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Telecommunications and Radio Engineering
SJR: 0.202 SNIP: 0.2 CiteScore™: 0.23

ISSN Imprimir: 0040-2508
ISSN On-line: 1943-6009

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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v61.i4.60
pages 344-355

Application of Conformal Mapping Theory to the Problem Solution of the Diffraction by a Rectangular Dielectric Cylinder

L. N. Ilyashenko
A. Usikov Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine, 12, Academician Proskura St., Kharkov 61085, Ukraine


The problem of electromagnetic wave diffraction by a rectangular dielectric cylinder is considered. The system of the Fredholm singular integral equations of the first kind appears from the field representation in terms of single-layer potential. Once the singular part of the integral operator kernel is developed and analytically inverted, the problem reduces to the infinite system of the Fredholm linear algebraic equations of the second kind which is numerically solved to any preassigned accuracy by the Galerkin's method with the basis elements as orthogonal eigenfunctions of the singular part of the integral operator. The conformal mapping between the rectangle and circle exteriors is performed, and the resulting parametric equations allow to reduce the initial diffraction problem to that of a circular dielectric cylinder. The calculation results are presented for variously sized rectangular cylinders under either E- or H-wave illumination at various angles.

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