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 - <p style="text-align: justify;">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.</p>