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Pseudospectral time-domain method for pressure-release rough surface scattering using a surface transformation and image method

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Abstract

When numerically analyzing acoustic scattering at a pressure-release rough surface, the conventional pseudospectral time domain (PSTD) method using Fourier transform requires rigorous stability conditions in order to solve the spatial derivative in the wave equation on the irregular boundaries between the two media due to the Gibbs phenomenon and short wavelength in air. To eliminate such disadvantages, a new algorithm is proposed based on the Fourier PSTD method utilizing a surface boundary transformation and an image method. Irregular surface boundaries are flattened by transformation and then an image method is applied to the half-space domain. The efficiency and accuracy of the proposed PSTD method are better than the conventional Fourier PSTD method. Numerical results are presented for a sloped and a sinusoidal pressure-release surface.

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References

  1. Yee, K.S.: Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propag. 14(3), 302–307 (1966)

    Article  MATH  Google Scholar 

  2. Kreiss, H.-O., Oliger, J.: Comparison of accurate methods for the integration of hyperbolic equations. Tellus 24, 199–215 (1972)

    Article  MathSciNet  Google Scholar 

  3. Orszag, S.A.: Comparison of pseudospectral and spectral approximation. Stud. Appl. Math. 51(3), 253–259 (1972)

    MATH  MathSciNet  Google Scholar 

  4. Fornberg, B.: On a Fourier method for the integration of hyperbolic equations. SIAM J. Numer. Anal. 12(4), 509–528 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  5. Kosloff, D., Baysal, E.: Forward modeling by a Fourier method. Geophysics 47(10), 1402–1412 (1982)

    Article  Google Scholar 

  6. Liu, Q.H.: The PSTD algorithm: a time-domain method requiring only two cells per wavelength. Microw. Opt. Technol. Lett. 15(3), 158–165 (1997)

    Article  Google Scholar 

  7. Zeng, Y.Q., Liu, Q.H., Zhao, G.: Multidomain pseudospectral time-domain (PSTD) method for acoustic waves in lossy media. J. Comput. Acoust. 12(3), 277–299 (2004)

    Article  MATH  Google Scholar 

  8. Fornberg, B.: The pseudospectral method: comparisons with finite differences for the elastic wave equations. Geophysics 52(4), 483–501 (1987)

    Article  Google Scholar 

  9. Konrady, J.A. Jr.: Scattering of sound from time-varying irregular free surfaces. J. Acoust. Soc. Am. 56(6), 1687–1694 (1974)

    Article  Google Scholar 

  10. Abarbanel, H.D.I.: Scattering from a random surface. J. Acoust. Soc. Am. 68(5), 1459–1466 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  11. Beilis, A., Tappert, F.D.: Coupled mode analysis of multiple rough surface scattering. J. Acoust. Soc. Am. 66(3), 811–826 (1979)

    Article  MATH  Google Scholar 

  12. Evans, R.B.: The flattened surface parabolic equation. J. Acoust. Soc. Am. 104(4), 2167–2173 (1998)

    Article  Google Scholar 

  13. Fornberg, B.: The pseudospectral method: accurate representation of interfaces in elastic wave calculations. Geophysics 53(4), 625–637 (1988)

    Article  Google Scholar 

  14. Tappert, F.D., Nghiem-Phu, L.: A new split-step Fourier algorithm for solving the parabolic wave equation with rough surface scattering. J. Acoust. Soc. Am. 77(Suppl. 1), s101 (1985)

    Article  Google Scholar 

  15. Berenger, J.-P.: A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114, 185–200 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  16. Fan, G.X., Liu, Q.H.: A well-posed PML absorbing boundary condition for lossy media. IEEE Antennas Propag. Soc. Int. Symp. 3, 2–5 (2001)

    Google Scholar 

  17. Liu, Q.H.: An FDTD algorithm with perfectly matched layers for conductive media. Microw. Opt. Technol. Lett. 14(2), 134–137 (1997)

    Article  Google Scholar 

  18. Moin, P.: Fundamentals of Engineering Numerical Analysis. Cambridge University Press, Cambridge, pp. 101–106 (2001)

    MATH  Google Scholar 

  19. Liu, Q.H.: The pseudospectral time-domain (PSTD) algorithm for acoustic waves in absorptive media. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45(3), 1044–1055 (1998)

    Google Scholar 

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Authors and Affiliations

  1. Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, 151–744, South Korea

    Yonghoon Ha, Keunwha Lee & Woojae Seong

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  1. Yonghoon Ha
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  2. Keunwha Lee
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  3. Woojae Seong
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Correspondence to Woojae Seong.

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Ha, Y., Lee, K. & Seong, W. Pseudospectral time-domain method for pressure-release rough surface scattering using a surface transformation and image method. Numer Algor 54, 411–430 (2010). https://doi.org/10.1007/s11075-009-9343-7

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  • DOI: https://doi.org/10.1007/s11075-009-9343-7

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