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Volume 37, Issue 3
The Factorization Method for a Mixed Scattering Problem from a Bounded Obstacle and an Open Arc

Qinghua Wu, Meilan Zeng, Wentao Xiong, Guozheng Yan & Jun Guo

DOI: 10.4208/jcm.1805-m2017-0151

J. Comp. Math., 37 (2019), pp. 384-402.

Published online: 2018-09

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  • Abstract

In this paper, we consider the scattering problem of time-harmonic electromagnetic waves from an infinite cylinder having an open arc $Γ$ and a bounded domain $D$ in $\mathbb{R}$2 as cross section. We focus on the inverse scattering problem, that is, to reconstruct the shape of $Γ$ and $D$ from the far-field pattern by using the factorization method. Through establishing a mixed reciprocity relation, we prove that the scatters $Γ$ and $D$ can be uniquely determined by the far-field pattern. Furthermore, the mathematical basis is given to explain that the factorization method is feasible to our problem. At the end of this paper, we give some numerical examples to show the efficaciousness of the algorithms.

  • Keywords

Factorization method, Inverse scattering problem, Mixed scattering, Time-harmonic electromagnetic wave.

  • AMS Subject Headings

35Q65, 35C15, 78A45

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wqhyimo@yeah.net (Qinghua Wu)

zml571@126.com (Meilan Zeng)

xiong-2009@foxmail.com (Wentao Xiong)

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

hssxgj@126.com (Jun Guo)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-384, author = {Wu , QinghuaZeng , MeilanXiong , WentaoYan , Guozheng and Guo , Jun}, title = {The Factorization Method for a Mixed Scattering Problem from a Bounded Obstacle and an Open Arc}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {37}, number = {3}, pages = {384--402}, abstract = {

In this paper, we consider the scattering problem of time-harmonic electromagnetic waves from an infinite cylinder having an open arc $Γ$ and a bounded domain $D$ in $\mathbb{R}$2 as cross section. We focus on the inverse scattering problem, that is, to reconstruct the shape of $Γ$ and $D$ from the far-field pattern by using the factorization method. Through establishing a mixed reciprocity relation, we prove that the scatters $Γ$ and $D$ can be uniquely determined by the far-field pattern. Furthermore, the mathematical basis is given to explain that the factorization method is feasible to our problem. At the end of this paper, we give some numerical examples to show the efficaciousness of the algorithms.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1805-m2017-0151}, url = {http://global-sci.org/intro/article_detail/jcm/12729.html} }
TY - JOUR T1 - The Factorization Method for a Mixed Scattering Problem from a Bounded Obstacle and an Open Arc AU - Wu , Qinghua AU - Zeng , Meilan AU - Xiong , Wentao AU - Yan , Guozheng AU - Guo , Jun JO - Journal of Computational Mathematics VL - 3 SP - 384 EP - 402 PY - 2018 DA - 2018/09 SN - 37 DO - http://doi.org/10.4208/jcm.1805-m2017-0151 UR - https://global-sci.org/intro/article_detail/jcm/12729.html KW - Factorization method, Inverse scattering problem, Mixed scattering, Time-harmonic electromagnetic wave. AB -

In this paper, we consider the scattering problem of time-harmonic electromagnetic waves from an infinite cylinder having an open arc $Γ$ and a bounded domain $D$ in $\mathbb{R}$2 as cross section. We focus on the inverse scattering problem, that is, to reconstruct the shape of $Γ$ and $D$ from the far-field pattern by using the factorization method. Through establishing a mixed reciprocity relation, we prove that the scatters $Γ$ and $D$ can be uniquely determined by the far-field pattern. Furthermore, the mathematical basis is given to explain that the factorization method is feasible to our problem. At the end of this paper, we give some numerical examples to show the efficaciousness of the algorithms.

Wu , QinghuaZeng , MeilanXiong , WentaoYan , Guozheng and Guo , Jun. (2018). The Factorization Method for a Mixed Scattering Problem from a Bounded Obstacle and an Open Arc. Journal of Computational Mathematics. 37 (3). 384-402. doi:10.4208/jcm.1805-m2017-0151
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