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.