Wide-angle one-way wave equations

Journal of the Acoustical Society of America

Volumn 84, Issue 4, 1988, Pages 1397-1404

  Halpern, Laurence ^a   Trefethen, Lloyd N ^b  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTICS; ARTICLE; MATHEMATICS;

ACOUSTICS; MATHEMATICS; SUPPORT, NON-U.S. GOV'T; SUPPORT, U.S. GOV'T, NON-P.H.S.;

EID: 0024102561     PISSN: 00014966     EISSN: NA     Source Type: Journal    
DOI: 10.1121/1.396586     Document Type: Article

References (30)

1. D. Lee, “The state-of-the-art parabolic equation approximation as applied to underwater acoustic propagation with discussions on intensive computations,” Tech. Doc. 7247, U. S. Naval Underwater Systems Center, New London, CT, 1984.
2. F. D. Tappert, “The parabolic approximation method,” in Wave Propagation and Underwater Acoustics, Lecture Notes in Physics No. 70, edited by J. B. Keller and J. S. Papadakis (Springer, Berlin, 1977), pp. 224-287.
3. A. J. Berkhout, “Wave field extrapolation techniques in seismic migration, a tutorial,” Geophysics 46, 1638-1656 (1981).
4. J. F. Claerbout, Imaging the Earth's Interior (Blackwell, London, 1985).
5. R. W. Clayton and B. Engquist, “Absorbing boundary conditions for wave equation migration,” Geophysics 45, 895-904 (1980).
6. B. Engquist and A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629-651 (1977).
7. B. Engquist and A. Majda, “Radiation boundary conditions for acoustic and elastic wave calculations,” Commun. Pure Appl. Math. 32, 313-357 (1979).
8. E. L. Lindman, “‘Free-space’ boundary conditions for the time dependent wave equation,” J. Comput. Phys. 18, 66-78 (1975).
9. R. R. Greene, “The rational approximation to the acoustic wave equation with bottom interaction,” J. Acoust. Soc. Am. 76, 1764-1773 (1984).
10. R. L. Higdon, “Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation,” Math. Comput. 47, 437-459(1986).
11. R. L. Higdon, “Numerical absorbing boundary conditions for the wave equation,” Math. Comput. 49, 65-90 (1987).
12. L. N. Trefethen and L Halpern, “Well-posedness of one-way wave equations and absorbing boundary conditions,” Math. Comput. 47, 421-435 (1986).
13. D. F. St. Mary and D. Lee, “Accurate computation of the wide-angle wave equation,” in Computational Acoustics, Vol. 1, edited by D. Lee, R. L. Sternberg, and M. H. Schultz (North-Holland, Amsterdam, 1988), pp. 409-422.
14. J. G. Blaschak and G. A. Kriegsmann, “A comparative study of absorbing boundary conditions,” J. Comp. Phys. 77, 109-139 (1988).
15. D. J. Newman, “Rational approximation to |x|,” Mich. Math. J. 11, 11-14(1964).
16. G. Botseas, D. Lee, and K. E. Gilbert, “IFD: Wide angle capability,” Tech. Doc. 6905, U. S. Naval Underwater Systems Center, New London, CT, 1983.
17. A. J. Berkhout, “Steep dip finite-difference migration,” Geophys. Prosp. 27,196-213(1979).
18. D. F. St. Mary, “Analysis of an implicit finite difference scheme for very wide angle underwater acoustic propagation,” in Proceedings of the 11th IMACS World Congress on System Simulation and Scientific Computation (1985), Vol. 2, pp. 153-156.
19. Ma Zai-tian, “A splitting-up method for solution of the higher-order migration equation by finite-difference scheme (Chinese),” Acta Geophys. Sin. 26, 389-400 (1983).
20. Zhang Guan-quan, “High-order approximation of one way wave equations,” J. Comput. Math. 3, 90-97 (1985).
21. M. J. D. Powell, Approximation Theory and Methods (Cambridge U. P., Cambridge, England, 1981).
22. E. W. Cheney and A. A. Goldstein, “Mean-square approximation by generalized rational functions,” Math. Z. 95, 232-241 (1967).
23. A. Bamberger, B. Engquist, L. Halpern, and P. Joly, “Construction et analyse d’approximations paraxiales en milieu heterogene I and II,” Rapps. Internes Nos. 114 and 128, Centre de Mathematiques Appliquees, Ecole Polytechnique, 1984-85.
24. L. Wagatha, “Approximation of pseudodifferential operators in absorbing boundary conditions for hyperbolic equations,” Numer. Math. 42, 51-64(1983).
25. E. W. Cheney, Introduction to Approximation Theory (McGraw-Hill, New York, 1966).
26. N. S. Vyaceslavov, “On the uniform approximation of |jc| by rational functions,” Sov. Math. Dokl. 16, 100-104 (1975).
27. C. Clenshaw and K. Lord, “Rational approximations from Chebyshev series,” in Studies in Numerical Analysis, edited by B. K. P. Scaife (Academic, New York, 1974), pp. 95-113.
28. W. B. Gragg and G. D. Johnson, “The Laurent-Pade table,” in Information Processing 74 (North-Holland, Amsterdam, 1974), pp. 632-637.
29. L. N. Trefethen and M. H. Gutknecht, “The Caratheodory-Fejer method for real rational approximation,” SIAM J. Numer. Anal. 20, 420-436 (1983).
30. F. Stenger, “Polynomial, sinc and rational function methods for approximating analytic functions,” in Rational Approximation and Interpolation, Lecture Notes in Mathematics, No. 1105, edited by P. R. Graves-Morris et al. (Springer, Berlin, 1984), pp. 49-72.