Exact discrete nonlocal boundary conditions for high-order Padé parabolic equations

Journal of the Acoustical Society of America

Volumn 116, Issue 5, 2004, Pages 2864-2875

  Mikhin, Dmitry ^a  

^a Acacia Research Pty Ltd   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; MATHEMATICAL MODELS; PROBLEM SOLVING; RADIATION;

FINITE DIFFERENCE SCHEME; NONLOCAL BOUNDARY CONDITIONS (NLBC); PARABOLIC EQUATIONS (PE);

BOUNDARY CONDITIONS;

ACCURACY; ACOUSTICS; ALGORITHM; ARTICLE; PRIORITY JOURNAL; RADIATION;

EID: 9644307911     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.1802811     Document Type: Article

References (37)

1. L. M. Brekhovskikh and O. A. Godin, Acoustics of Layered Media. 1: Plain and Quasi-plane Waves, Vol. 5 of Springer Series on Wave Phenomena (Springer, Berlin, 1990).
2. L. M. Brekhovskikh and O. A. Godin, Acoustics of Layered Media. 2: Point Sources and Bounded Beams, Vol. 10 of Springer Series on Wave Phenomena (Springer, Berlin, 1992).
3. F. B. Jensen, W. A. Kuperman, M. B. Porter, and H. Schmidt, Computational Ocean Acoustics (AIP, New York, 1994).
4. W. A. Kuperman and H. Schmidt, "Rough surface elastic wave scattering in a horizontally stratified ocean," J. Acoust. Soc. Am. 79, 1767-1777 (1986)
5. J. A. Davis, D. White, and R. C. Cavanagh, "NORDA Parabolic Equation workshop," NORDA Technical Note 143, Naval Ocean Research and Development Activity, Stennis Space Center, MS (1982).
6. R. B. Evans and K. E. Gilbert, "Acoustic propagation in a refracting ocean waveguide with an irregular interface," Comput. Math. Appl. 11, 795-805 (1985).
7. R. B. Evans and K. E. Gilbert, "The periodic extension of stepwise coupled modes," J. Acoust. Soc. Am. 77, 983-988 (1985).
8. K. E. Gilbert and M. J. White, "Application of the parabolic equation to sound propagation in a refracting atmosphere," J. Acoust. Soc. Am. 85, 630-637 (1989).
9. M. F. Levy, "Transparent boundary conditions for parabolic equation solutions of radiowave propagation problems," IEEE Trans. Antennas Propag. 45, 66-72 (1997).
10. M. F. Levy, "Horizontal parabolic equation solution of radiowave propagation problems on large domains," IEEE Trans. Antennas Propag. 43, 137-144 (1995).
11. J. S. Papadakis, "Impedance formulation of the bottom boundary condition for the parabolic equation model in underwater acoustics," NORDA Technical Note 143, Naval Ocean Research and Development Activity, Stennis Space Center, MS (1982).
12. J. S. Papadakis, M. I. Taroudakis, P. J. Papadakis, and B. Mayfield, "A new method for a realistic treatment of the sea bottom in the parabolic approximation," J. Acoust. Soc. Am. 92, 2030-2038 (1992).
13. J. S. Papadakis, "Exact, non-reflecting boundary conditions for parabolic-type approximations in underwater acoustics," J. Comput. Acoust. 2, 83-98 (1994).
14. V. A. Baskakov and A. V. Popov, "Implementation of transparent boundaries for numerical solution of the Schrödinger equation," Wave Motion 14, 123-128 (1991).
15. S. W. Marcus, "A generalized impedance method for application of the parabolic approximation to underwater acoustics," J. Acoust. Soc. Am. 90, 391-398 (1991).
16. A. V. Popov, "Artificial transparent boundaries in computational quasi-optics," in 11th Annual Review of Progress in Applied Computational Electromagnetics (Applied Computational Electromagnetics Society, Monterey, CA, 1995), pp. 195-201.
17. A. V. Popov, "Accurate modeling of transparent boundaries in quasi-optics," Radio Sci. 31, 1781-1790 (1996).
18. D. Yevick and D. J. Thomson, "Nonlocal boundary conditions for finite-difference parabolic equation solvers," J. Acoust. Soc. Am. 106, 143-150 (1999).
19. D. J. Thomson and M. E. Mayfield, "An exact radiation condition for use with the a posteriori PE method," J. Comput. Acoust. 2, 113-132 (1994).
20. G. H. Brooke and D. J. Thomson, "Nonlocal boundary conditions for high-order parabolic equation algorithms," Wave Motion 31, 117-129 (2000).
21. A. Arnold and M. Ehrhardt, "Discrete transparent boundary conditions for wide angle parabolic equations in underwater acoustics," J. Comput. Phys. 145, 611-638 (1998).
22. R. A. Dalrymple and P. A. Martin, "Perfect boundary conditions for parabolic water-wave models," Proc. R. Soc. London, Ser. A 437, 41-54 (1992).
23. F. Schmidt, T. Friese, and D. Yevick, "Transparent boundary conditions for split-step Padé approximations of the one-way Helmholtz equation," J. Comput. Phys. 170, 696-719 (2001).
24. F. Schmidt and D. Yevick, "Discrete transparent boundary conditions for Schrödinger-type equations," J. Comput. Phys. 134, 96-107 (1997).
25. D. Yevick, T. Friese, and F. Schmidt, "A comparison of transparent boundary conditions for the Fresnel equation," J. Comput. Phys. 168, 433-444 (2001).
26. D. Yu. Mikhin, "Energy-conserving and reciprocal solutions for higher-order parabolic equations," J. Comput. Acoust. 9, 183-203 (2001).
27. O. A. Godin, "Reciprocity and energy conservation within the parabolic approximation," Wave Motion 29, 175-194 (1999).
28. D. Yu. Mikhin, "Generalizations of the energy-flux parabolic equation," J. Comput. Acoust. (to be published).
29. F. D. Tappert, "The parabolic approximation method," in Wave Propagation and Underwater Acoustics, Vol. 70 of Lecture Notes in Physics, edited by J. B. Keller and J. S. Papadakis (Springer, New York, 1977), pp. 224-284.
30. M. D. Collins, "A split-step Padé solution for the parabolic equation method," J. Acoust. Soc. Am. 93(4), 1736-1742 (1993).
31. A. Bamberger, B. Engquist, L. Halpern, and P. Joly, "Higher order parabolic wave equation approximations in heterogeneous media," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 48(1), 129-154 (1988).
32. M. D. Collins, "Higher-order Padé approximations for accurate and stable elastic parabolic equations with application to interface wave propagation," J. Acoust. Soc. Am. 89(3), 1050-1057 (1991).
33. F. A. Milinazzo, C. A. Zala, and G. H. Brooke, "Rational square-root approximations for parabolic equation algorithms," J. Acoust. Soc. Am. 101, 760-766 (1997).
34. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1968).
35. J. N. Lyness and G. Sande, "Algorithm 413. ENTCAF and ENTCRE: Evaluation of normalized Taylor coefficients of an analytic function," Commun. ACM 14, 669-675 (1971).
36. C. Lubich, "Convolution quadrature and discretized operational calculus II," Numer. Math. 52, 413-425 (1988).
37. F. B. Jensen and C. M. Ferla, "Numerical solutions of range-dependent benchmark problems," J. Acoust. Soc. Am. 87, 1499-1510 (1990).