메뉴 건너뛰기




Volumn 9, Issue 3, 2011, Pages 663-683

Frozen Gaussian approximation for high frequency wave propagation

Author keywords

Asymptotics; Frozen Gaussian approximation; High frequency wave propagation; Phase plane analysis; Wave equation

Indexed keywords


EID: 79953052469     PISSN: 15396746     EISSN: None     Source Type: Journal    
DOI: 10.4310/CMS.2011.v9.n3.a2     Document Type: Article
Times cited : (48)

References (29)
  • 1
    • 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, 973-1008, 2009.
    • (2009) Commun. Math. Sci. , vol.7 , pp. 973-1008
    • Bougacha, S.1    Akian, J.L.2    Alexandre, R.3
  • 2
    • 0000392733 scopus 로고    scopus 로고
    • Semiclassical spreading of quantum wave packets and applications near unstable fixed points of the classical flow
    • M. Combescure and D. Robert, Semiclassical spreading of quantum wave packets and applications near unstable fixed points of the classical flow, Asympt. Anal., 14, 377-404, 1997.
    • (1997) Asympt. Anal. , vol.14 , pp. 377-404
    • Combescure, M.1    Robert, D.2
  • 3
    • 24644487123 scopus 로고    scopus 로고
    • Computational high frequency wave propagation
    • B. Engquist and O. Runborg, Computational high frequency wave propagation, Acta Numer., 12, 181-266, 2003.
    • (2003) Acta Numer. , vol.12 , pp. 181-266
    • Engquist, B.1    Runborg, O.2
  • 4
    • 0003332429 scopus 로고
    • Harmonic Analysis in Phase Space
    • Princeton University Press, Princeton
    • G.B. Folland, Harmonic Analysis in Phase Space, Annals of Mathematics Studies, Princeton University Press, Princeton, 122, 1989.
    • (1989) Annals of Mathematics Studies , pp. 122
    • Folland, G.B.1
  • 5
    • 36749113388 scopus 로고
    • Frozen Gaussians: A very simple semiclassical approximation
    • E.J. Heller, Frozen Gaussians: A very simple semiclassical approximation, J. Chem. Phys., 75, 2923-2931, 1981.
    • (1981) J. Chem. Phys. , vol.75 , pp. 2923-2931
    • Heller, E.J.1
  • 6
    • 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, 27-34, 1984.
    • (1984) Chem. Phys. , vol.91 , pp. 27-34
    • Herman, M.F.1    Kluk, E.2
  • 8
    • 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. Huang, Bloch decomposition-based Gaussian beam method for the Schrödinger equation with periodic potentials, J. Comput. Phys., 229, 4869-4883, 2010.
    • (2010) J. Comput. Phys. , vol.229 , pp. 4869-4883
    • Jin, S.1    Wu, H.2    Yang, X.3    Huang, Z.4
  • 9
    • 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, 995-1020, 2008.
    • (2008) Commun. Math. Sci. , vol.6 , pp. 995-1020
    • Jin, S.1    Wu, H.2    Yang, X.3
  • 10
    • 77950359784 scopus 로고    scopus 로고
    • A numerical study of the Gaussian beam methods for one-dimensional Schrödinger-Poisson equations
    • S. Jin, H. Wu, and X. Yang, A numerical study of the Gaussian beam methods for one-dimensional Schrödinger-Poisson equations, J. Comput. Math., 28, 261-272, 2010.
    • (2010) J. Comput. Math. , vol.28 , pp. 261-272
    • Jin, S.1    Wu, H.2    Yang, X.3
  • 11
    • 79551510529 scopus 로고    scopus 로고
    • Semi-Eulerian and high order Gaussian beam methods for the Schrödinger equation in the semiclassical regime
    • S. Jin, H. Wu, and X. Yang, Semi-Eulerian and high order Gaussian beam methods for the Schrödinger equation in the semiclassical regime, Commun. Comput. Phys., 9, 668-687, 2011.
    • (2011) Commun. Comput. Phys. , vol.9 , pp. 668-687
    • Jin, S.1    Wu, H.2    Yang, X.3
  • 12
    • 36449004965 scopus 로고
    • Integral expressions for the semi-classical time-dependent propagator
    • K. Kay, Integral expressions for the semi-classical time-dependent propagator, J. Chem. Phys., 100, 4377-4392, 1994.
    • (1994) J. Chem. Phys. , vol.100 , pp. 4377-4392
    • Kay, K.1
  • 13
    • 33244471525 scopus 로고    scopus 로고
    • The Herman-Kluk approximation: Derivation and semiclassical corrections
    • K. Kay, The Herman-Kluk approximation: Derivation and semiclassical corrections, Chem. Phys., 322, 3-12, 2006.
    • (2006) Chem. Phys. , vol.322 , pp. 3-12
    • Kay, K.1
  • 14
    • 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. Simul., 8, 428-444, 2009.
    • (2009) Multiscale Model. Simul. , vol.8 , pp. 428-444
    • Liu, H.1    Ralston, J.2
  • 15
    • 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, 622-644, 2010.
    • (2010) Multiscale Model. Simul. , vol.8 , pp. 622-644
    • Liu, H.1    Ralston, J.2
  • 18
    • 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, 421-439, 2010.
    • (2010) Wave Motion , vol.47 , pp. 421-439
    • Motamed, M.1    Runborg, O.2
  • 19
    • 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
  • 20
    • 34548534954 scopus 로고    scopus 로고
    • Eulerian Gaussian beams for high-frequency wave propagation
    • J. Qian, S. Leung, and R. Burridge, Eulerian Gaussian beams for high-frequency wave propagation, Geophysics, 72, 61-76, 2007.
    • (2007) Geophysics , vol.72 , pp. 61-76
    • Qian, J.1    Leung, S.2    Burridge, R.3
  • 21
    • 61349126449 scopus 로고    scopus 로고
    • Eulerian Gaussian beams for Schrödinger equations in the semi-classical regime
    • J. Qian and S. Leung, 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
    • Qian, J.1    Leung, S.2
  • 22
    • 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, 7848-7873, 2010.
    • (2010) J. Comput. Phys. , vol.229 , pp. 7848-7873
    • Qian, J.1    Ying, L.2
  • 23
    • 85036721720 scopus 로고    scopus 로고
    • Fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beams for the wave equation
    • to appear
    • J. Qian and L. Ying, Fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beams for the wave equation, Multiscale Model. Simul., to appear.
    • Multiscale Model. Simul.
    • Qian, J.1    Ying, L.2
  • 24
    • 0000952462 scopus 로고
    • Gaussian beams and the propagation of singularities
    • J. Ralston, Gaussian beams and the propagation of singularities, Studies in PDEs, MAA Stud. Math., 23, 206-248, 1982.
    • (1982) Studies in PDEs, MAA Stud. Math. , vol.23 , pp. 206-248
    • Ralston, J.1
  • 25
    • 78649525352 scopus 로고    scopus 로고
    • On the Herman-Kluk semiclassical approximation
    • D. Robert, On the Herman-Kluk semiclassical approximation, Rev. Math. Phys., 22, 1123-1145, 2010.
    • (2010) Rev. Math. Phys. , vol.22 , pp. 1123-1145
    • Robert, D.1
  • 26
    • 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
  • 27
    • 58849104349 scopus 로고    scopus 로고
    • A mathematical justification of the Herman-Kluk propagator
    • T. Swart and V. Rousse, A mathematical justification of the Herman-Kluk propagator, Commun. Math. Phys., 286, 725-750, 2009.
    • (2009) Commun. Math. Phys. , vol.286 , pp. 725-750
    • Swart, T.1    Rousse, V.2
  • 29
    • 49349099865 scopus 로고    scopus 로고
    • Superpositions and higher order Gaussian beams
    • N.M. Tanushev, Superpositions and higher order Gaussian beams, Commun. Math. Sci., 6, 449-475, 2008.
    • (2008) Commun. Math. Sci. , vol.6 , pp. 449-475
    • Tanushev, N.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.