Year: 2015
Author: Qinghua Wu, Guozheng Yan
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 5 : pp. 517–532
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1505-m2014-0101
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 5 : pp. 517–532
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Factorization method inverse scattering problem crack scattering