Application of a Chebyshev Collocation Method to Solve a Parabolic Equation Model of Underwater Acoustic Propagation

Jensen, F.B., Kuperman, W.A., Porter, M.B., Schmidt, H.: Computational Ocean Acoustics. Springer, New York (2011)

Tappert, F.T.: The Parabolic Equation Approximation Method in Wave Propagation and Underwater Acoustics, vol. 70. Springer, New York (1977)

Desanto, J.A.: Relation between the solutions of the helmholtz and parabolic equations for sound propagation. J. Acoust. Soc. Am. 62, 295–297 (1977)

Fain, G., Estes, L.E.: Numerical technique for computing the wide-angle acoustic field in an ocean with rang-dependent velocity profiles. J. Acoust. Soc. Am. 62, 38–43 (1977)

Lee, D., Mcdaniel, S.T.: A finite-difference treatment of interface conditions for the parabolic wave equation: the horizontal interface. J. Acoust. Soc. Am. 71, 855–858 (1982)

Jacobson, M.J., Robertson, J.S., Siegmann, W.L.: A treatment of three-dimensional underwater propagation through a steady shear flow. J. Acoust. Soc. Am. 86, 1484–1489 (1989)

Wang, D.P., Wang, C.W.: Application of parabolic equation model to shallow water acoustic propagation,in environmental acoustics. World Sci. pp 755–792 (1994)

Collins, M.D.: Higher-order pade approximations for accurate and stable elastic parabolic equations with applications to interface wave propagation. J. Acoust. Soc. Am. 89, 1050–1057 (1991)

Thomson, D.J.: Wide-angle parabolic equation solutions to range-dependent benchmark problems. J. Acoust. Soc. Am. 87, 1514–1520 (1990)

Collins, M.D.: A self-starter for the parabolic equation method. J. Acoust. Soc. Am. 92, 2069–2074 (1992)

Spiesberger, J.L., Boden, L., Bowlin, J.B.: Time domain analysis of normal mode, parabolic, and ray solutions of the wave equation. J. Acoust. Soc. Am. 90, 954–958 (1991)

Salomons, E.M.: Improved green’s function parabolic equation method for atmospheric sound propagation. J. Acoust. Soc. Am. 104, 100–111 (1998)

Collins, M.D., Siegmann, W.L.: A complete energy conserving correction for the elastic parabolic equation. J. Acoust. Soc. Am. 105, 687–692 (1999)

Collins, M.D.: User’s guide for RAM versions 1.0 and 1.0p (1999). https://oalib-acoustics.org/PE/index.html

Henderson, L.: FOR3D (2015). https://oalib-acoustics.org/PE/index.html

Shang, E.C., Lee, D., Pierce, A.D.: Parabolic equation development in the twentieth century. J. Comput. Acoust. 8, 4 (2000)

Zheng, Q.L.: Experiments on the 30-day long-range numerical weather prediction in a seven-level spectral model. J. Acad. Meteorol. Sci. 10, 234–246 (1989)

Hu, Z.D., Ding, H.B., Cao, Y.: Application of pseudo-spectral method in rapid orbit optimization for SGKW. Aerospace Control (2009)

Boyd, J.P.: Chebyshev and Fourier Spectral Methods, 2nd edn. Dover, New York (2001)

Nuttawit, W., Arisara, C., Sacharuck, P.: Chebyshev collocation approach for vibration analysis of functionally graded porous beams based on third-order shear deformation theory. Acta Mech. Sin. 34(6), 1124–1135 (2018)

Sinan, D., Mehmet, S.: Rational chebyshev collocation method for solving nonlinear heat transfer equations. Int. Commun. Heat Mass Transf. 114, 104595 (2020)

Wang, Y.Q., Zhao, H.L.: Free vibration analysis of metal foam core sandwich beams on elastic foundation using chebyshev collocation method. Arch. Appl. Mech. (2019)

Khaneh, M.P., Ovesy, H.R.: Chebyshev collocation method for static intrinsic equations of geometrically exact beams. Int. J. Solids Struct. (2014)

Evans, R.B., Di X., Kenneth, E.G.: A Legendre–Galerkin technique for differential eigenvalue problems with complex and discontinuous coefficients, arising in underwater acoustics (2020)

Tu, H., Wang, Y., Liu, W., Ma, X., Xiao, W., Lan, Q.: A chebyshev spectral method for normal mode and parabolic equation models in underwater acoustics. Math. Prob. Eng. 2020, 1–12 (2020)

Tu, H., Wang, Y., Lan, Q., Liu, W., Xiao, W., Ma, S.: A chebyshev-tau spectral method for normal modes of underwater sound propagation with a layered marine environment. J. Sound Vib. 492, 1–16 (2021)

Tu, H.: A Chebyshev-Tau spectral method for normal modes of underwater sound propagation with a layered marine environment in matlab and fortran (2021). https://oalib-acoustics.org/Modes/NM-CT/

Tu, H., Wang, Y., Ma, X., Zhu, X.: Applying chebyshev-tau spectral method to solve the parabolic equation model of wide-angle rational approximation in ocean acoustics. arXiv:2012.02405 (2020)

Colbrook, M.J., Ayton, L.J.: A spectral collocation method for acoustic scattering by multiple elastic plates. J. Sound Vib. 461, 114904 (2019)

Jie, S., Tao, T., Lilian, W.: Spectral Methods Algorithms, Analysis and Applications. Springer, Berlin (2011)

Gottlieb, David, Orszag, Steven A.: Numerical analysis of spectral methods, theory and applications. Society for Industrial and Applied Mathematics, Philadelphia (1977)

Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods Fundamentals in Single Domains. Spring, Berlin (2006)

Zhang, Z.: Super convergence of a chebyshev spectral collocation method. J. Sci. Comput. 34, 237–246 (2008)

Porter, M.B.: The Kraken Normal Mode Program. SACLANT Undersea Research Centre (2001). https://oalib-acoustics.org/Modes/Kraken/

Chowdhury, A.D., Vendhan, C.P., Bhattacharyya, S.K., Mudaliar, S.: A Rayleigh-Ritz model for the depth eigenproblem of heterogeneous pekeris waveguides. Acta Acust. United Acust. 104, 597–610 (2018)

Yang, K., Lei, B., Lu, Y.: Principle and Application of Typical Sound Field Model of Ocean Acoustics (in Chinese). Northwestern Polytechnical University Press, Xi’an (2018)