Semi-eulerian and high order gaussian beam methods for the Schrödinger equation in the semiclassical regime

Communications in Computational Physics

Volumn 9, Issue 3, 2011, Pages 668-687

  Jin, Shi ^a   Wu, Hao ^b   Yang, Xu ^c  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b TSINGHUA UNIVERSITY   (China)

^c PRINCETON UNIVERSITY   (United States)

Author keywords

High order methods; Schr dinger equation; Semi Eulerian Gaussian beam method

Indexed keywords

EID: 79551510529     PISSN: 18152406     EISSN: 19917120     Source Type: Journal    
DOI: 10.4208/cicp.091009.160310s     Document Type: Article

References (21)

1. W. Bao, S. Jin and P. A. Markowich, On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime, J. Comput. Phys., 175 (2002), 487-524.
2. V. Cerveny, M. M. Popov and I. Psencik, Computation of wave fields in inhomogeneous media-Gaussian beam approach, Geophys. J. R. Astr. Soc., 70 (1982), 109-128.
3. E. J. Heller, Cellular dynamics: a new semiclassical approach to time-dependent quantum mechanics, J. Chem. Phys., 94 (1991), 2723-2729.
4. E. J. Heller, Guided Gaussian wave packets, Accounts. Chem. Res., 39 (2006), 127-134.
5. N. R. Hill, Gaussian beam migration, Geophys., 55 (1990), 1416-1428.
6. N. R. Hill, Prestack Gaussian-beam depth migration, Geophys., 66 (2001), 1240-1250.
7. S. Jin and S. Osher, A level set method for the computation of multivalued solutions to quasi-linear hyperbolic PDEs and Hamilton-Jacobi equations, Commun.Math. Sci., 1 (2003), 575-591.
8. 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.
9. S. Jin, H. Wu and X. Yang, A numerical study of the Gaussian beam methods for onedimensional Schrödinger-Poisson equations, J. Comput. Math., 28 (2010), 261-272.
10. 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.
11. S. Leung and J. Qian, Eulerian Gaussian beams for Schrödinger equations in the semiclassical regime, J. Comput. Phys., 228 (2009), 2951-2977.
12. S. Leung, J. Qian and R. Burridge, Eulerian Gaussian beams for high-frequency wave propagation, Geophys., 72 (2007), 61-76.
13. H. L. Liu and J. Ralston, Recovery of high frequency wave fields for the acoustic wave equation, Multiscale. Model. Simul., 8 (2009), 428-444.
14. H. L. Liu and J. Ralston, Recovery of high frequency wave fields from phase space based measurements, Multiscale. Model. Simul., 8 (2010), 622-644.
15. M. Motamed and O. Runborg, Taylor expansion and discretization errors in Gaussian beam superposition, Wave. Motion., to appear.
16. M. M. Popov, A new method of computation of wave fields using gaussian beams, Wave. Motion., 4 (1982), 85-97.
17. J. Ralston, Gaussian beams and the propagation of singularities, Studies in PDEs, MAA. Stud. Math., 23 (1982), 206-248.
18. N. M. Tanushev, Superpositions and higher order Gaussian beams, Commun. Math. Sci., 6 (2008), 449-475.
19. N. M. Tanushev, B. Engquist and R. Tsai, Gaussian beam decomposition of high frequency wave fields, J. Comput. Phys., 228 (2009), 8856-8871.
20. N.M. Tanushev, J. Qian and J. V. Ralston, Mountain waves and Gaussian beams,Multiscale. Model. Simul., 6 (2007), 688-709.
21. D. Yin and C. Zheng, Fourth order Gaussian beam and interface conditions for the onedimensional linear Schrödinger equation with singular potentials, preprint.