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Abstract: Flattening of the interfaces is necessary in computing wave propagation along stratified waveguides in large range step sizes while using marching methods. When the supposition that there exists one horizontal straight line in two adjacent interfaces does not hold, the previously suggested local orthogonal transform method with an analytical formulation is not feasible. This paper presents a numerical coordinate transform and an equation transform to perform the transforms numerically for waveguides without satisfying the supposition. The boundary value problem is then reduced to an initial value problem by one-way reformulation based on the Dirichlet-to-Neumann (DtN) map. This method is applicable in solving long-range wave propagation problems in slowly varying waveguides with a multilayered medium structure.

[1]Abrahamsson, L., Kreiss, H.O., 1994. Numerical solution of the coupled mode equations in duct acoustic. J. Comput. Phys., 111(1):1-14.

[2]Andersson, A., 2008. A modified Schwarz-Christoffel mapping for regions with piecewise smooth boundaries. J. Comput. Appl. Math., 213(1):56-70.

[3]Andersson, A., 2009. Modified Schwarz Christoffel mappings using approximate curve factors. J. Comput. Appl. Math., 233(4):1117-1127.

[4]Cullum, J., 1971. Numerical differentiation and regularization. emph{SIAM J. Numer. Anal.}, 8(2):254-265.

[5]Delillo, T., Isakov, V., Valdivia, N., Wang, L., 2001. The detection of the source of acoustical noise in two dimensions. emph{SIAM J. Appl. Math.}, 61(6):2104-2121.

[6]Fishman, L., 1993. One-way wave propagation methods in direct and inverse scalar wave propagation modeling. Radio Sci., 28(5):865-876.

[7]Fishman, L., Gautesen, A.K., Sun, A.K., 1997. Uniform high-frequency approximations of the square root Helmholtz operator symbol. Wave Motion, 26:127-161.

[8]Jensen, F.B., Kuperman, W.A., Porter, M.B., Schmidt, H., 1994. Computational Ocean Acoustics. American Institute of Physics, New York.

[9]Jin, B.T., Marin, L., 2008. The plane wave method for inverse problems associated with Helmholtz-type equations. emph{Eng. Anal. Bound. Elem.}, 32(3):223-240.

[10]Jin, B.T., Zheng, Y., 2006. A meshless method for some inverse problems associated with the Helmholtz equation. emph{Comput. Methods Appl. Mech. Eng.}, 195:2270-2288.

[11]Larsson, E., Abrahamsson, L., 1998. Parabolic Wave Equation versus the Helmholtz Equation in Ocean Acoustics. In: DeSanto, J.A. (Ed.), Mathematics and Numerical Aspects of Wave Propagation. SIAM, Philadelphia, p.582-584.

[12]Lee, D., Pierce, A.D., 1995. Parabolic equation development in recent decade. J. Comput. Acoust., 3(2):95-173.

[13]Li, P., Chen, Z.H., Zhu, J.X., 2008. An operator marching method for inverse problems in range dependent waveguides. emph{Comput. Methods Appl. Mech. Eng.}, 197(49-50):4077-4091.

[14]Lu, Y.Y., 1999. One-way large range step methods for Helmholtz waveguides. J. Comput. Phys., 152(1):231-250.

[15]Lu, Y.Y., McLaughlin, J.R., 1996. The Riccati method for the Helmholtz equation. J. Acoust. Soc. Am., 100(3):1432-1446.

[16]Lu, Y.Y., Huang, J., McLauphilin, J.R., 2001. Local orthogonal transformation and one-way methods for acoustics waveguides. Wave Motion, 34(2):193-207.

[17]Marin, L., 2005. A meshless method for the numerical solution of the Cauchy problem associated with three-dimensional Helmholtz-type equations. Appl. Math. Comput., 165(2):355-374.

[18]Marin, L., Elliott, L., Heggs, P.J., Ingham, D.B., Lesnic, D., Wen, X., 2003. Conjugate gradient-boundary element solution to the Cauchy problem for Helmholtz-type equations. Comput. Mech., 31:367-372.

[19]Nilsson, B., 2002. Acoustic transmission in curved ducts with varying cross-sections. Proc. R. Soc. A, 458(2023):1555-1574.

[20]Tarppet, F.D., 1977. The Parabolic Approximation Method. In: Keller, J.B., Papadakis, J.S. (Eds.), Wave Propagation and Underwater Acoustics: Lecture Notes in Physics. Springer-Verlag, Berlin New York, 70:224-287.

[21]Zhu, J.X., Li, P., 2007. Local orthogonal transform for a class of acoustic waveguide. Progr. Nat. Sci., 17:18-28.

[22]Zhu, J.X., Li, P., 2008. Mathematical treatment of wave propagation in acoustic waveguides with n curved interfaces. J. Zhejiang Univ.-Sci. A, 9(10):1463-1472.

[23]Zhu, J.X., Lu, Y.Y., 2002. Large range step method for acoustic waveguide with two layer media. Progr. Nat. Sci., 12:820-825.