TY - JOUR
T1 - The Factorization Method for an Open Arc
AU - Wu , Qinghua
AU - Yan , Guozheng
JO - Journal of Computational Mathematics
VL - 5
SP - 517
EP - 532
PY - 2015
DA - 2015/10
SN - 33
DO - http://doi.org/10.4208/jcm.1505-m2014-0101
UR - https://global-sci.org/intro/article_detail/jcm/9857.html
KW - Factorization method, inverse scattering problem, crack scattering
AB - <p style="text-align: justify;">We consider the inverse scattering problem of determining the shape of a thin dielectric infinite cylinder having an open arc as cross section. Assuming that the electric field is polarized in the TM mode, this leads to a mixed boundary value problem for the Helmholtz equation defined in the exterior of an open arc in $R^2$. We suppose that the arc has mixed Dirichlet-impedance boundary condition, and try to recover the shape of the arc through the far field pattern by using the factorization method. However, we are not able to apply the basic theorem introduced by Kirsch to treat the far field operator $F$, and some auxiliary operators have to be considered. The theoretical validation of the factorization method to our problem is given in this paper, and some numerical results are presented to show the viability of our method.</p>