No Access

A LOCAL ORTHOGONAL TRANSFORM FOR ACOUSTIC WAVEGUIDES WITH AN INTERNAL INTERFACE

YA YAN LU

Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China

Search for more papers by this author

and

JIANXIN ZHU

Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Search for more papers by this author

https://doi.org/10.1142/S0218396X04002183Cited by:13 (Source: Crossref)

Abstract

A numerical method is developed for solving the two-dimensional Helmholtz equation in a two layer region bounded by a flat top, a flat bottom and a curved interface. A local orthogonal transform is used to flatten the curved interface of the waveguide. The one-way reformulation based on the Dirichlet-to-Neumann (DtN) map is then used to reduce the boundary value problem to an initial value problem. Numerical implementation of the resulting operator Riccati equation uses a large range step method for discretizing the range variable and a truncated local eigenfunction expansion for approximating the operators. This method is particularly useful for solving long range wave propagation problems in slowly varying waveguides.

Keywords:

References

F. B. Jensen et al. , Computational Ocean Acoustics ( American Institute of Physics , 1994 ) . Google Scholar
F. D. Tappert , Wave Propagation and Underwater Acoustics , eds. J. B. Keller and J. S. Papadakis ( Springer-Verlag , 1977 ) . Crossref, Google Scholar
M. D. Collins, J. Acoust. Soc. Am. 86(4), 1097 (1989). Crossref, Web of Science, Google Scholar
D. Lee and A. D. Pierce, J. Comput. Acoust. 3, 95 (1995). Link, Google Scholar
A. D. Pierce, J. Acoust. Soc. Am. 37, 19 (1965). Crossref, Web of Science, Google Scholar
S. R. Rutherford and K. E. Hawker, J. Acoust. Soc. Am. 70, 554 (1981). Crossref, Web of Science, Google Scholar
C. A. Boyles, J. Acoust. Soc. Am. 73, 800 (1983). Crossref, Web of Science, Google Scholar
R. Evans, J. Acoust. Soc. Am. 74, 188 (1983). Crossref, Web of Science, Google Scholar
L. Abrahamsson and H.-O. Kreiss, J. Comput. Phys. 111, 1 (1994). Crossref, Web of Science, Google Scholar
E. Larsson and L. Abrahamsson, Mathematics and Numerical Aspects of Wave Propagation, ed. J. A. DeSanto (SIAM, Philadelphia, 1998) pp. 582–584. Google Scholar
R. Evans, J. Acoust. Soc. Am. 104, 2167 (1998). Crossref, Web of Science, Google Scholar
E. Tessmer, D. Kosloff and A. Bethe, Geophys. J. Int. 108, 621 (1992). Crossref, Web of Science, Google Scholar
V. A. Dougalis and N. A. Kampanis, J. Comput. Acoust. 4, 55 (1996). Link, Web of Science, Google Scholar
Y. Y. Lu, J. Huang and J. R. McLaughlin, Wave Motion 34(2), 193 (2001). Crossref, Web of Science, Google Scholar
L. Fishman, Radio Sci. 28(5), 865 (1993). Crossref, Web of Science, Google Scholar
A. J. Haines and M. V. de Hoop, J. Math. Phys. 37(8), 3854 (1996). Crossref, Web of Science, Google Scholar
Y. Y. Lu and J. R. McLaughlin, J. Acoust. Soc. Am. 100(3), 1432 (1996). Crossref, Web of Science, Google Scholar
Y. Y. Lu, Mathematical and Numerical Aspects of Wave Propagation, ed. J. DeSanto (SIAM, Philadelphia, 1998) pp. 626–628. Google Scholar
Y. Y. Lu, J. Comput. Phys. 152, 231 (1999). Crossref, Web of Science, Google Scholar
L. Dieci, SIAM J. Numer. Anal. 29(3), 781 (1992). Crossref, Web of Science, Google Scholar