The Factorization Method for an Open Arc

The Factorization Method for an Open Arc

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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

Author Details

Qinghua Wu

Guozheng Yan

  1. The factorization method for a penetrable cavity scattering with interior near-field measurements

    Wu, Qinghua | Guo, Jun | Yan, Guozheng

    Journal of Inverse and Ill-posed Problems, Vol. 0 (2023), Iss. 0

    https://doi.org/10.1515/jiip-2018-0111 [Citations: 0]
  2. Remarks on the factorization and monotonicity method for inverse acoustic scatterings

    Furuya, Takashi

    Inverse Problems, Vol. 37 (2021), Iss. 6 P.065006

    https://doi.org/10.1088/1361-6420/abf75f [Citations: 3]