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Volume 33, Issue 5
The Factorization Method for an Open Arc

Qinghua Wu & Guozheng Yan

DOI: 10.4208/jcm.1505-m2014-0101

J. Comp. Math., 33 (2015), pp. 517-532.

Published online: 2015-10

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  • 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.

  • Keywords

Factorization method, inverse scattering problem, crack scattering

  • AMS Subject Headings

35Q65, 35C15, 78A45.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wqhyimo@yeah.net (Qinghua Wu)

yangz@mail.ccnu.edu.cn (Guozheng Yan)

  • BibTex
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  • TXT
@Article{JCM-33-517, author = {Wu , Qinghua and Yan , Guozheng}, title = {The Factorization Method for an Open Arc}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1505-m2014-0101}, url = {http://global-sci.org/intro/article_detail/jcm/9857.html} }
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 -

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.

Qinghua Wu & Guozheng Yan. (2020). The Factorization Method for an Open Arc. Journal of Computational Mathematics. 33 (5). 517-532. doi:10.4208/jcm.1505-m2014-0101
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