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Analytic Error Caused by the Inconsistency of the Approximation Order between the Non Local Boundary Condition and the Parabolic Governing Equation  

Lee Keun-Hwa (서울대학교 공과대학 조선해양공학과)
Seong Woo-Jae (서울대학교 공과대학 조선해양공학과)
Publication Information
The Journal of the Acoustical Society of Korea / v.25, no.5, 2006 , pp. 229-238 More about this Journal
Abstract
This paper shows the analytic error caused by the inconsistency of the approximation order between the non local boundary condition (NLBC) and the parabolic governing equation. To obtain the analytic error, we first transform the NLBC to the half space domain using plane wave analysis. Then, the analytic error is derived on the boundary between the true numerical domain and the half space domain equivalent to the NLBC. The derived analytic error is physically expressed as the artificial reflection. We examine the characteristic of the analytic error for the grazing angle, the approximation order of the PE or the NLBC. Our main contribution is to present the analytic method of error estimation and the application limit for the high order parabolic equation and the NLBC.
Keywords
High order parabolic equation; $Pad{\acute{e}}$ approximation; Non local boundary condition; Standard parabolic equation;
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1 D. Mikhin, 'Exact discrete non-local boundary conditions for high-order Pade parabolic equations,' J. Acoust. Soc. Am. 116 (5), 2864-2875, 2004   DOI   ScienceOn
2 J. S. Papadakis et al., 'A new method for a realistic treatment of the sea bottom in the parabolic approximation,' J. Acoust. Soc. Am. 92 (4), 2030-2038, 1992   DOI
3 김태현, '해양 음파 전달 해석의 포물선 근사 해법에 대한 보고', 서울대학교 조선해양공학과 학사 학위 논문, 2000
4 S. T. McDaniel, 'Propagation of normal mode in the parabolic approximation,' J. Acoust. Soc. Am. 57 (2), 307-311, 1975   DOI   ScienceOn
5 P. M. Morse and H. Feshbach, Methods of Theoretical Physics Part t. (Mcgraw-Hill, New York, 1953), page 411
6 J. S. Papadakis, 'Exact, non-reflecting boundary condition for parabolic approximation in the underwater acoustics,' J. Comet. Acoust. 2 (1), 83-98, 1994   DOI
7 M. Levy, Parabolic equation methods for electromagnetic wave propagation (IEE, London, 2000)
8 D. Givoli, Numerical Mehtods for Problems in Infinite Domains (Elsevier. Amsterdam, 1992)
9 G. H. Brooke et al., PECAN: A Canadian Parabolic Equation Model for Underwater Sound Propagation (2000)
10 D. Yevick and D. J. Thomson, 'Non-local boundary conditions for finite difference parabolic equation algorithms,' J. Acoust. Soc. Am. 106 (1), 143-150, 1999   DOI
11 F. B. Jenson et al., Computational Ocean Acoustics (AIP press, New York, 1993)
12 J. S. Papadakis, 'Impedance formulation of the bottom boundary conditions for the parabolic model in underwater acoustics,' NORDA Technical note 143, NORDA, Stennis Space Center, MS (1982)
13 A. Z. Hyaric, 'Wide angle non-local boundary conditions for the parabolic wave equation,' IEEE Trans. Antennas Propasat. 49 (6), 916-922, 2001   DOI   ScienceOn
14 S. W. Marcus, 'A generalized impedance method for application of the parabolic approximation to underwater acoustics,' J. Acoust. Soc. Am. 90 (1), 391-398, 1991   DOI
15 The Mathworks, Inc., Symbolic math toolbox user's guide (2006)
16 H. A. Koenig, Modern Computational Methods (Taylor & Francis, Philadelphia, 1999)
17 G. H. Brooke and D. J. Thomson, 'Non-local boundary conditions for high-order parabolic equation algorithms,' Wave Motion 31, 117-129,2000   DOI   ScienceOn