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A Method for Solving the Inverse Scattering Problem for Shape and Impedance of Crack

  • Ali Yang (a1), Liantang Wang (a2) and Xiaohua Li (a3)

Abstract

The inverse problem considered in this paper is to determine the shape and the impedance of crack from a knowledge of the time-harmonic incident field and the corresponding far field pattern of the scattered waves in two-dimension. The combined single- and double-layer potential is used to approach the scattered waves. As an important feature, this method does not require the solution of u and ∂u/∂v at each iteration. An approximate method is presented and the convergence of this method is proven. Numerical examples are given to show that this method is both accurate and simple to use.

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Corresponding author.Email address:yangali0206@126.com

References

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[1]Kress, R. and Serranho, P., A hybrid method for two-dimensional crack reconstruction, Inverse Problem, 21 (2005), pp. 772784.
[2]Cakoni, F., The direct and inverse scattering problem for cracks, Winter School on Direct and Inverse Scattering Problems, January 2003, pp. 2731.
[3]Lee, K.-M., inverse scattering via nonlinear integral equations for a Neumann crack, Inverse Problem, 22 (2006), pp. 19892000.
[4]Yang, A. L. and Wang, L. T., A method for solving the inverse scattering problem for shape and impedance, J. Comp. Math., 26 (2008), pp. 624632.
[5]Lee, K.-M., Inverse scattering problem for an impedance crack, Wave Motion, 45 (2008), pp. 254263.
[6]Colton, D. and Kress, R., Inverse Acoustic and Electromagnetic Scattering Theory, Spring-Verlag, Berlin, 1992.
[7]Kress, R. and Lee, K.-M., Integral equation methedsfor scattering from an impedance crack, J. Comput. Appl. Math., 161 (2003), pp. 161177.
[8]Serranho, P., A Hybrid method for inverse scattering for shape and impedance, Inverse Problem, 22 (2006), pp. 663680.
[9]Colton, D. and Kress, R., Integral Equation Methods in Scattering Theory, Wiley-Intesciece, New York, 1983.

Keywords

A Method for Solving the Inverse Scattering Problem for Shape and Impedance of Crack

  • Ali Yang (a1), Liantang Wang (a2) and Xiaohua Li (a3)

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