The Electromagnetic Scattering Problem by a Cylindrical Doubly-Connected Domain at Oblique Incidence: An Inverse Problem

Authors

  • Leonidas Mindrinos Department of Natural Resources Development and Agricultural Engineering, Agricultural University of Athens, Athens118 55, Greece https://orcid.org/0000-0002-7807-8153

DOI:

https://doi.org/10.15377/2409-5761.2023.10.2

Keywords:

Inverse problem, Electromagnetic scattering, Singular integral equations

Abstract

In this work, we examine the inverse problem to reconstruct the inner boundary of a cylindrical doubly-connected infinitely long medium from measurements of the scattered electromagnetic wave in the far-field. We consider the integral representation of the solution to derive a non-linear system of equations for the unknown radial function. We propose an iterative scheme using linearization and regularization techniques.

Downloads

Download data is not yet available.

References

Colton D. Qualitative methods in inverse scattering theory. In: Engl HW, Louis AK, Rundell W, Eds. Inverse problems in medical imaging and nondestructive testing. Vienna: Springer; 1997. https://doi.org/10.1007/978-3-7091-6521-8_4 DOI: https://doi.org/10.1007/978-3-7091-6521-8_4

Kress R. Linear integral equations. vol. 82, 3rd ed. New York, NY: Springer; 2014. https://doi.org/10.1007/978-1-4614-9593-2 DOI: https://doi.org/10.1007/978-1-4614-9593-2

Kress R. A collocation method for a hypersingular boundary integral equation via trigonometric differentiation. J Integral Equations Appl. 2014; 26: 197-213. https://doi.org/10.1216/JIE-2014-26-2-197 DOI: https://doi.org/10.1216/JIE-2014-26-2-197

Yousif HA, Köhler S. Scattering by two penetrable cylinders at oblique incidence I The analytical solution. J Opt Soc Am A. 1988; 5(7): 1085-96. https://doi.org/10.1364/JOSAA.5.001085 DOI: https://doi.org/10.1364/JOSAA.5.001085

Wait JR. Scattering of a plane wave from a circular dielectric cylinder at oblique incidence. Can J Phys. 1955; 33: 189-95. https://doi.org/10.1139/p55-024 DOI: https://doi.org/10.1139/p55-024

Nakamura G, Wang H. The direct electromagnetic scattering problem from an imperfectly conducting cylinder at oblique incidence. J Math Anal Appl. 2013; 397: 142-55. https://doi.org/10.1016/j.jmaa.2012.07.049 DOI: https://doi.org/10.1016/j.jmaa.2012.07.049

Wang H, Nakamura G. The integral equation method for electromagnetic scattering problem at oblique incidence. Appl Num Math. 2012; 62: 860-73. https://doi.org/10.1016/j.apnum.2012.02.006 DOI: https://doi.org/10.1016/j.apnum.2012.02.006

Gintides D, Mindrinos L. The direct scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder. J Integral Equations Appl. 2016; 28: 91-122. https://doi.org/10.1216/JIE-2016-28-1-91 DOI: https://doi.org/10.1216/JIE-2016-28-1-91

Gintides D, Mindrinos L. The inverse electromagnetic scattering problem by a penetrable cylinder at oblique incidence. Appl Analysis. 2019; 98: 781-98. https://doi.org/10.1080/00036811.2017.1402891 DOI: https://doi.org/10.1080/00036811.2017.1402891

Mindrinos L. The electromagnetic scattering problem by a cylindrical doubly connected domain at oblique incidence: the direct problem. IMA J Appl Math. 2019; 84: 292-311. https://doi.org/10.1093/imamat/hxy059 DOI: https://doi.org/10.1093/imamat/hxy059

Kress R, Rundell W. Nonlinear integral equations and the iterative solution for an inverse boundary value problem. Inverse Probl. 2005; 21: 1207-23. https://doi.org/10.1088/0266-5611/21/4/002 DOI: https://doi.org/10.1088/0266-5611/21/4/002

Johansson T, Sleeman BD. Reconstruction of an acoustically sound-soft obstacle from one incident field and the far-field pattern. IMA J Appl Math. 2007; 72: 7296-112. https://doi.org/10.1093/imamat/hxl026 DOI: https://doi.org/10.1093/imamat/hxl026

Altundag A, Kress R. On a two-dimensional inverse scattering problem for a dielectric. Appl Analysis. 2012; 91: 757-71. https://doi.org/10.1080/00036811.2011.619981 DOI: https://doi.org/10.1080/00036811.2011.619981

Chapko R, Gintides D, Mindrinos L. The inverse scattering problem by an elastic inclusion. Adv Comput Math. 2017; 44: 1-24. https://doi.org/10.1007/s10444-017-9550-z DOI: https://doi.org/10.1007/s10444-017-9550-z

Lee K-M. Inverse scattering problem from an impedance crack via a composite method. Wave Motion. 2015; 56: 43–51. https://doi.org/10.1016/j.wavemoti.2015.02.002 DOI: https://doi.org/10.1016/j.wavemoti.2015.02.002

Downloads

Published

2023-08-07

Issue

Section

Articles

How to Cite

The Electromagnetic Scattering Problem by a Cylindrical Doubly-Connected Domain at Oblique Incidence: An Inverse Problem . (2023). Journal of Advances in Applied & Computational Mathematics, 10, 18-25. https://doi.org/10.15377/2409-5761.2023.10.2

Similar Articles

21-30 of 47

You may also start an advanced similarity search for this article.