Convergence of frozen Gaussian approximation for high-frequency wave propagation

Communications on Pure and Applied Mathematics

Volumn 65, Issue 6, 2012, Pages 759-789

  Lu, Jianfeng ^a   Yang, Xu ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84858792565     PISSN: 00103640     EISSN: 10970312     Source Type: Journal    
DOI: 10.1002/cpa.21384     Document Type: Article

References (22)

1. Bougacha, S.; Akian, J.-L.; Alexandre, R. Gaussian beams summation for the wave equation in a convex domain. Commun. Math. Sci. 7 ( 2009), no. 4, 973-1008.
2. Červený, V.; Popov, M. M.; Pšenčík, I. Computation of wave fields in inhomogeneous media-Gaussian beam approach. Geophys. J. Roy. Astr. Soc. 70 ( 1982), 109-128.
3. Engquist, B.; Runborg, O. Computational high frequency wave propagation. Acta Numer. 12 ( 2003), 181-266.
4. Herman, M. F.; Kluk, E. A semiclasical justification for the use of non-spreading wavepackets in dynamics calculations. Chem. Phys. 91 ( 1984), no. 1, 27-34. doi: 10.1016/0301-0104(84)80039-7
5. Hill, N. R. Gaussian beam migration. Geophys. 55 ( 1990), no. 11, 1416-1428. doi: 10.1190/1.1442788.
6. Kay, K. G. Integral expressions for the semiclassical time-dependent propagator. J. Chem. Phys. 100 ( 1994), no. 6, 4377-4392. doi: 10.1063/1.466320.
7. Kay, K. G. The Herman-Kluk approximation: derivation and semiclassical corrections. Chem. Phys. 322 ( 2006), no. 1-2, 3-12.
8. Liu, H.; Ralston, J. Recovery of high frequency wave fields for the acoustic wave equation. Multiscale Model. Simul. 8 ( 2009/10), no. 2, 428-444.
9. Liu, H.; Ralston, J. Recovery of high frequency wave fields from phase space-based measurements. Multiscale Model. Simul. 8 ( 2009/10), no. 2, 622-644.
10. Liu, H.; Runborg, O.; Tanushev, N. M. Error estimates for Gaussian beam superpositions. Preprint, 2010. Available at: .1320arXiv:1008.1320.
11. Lu, J.; Yang, X. Frozen Gaussian approximation for general linear strictly hyperbolic system: formulation and Eulerian methods. Preprint, 2010. Available at: .1969arXiv:1010.1969.
12. Lu, J.; Yang, X. Frozen Gaussian approximation for high frequency wave propagation. Commun. Math. Sci. 9 ( 2011), no. 3, 663-683.
13. Martinez, A. An introduction to semiclassical and microlocal analysis. Universitext. Springer, New York, 2002.
14. Motamed, M.; Runborg, O. Taylor expansion and discretization errors in Gaussian beam superposition. Wave Motion 47 ( 2010), no. 7, 421-439.
15. Popov, M. M. A new method of computation of wave fields using Gaussian beams. Wave Motion 4 ( 1982), no. 1, 85-97.
16. Qian, J.; Ying, L. Fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beams for the wave equation. Multiscale Model. Simul. 8 ( 2010), no. 5, 1803-1837.
17. Ralston, J. Gaussian beams and the propagation of singularities. Studies in partial differential equations, 206-248. MAA Studies in Mathematics, 23. Math. Assoc. America, Washington, D.C., 1982.
18. Robert, D. On the Herman-Kluk semiclassical approximation. Rev. Math. Phys. 22 ( 2010), no. 10, 1123-1145.
19. 2-boundedness theorems for semiclassical Fourier integral operators with complex phase. Preprint, 2007. Available at: .4200arXiv:0710.4200v3.
20. Runborg, O. Mathematical models and numerical methods for high frequency waves. Commun. Comput. Phys. 2 ( 2007), no. 5, 827-880.
21. Swart, T.; Rousse, V. A mathematical justification for the Herman-Kluk propagator. Comm. Math. Phys. 286 ( 2009), no. 2, 725-750.
22. Taylor, M. E. Pseudodifferential operators. Princeton Mathematical Series, 34. Princeton University Press, Princeton, N.J., 1981.