Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T20:00:30.746Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  28 May 2015

Ali Yang ,
Liantang Wang  and
Xiaohua Li
Ali Yang*
Affiliation:
School of Science, Xi’an Polytechnic University, Xi’an 710048, Shannxi, China
Liantang Wang
Affiliation:
Mathematics Department of Northwest University, Xi’an 710069, Shannxi, China
Xiaohua Li
Affiliation:
School of Science, Xi’an University of Science and Technology, Xi’an 710054, Shannxi, China
*
Corresponding author.Email address:[email protected]
Get access

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.

Keywords

34L2581U40Impedance boundary conditionHelmholtz equationinverse scattering problem
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 2 , May 2013 , pp. 343 - 352
Copyright
Copyright © Global Science Press Limited 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Kress, R. and Serranho, P., A hybrid method for two-dimensional crack reconstruction, Inverse Problem, 21 (2005), pp. 772–784.CrossRefGoogle Scholar
[2]Cakoni, F., The direct and inverse scattering problem for cracks, Winter School on Direct and Inverse Scattering Problems, January 2003, pp. 27–31.Google Scholar
[3]Lee, K.-M., inverse scattering via nonlinear integral equations for a Neumann crack, Inverse Problem, 22 (2006), pp. 1989–2000.CrossRefGoogle Scholar
[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. 624–632.Google Scholar
[5]Lee, K.-M., Inverse scattering problem for an impedance crack, Wave Motion, 45 (2008), pp. 254–263.CrossRefGoogle Scholar
[6]Colton, D. and Kress, R., Inverse Acoustic and Electromagnetic Scattering Theory, Spring-Verlag, Berlin, 1992.Google Scholar
[7]Kress, R. and Lee, K.-M., Integral equation methedsfor scattering from an impedance crack, J. Comput. Appl. Math., 161 (2003), pp. 161–177.CrossRefGoogle Scholar
[8]Serranho, P., A Hybrid method for inverse scattering for shape and impedance, Inverse Problem, 22 (2006), pp. 663–680.CrossRefGoogle Scholar
[9]Colton, D. and Kress, R., Integral Equation Methods in Scattering Theory, Wiley-Intesciece, New York, 1983.Google Scholar