Volume 6, Issue 2
A Method for Solving the Inverse Scattering Problem for Shape and Impedance of Crack

Ali Yang, Liantang Wang & Xiaohua Li

Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 343-352.

Published online: 2013-06

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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 $\partial u / \partial \nu$ 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

Impedance boundary condition, Helmholtz equation, inverse scattering problem.

  • AMS Subject Headings

34L25, 81U40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-6-343, author = {}, title = {A Method for Solving the Inverse Scattering Problem for Shape and Impedance of Crack}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2013}, volume = {6}, number = {2}, pages = {343--352}, 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 $\partial u / \partial \nu$ 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.1042nm}, url = {http://global-sci.org/intro/article_detail/nmtma/5907.html} }
TY - JOUR T1 - A Method for Solving the Inverse Scattering Problem for Shape and Impedance of Crack JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 343 EP - 352 PY - 2013 DA - 2013/06 SN - 6 DO - http://doi.org/10.4208/nmtma.2013.1042nm UR - https://global-sci.org/intro/article_detail/nmtma/5907.html KW - Impedance boundary condition, Helmholtz equation, inverse scattering problem. AB -

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 $\partial u / \partial \nu$ 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.

Ali Yang, Liantang Wang & Xiaohua Li. (2020). A Method for Solving the Inverse Scattering Problem for Shape and Impedance of Crack. Numerical Mathematics: Theory, Methods and Applications. 6 (2). 343-352. doi:10.4208/nmtma.2013.1042nm
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