wu, X. Yang, and Z.Y. Huang Bloch decomposition-based Gaussian beam method for the Schrödinger equation with periodic potentials J. Comput. Phys. 229 2010 4869 4883
    • (2010) J. Comput. Phys. , vol.229 , pp. 4869-4883
    • Jin, S.1    Wu, H.2    Yang, X.3    Huang, Z.Y.4
  • 26
    • 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 2009 2951 2977
    • (2009) J. Comput. Phys. , vol.228 , pp. 2951-2977
    • Leung, S.1    Qian, J.2
  • 27
    • 84864553871 scopus 로고    scopus 로고
    • Mathematical and computational models for semiclassical Schrödinger equations
    • S. Jin, P. Markowich, and C. Sparber Mathematical and computational models for semiclassical Schrödinger equations Acta Numer. 21 2012 1 89
    • (2012) Acta Numer. , vol.21 , pp. 1-89
    • Jin, S.1    Markowich, P.2    Sparber, C.3
  • 28
    • 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 2009 8856 8871
    • (2009) J. Comput. Phys. , vol.228 , pp. 8856-8871
    • Tanushev, N.M.1    Engquist, B.2    Tsai, R.3
  • 29
    • 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 2011 2303 2321
    • (2011) J. Comput. Phys. , vol.230 , pp. 2303-2321
    • Ariel, G.1    Engquist, B.2    Tanushev, N.M.3    Tsai, R.4
  • 30
    • 0002198407 scopus 로고
    • Traveltime and amplitude estimation using wavefront construction
    • V. Vinje, E. Iversen, and H. Gjoystdal Traveltime and amplitude estimation using wavefront construction Eur. Ass. Expl. Geophys. 1992 504 505
    • (1992) Eur. Ass. Expl. Geophys. , pp. 504-505
    • Vinje, V.1    Iversen, E.2    Gjoystdal, H.3
  • 31
    • 0027790423 scopus 로고
    • Traveltime and amplitude estimation using wavefront construction
    • V. Vinje, E. Iversen, and H. Gjoystdal Traveltime and amplitude estimation using wavefront construction Geophysics 58 1993 1157 1166
    • (1993) Geophysics , vol.58 , pp. 1157-1166
    • Vinje, V.1    Iversen, E.2    Gjoystdal, H.3
  • 32
    • 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 J. Comput. Phys. 229 2010 7848 7873
    • (2010) J. Comput. Phys. , vol.229 , pp. 7848-7873
    • Qian, J.1    Ying, L.2
  • 34
    • 85009429888 scopus 로고
    • Computaton of 2D multiple arrival traveltime fields by an interpolative shooting method
    • Extended Abstracts
    • Y. Sun Computaton of 2D multiple arrival traveltime fields by an interpolative shooting method Soc. Expl. Geophys. 1992 1320 1323 Extended Abstracts
    • (1992) Soc. Expl. Geophys. , pp. 1320-1323
    • Sun, Y.1
  • 35
    • 77952739941 scopus 로고    scopus 로고
    • Gaussian beam summation for diffraction in inhomogeneous media based on the grid based particle method
    • S. Leung, and H. Zhao Gaussian beam summation for diffraction in inhomogeneous media based on the grid based particle method Commun. Comput. Phys. 8 2010 758 796
    • (2010) Commun. Comput. Phys. , vol.8 , pp. 758-796
    • Leung, S.1    Zhao, H.2
  • 36
    • 70350448871 scopus 로고    scopus 로고
    • Fast interface tracking via a multiresolution representation of curves and surfaces
    • O. Runborg Fast interface tracking via a multiresolution representation of curves and surfaces Commun. Math. Sci. 7 2009 365 398
    • (2009) Commun. Math. Sci. , vol.7 , pp. 365-398
    • Runborg, O.1
  • 37
    • 84908141175 scopus 로고    scopus 로고
    • Analysis of high order fast interface tracking methods
    • O. Runborg Analysis of high order fast interface tracking methods Numer. Math. 128 2014 339 375
    • (2014) Numer. Math. , vol.128 , pp. 339-375
    • Runborg, O.1
  • 38
    • 84926411725 scopus 로고    scopus 로고
    • Asymptotic approximations of high frequency wave propagation problems
    • B. Engquist, A. Fokas, E. Hairer, A. Iserles, London Mathematical Society Lecture Note Serie Cambridge University Press
    • M. Motamed, and O. Runborg Asymptotic approximations of high frequency wave propagation problems B. Engquist, A. Fokas, E. Hairer, A. Iserles, Highly Oscillatory Problems London Mathematical Society Lecture Note Serie vol. 366 2009 Cambridge University Press 72 97
    • (2009) Highly Oscillatory Problems , vol.366 , pp. 72-97
    • Motamed, M.1    Runborg, O.2
  • 39
    • 84981755544 scopus 로고
    • Uniform asymptotic expansions at a caustic
    • D. Ludwig Uniform asymptotic expansions at a caustic Comm. Pure Appl. Math. 19 1966 215 250
    • (1966) Comm. Pure Appl. Math. , vol.19 , pp. 215-250
    • Ludwig, D.1
  • 40
    • 84986356242 scopus 로고
    • Application of the Gaussian beam method to elasticity theory
    • A.P. Katchalov, and M.M. Popov Application of the Gaussian beam method to elasticity theory Geophys. J. R. Astron. Soc. 81 1985 205 214
    • (1985) Geophys. J. R. Astron. Soc. , vol.81 , pp. 205-214
    • Katchalov, A.P.1    Popov, M.M.2
  • 41
    • 0024879244 scopus 로고
    • Optimization of the shape of Gaussian beams of a fixed length
    • L. Klimeš Optimization of the shape of Gaussian beams of a fixed length Stud. Geophys. Geod. 33 1989 146 163
    • (1989) Stud. Geophys. Geod. , vol.33 , pp. 146-163
    • Klimeš, L.1
  • 42
    • 0029770069 scopus 로고    scopus 로고
    • Two-dimensional multivalued traveltime and amplitude maps by uniform sampling of ray field
    • G. Lambaré, P.S. Lucio, and A. Hanyga Two-dimensional multivalued traveltime and amplitude maps by uniform sampling of ray field Geophys. J. Int. 125 1996 584 598
    • (1996) Geophys. J. Int. , vol.125 , pp. 584-598
    • Lambaré, G.1    Lucio, P.S.2    Hanyga, A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.