Marching schemes for Cauchy wave propagation problems in laterally varying waveguides

References

[1] G. Beylkin and K. Sandberg, Wave propagation using bases for bandlimited functions, Wave Motion 41 (2005), no. 3, 263–291. 10.1016/j.wavemoti.2004.05.008Search in Google Scholar

[2] M. D. Collins and W. A. Kuperman, Inverse problems in ocean acoustics, Inverse Problems 10 (1994), no. 5, 1023–1040. 10.1088/0266-5611/10/5/003Search in Google Scholar

[3] M. D. Collins and W. L. Siegmann, Parabolic Wave Equations with Applications, Springer, New York, 2001. Search in Google Scholar

[4] T. Delillo, V. Isakov, N. Valdivia and L. Wang, The detection of the source of acoustical noise in two dimensions, SIAM J. Appl. Math. 61 (2001), no. 6, 2104–2121. 10.1137/S0036139900367152Search in Google Scholar

[5] T. DeLillo, V. Isakov, N. Valdivia and L. Wang, The detection of surface vibrations from interior acoustical pressure, Inverse Problems 19 (2003), no. 3, 507–524. 10.1088/0266-5611/19/3/302Search in Google Scholar

[6] L. Fishman, One-way wave propagation methods in direct and inverse scalar wave propagation modeling, Radio Sci. 28 (1993), 865–876. 10.1029/93RS01632Search in Google Scholar

[7] F. B. Jensen, W. A. Kuperman, M. B. Porter and H. Schmidt, Computational Ocean Acoustics, AIP Ser. Modern Acoustics Signal Process., American Institute of Physics, New York, 1994. 10.1063/1.2808704Search in Google Scholar

[8] B. Jin and Y. Zheng, A meshless method for some inverse problems associated with the Helmholtz equation, Comput. Methods Appl. Mech. Engrg. 195 (2006), no. 19–22, 2270–2288. 10.1016/j.cma.2005.05.013Search in Google Scholar

[9] C. S. Kenney and A. J. Laub, The matrix sign function, IEEE Trans. Automat. Control 40 (1995), no. 8, 1330–1348. 10.1109/9.402226Search in Google Scholar

[10] C. H. Knightly and D. F. St. Mary, Stable marching schemes based on elliptic models of wave propagation, J. Acoustical Soc. Amer. 93 (1993), 1866–1872. 10.1121/1.406701Search in Google Scholar

[11] P. Li, Z. Chen and J. Zhu, An operator marching method for inverse problems in range-dependent waveguides, Comput. Methods Appl. Mech. Engrg. 197 (2008), no. 49–50, 4077–4091. 10.1016/j.cma.2008.04.001Search in Google Scholar

[12] P. Li, K. Liu, W. Zuo and W. Zhong, Error analysis for the operator marching method applied to range dependent waveguides, J. Inverse Ill-Posed Probl. 24 (2016), no. 5, 625–636. 10.1515/jiip-2015-0069Search in Google Scholar

[13] P. Li, W. Z. Zhong, G. S. Li and Z. H. Chen, A numerical local orthogonal transform method for stratified waveguides, J. Zhejiang Univ. Sci. (C) 11 (2010), no. 12, 998–1008. 10.1631/jzus.C0910732Search in Google Scholar

[14] Y. Y. Lu, One-way large range step methods for Helmholtz waveguides, J. Comput. Phys. 152 (1999), no. 1, 231–250. 10.1006/jcph.1999.6243Search in Google Scholar

[15] Y. Y. Lu and J. R. McLaughlin, The Riccati method for the Helmholtz equation, J. Acoustical Soc. Amer. 100 (1996), 1432–1446. 10.1121/1.415990Search in Google Scholar

[16] Y. Y. Lu, J. Huang and J. R. McLauphlin, Local orthogonal transformation and one-way methods for acoustics waveguides, Wave Motion 34 (2001), 193–207. 10.1016/S0165-2125(00)00083-4Search in Google Scholar

[17] Y. Y. Lu and J. Zhu, A local orthogonal transform for acoustic waveguides with an interval interface, J. Comput. Acoust. 12 (2004), no. 1, 37–53. 10.1142/S0218396X04002183Search in Google Scholar

[18] F. Natterer and F. Wübbeling, A propagation-backpropagation method for ultrasound tomography, Inverse Problems 11 (1995), no. 6, 1225–1232. 10.1088/0266-5611/11/6/007Search in Google Scholar

[19] F. Natterer and F. Wübbeling, Marching schemes for inverse acoustic scattering problems, Numer. Math. 100 (2005), no. 4, 697–710. 10.1007/s00211-004-0580-3Search in Google Scholar

[20] B. N. Parlett, The Rayleigh quotient iteration and some generalizations for nonnormal matrices, Math. Comp. 28 (1974), 679–693. 10.1090/S0025-5718-1974-0405823-3Search in Google Scholar

[21] K. Sandberg, Forward and Inverse Wave Propagation Using Bandlimited Functions and a Fast Reconstruction Algorithm for Electron Microscopy, ProQuest LLC, Ann Arbor, 2003. Search in Google Scholar

[22] K. Sandberg and G. Beylkin, Full-wave-equation depth extrapolation for migrations, Geophys. 74 (2009), no. 6, 121–128. 10.1190/1.3202535Search in Google Scholar

[23] K. Sandberg, G. Beylkin and A. Vassiliou, Full-wave-equation depth migration using multiple reflections, preprint (2010), http://www.geoenergycorp.com/publications/SEG2010_Two_Way_WEM.pdf. 10.1190/1.3513538Search in Google Scholar

[24] R. C. Song, J. X. Zhu and X. C. Zhang, Full-vectorial modal analysis for circular optical waveguides based on the multidomain Chebyshev pseudospectral method, J. Optical Soc. Amer. B 27 (2010), no. 9, 1722–1730. 10.1364/JOSAB.27.001722Search in Google Scholar

[25] M. Vögeler, Reconstruction of the three-dimensional refractive index in electromagnetic scattering by using a propagation-backpropagation method, Inverse Problems 19 (2003), no. 3, 739–753. 10.1088/0266-5611/19/3/316Search in Google Scholar

[26] Z. Wang and S. F. Wu, Helmholtz equation-least-squares method for reconstructing the acoustic pressure field, J. Acoustical Soc. Amer. 102 (1997), no. 4, 2020–2032. 10.1121/1.419691Search in Google Scholar

[27] J. H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965. Search in Google Scholar

[28] S. F. Wu and J. Yu, Reconstructing interior acoustic pressure fields via Helmholtz equation least-squares method, J. Acoustical Soc. Amer. 104 (1998), no. 4, 2054–2060. 10.1121/1.423719Search in Google Scholar

[29] X. Zhang, Mapped barycentric Chebyshev differentiation matrix method for the solution of regular Sturm–Liouville problems, Appl. Math. Comput. 217 (2010), no. 5, 2266–2276. 10.1016/j.amc.2010.07.027Search in Google Scholar

[30] J. Zhu and P. Li, Local orthogonal transform for a class of acoustic waveguides, Progr. Natur. Sci. (English Ed.) 17 (2007), no. 10, 1136–1146. Search in Google Scholar

[31] J. Zhu and Y. Lu, Large range step method for acoustic waveguide with two layer media, Progr. Natur. Sci. (English Ed.) 12 (2002), no. 11, 820–825. Search in Google Scholar

[32] J. Zhu and Y. Y. Lu, Validity of one-way models in the weak range dependence limit, J. Comput. Acoust. 12 (2004), no. 1, 55–66. 10.1142/S0218396X0400216XSearch in Google Scholar

[33] J. X. Zhu and P. Li, The mathematical treatment of wave propagation in the acoustical waveguides with n curved interfaces, J. Zhejiang Univ. Sci. (A) 9 (2008), no. 10, 1463–1472. 10.1631/jzus.A0720064Search in Google Scholar

[34] J. X. Zhu and R. C. Song, Fast and stable computation of optical propagation in micro-waveguides with loss, Mircroelectronics Reliab. 49 (2009), no. 12, 1529–1536. 10.1016/j.microrel.2009.06.004Search in Google Scholar

[35] J. X. Zhu and Q. X. Zhou, Eigenvalue computation in slab waveguides with some perfectly matched layer, Proc. SPIE 5279 (2004), 172–180. 10.1117/12.520171Search in Google Scholar