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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:yangali0206@126.com
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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

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References

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