Diffraction problem of scattering and propagation TM wave on pre-fractal impedance strips above shielded dielectric layer

Authors

  • Kateryna Vitaliivna Nesvit Karazin Kharkiv National University

DOI:

https://doi.org/10.14419/ijamr.v3i1.1444

Published:

2013-12-18

Abstract

In this paper a discrete mathematical model of the diffraction of a plane electromagnetic wave by pre-Cantor impedance strips on a shielded dielectric layer is developed. The TM wave case is considered. The mathematical model is based on the boundary singular integral equation (SIE) of the first kind with supplementary conditions and the Volterra integral equation (IE) of the second kind. Numerical experiments may be carried out based on this discrete mathematical model using the discrete singularities method (DSM).

References

Yu. V. Gandel, V. D. Dushkin, Mathematical models of two-dimensional diffraction problems: Singular integral equations and numerical discrete singularities method (in Russian), Monograph, Kharkov: Academy of Internal Defence of the MIA of Ukraine, (2012).

Yu. V. Gandel, V. L. Sidelnikov, Method of integral equations in third boundary-value diffraction problem on boundary grating above a °at screen reflector (in Russian). Differential equations. Vol. 35, No. 9, (1999), pp. 1155-1161.

K. V. Nesvit, Discrete mathematical model of diffraction on periodic pre-Cantor gratings with shield and numerical experiment. Bulletin of Karazin Kharkiv National University 1037 Series "Mathematical modeling. Information Technology. Automated Control Systems, Issue 20, (2012), pp. 146-157.

Yu. V. Gandel, Introduction to methods of evaluation of singular and hypersingular integrals (in Russian). Textbook, Kharkov, Ukraine, (2002).

I. K. Lifanov, The method of singular integral equations and numerical experiment (in Russian), TOO "Janus", Moscow, Russia, (1995).

B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman and Company, New York, (1983).

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