Abstract
In this paper the approximate solution to the problem of a time-harmonic acoustic wave scattering from a obeject with a sound soft surface in a shallow ocean is investigated by means of wavelets. We reduce the problem into a boundary integral equation in which the kernel function is an infinite series. The Daubechies orthonormal wavelet basis is periodized and its corresponding properties are discussed. The kernel function first is truncated approximately and then is approximated via periodic wavelet. Error estimates are obtained and convergence discussions are given. Finally some numerical examples are presented.
This Research was Supported in Part by the National Natural Science Foundation of China & the Guangdong Natural Science Foundation
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References
Colton, D. and R. Kress. (1983). Integral Equation Methods in Scattering Theory, John Wiley, New York.
Colton, D. and P. Monk. (1988). The inverse scattering problem for time-harmonic acoustic waves in an inhomogeneous medium, Mech.Appl. Math., Vol. 41.
Daubechies, I. (1988). Orthonormal bases of compactly supported wavelets, Comm. Pure and Applied Math., Vol. XLI.
Daubechies, I. Ten Lectures on Wavelets,CBMS Lecture Notes nr. 61, SIAM, Philadephia.
Gilbert, R. P. and Lin Wei. (1993). Wavelet solutions for time harmonic acoustic waves in a finite ocean, J.Comput. Acoust., Vol. 1 (1), (pages 3160 ).
Gilbert, R. P. and Yongzhi Xu. (1992). Acoustic waves and far-field patterns in two dimensional oceans with porous-elastic seabeds, Result in Mathematics, Vol. 22, (pages 685–700 ).
Lin, W., Yongzhi Xu and Yuqiu Zhao. (1996). Normal modes analysis for sounds waves in an ocean with an ice cap and a perfectly reflecting bottom, Applicable Analysis, Vol. 63, (pages 167–182 ).
Tappert, R. D. (1977). The parabolic approximation method, Wave Propagation and Underwater Acoustics, (eds. J.B. Keller and J.S. Papadakis), Springer-Verlag, Berlin, Chap. V, (pages 224–287 ).
Xu, Yongzhi. (1991). An injective far-field pattern operator and inverse scattering problem in a finite depth ocean, Proc.Edinburgh Mathematical Society, Vol. 34, (pages 295–311 ).
Xu, Y. and Y. Yan. (1992). Boundary integral equation method for source localization with a continuous wave sonar,J. Acoust. Soc. AM., Vol. 92(2), (pages 995–1002).
Wang, X. B. and W. Lin (1998). ID-wavelet method for Hammerstein integral equations, to appear in JCM.
Yan, Y. (1991). A Fast Boundary Integral Equation Method for the Two Dimensional Helmholtz Equation.
Grodshteyn, I. S. and I. M. Ryzhik. (1980). Table of Integrals, Series and Products, Academic Press Inc.
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Lin, W., Wang, X. (2000). Numerical Solutions to Acoustic Scattering in Shallow Oceans by Periodic Wavelets. In: Gilbert, R.P., Kajiwara, J., Xu, Y.S. (eds) Direct and Inverse Problems of Mathematical Physics. International Society for Analysis, Applications and Computation, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3214-6_15
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DOI: https://doi.org/10.1007/978-1-4757-3214-6_15
Publisher Name: Springer, Boston, MA
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