Geodesic
Modelling equation of electromagnetic scattering on thin dielectric structures
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 47, Tome 461 (2017), pp. 95-106

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In this research we study the scattering of electromagnetic waves by the dielectric impediment in 2D geometry. The impediment is determined through the inhomogeneous component of the refractive index in the Helmholtz equation. It is supposed that the characteristic gauge of one of the two impediment sizes is much less in comparison with the length of the waves generated by the monochromatic point source. Nevertheless, we don't neglect the structure of the impediment in the process of calculation of the scattered field. The scattered field is defined by the derived model integral equation whose unique solvability is proved. 
@article{ZNSL_2017_461_a4,
     author = {S. A. Vavilov and M. S. Lytaev},
     title = {Modelling equation of electromagnetic scattering on thin dielectric structures},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {95--106},
     publisher = {mathdoc},
     volume = {461},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_461_a4/}
}
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S. A. Vavilov; M. S. Lytaev. Modelling equation of electromagnetic scattering on thin dielectric structures. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 47, Tome 461 (2017), pp. 95-106. http://geodesic.mathdoc.fr/item/ZNSL_2017_461_a4/