Geodesic
Synthesis of surface H-polarized currents on an unclosed cylindrical surface
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 4, pp. 135-141 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article describes the inverse problem of diffraction of electromagnetic waves, finding surface H-polarized currents on an unclosed cylindrical surface according to a given radiation pattern. The work is based on modelling an operator equation with a small parameter. The operator is represented as the sum of a positive-definite, continuously invertible operator and a compact positive operator. The positive-definite operator exactly coincides with the main operator of the corresponding direct problem of diffraction of electromagnetic waves. Due to this fact, the solution to the simulated equation satisfies the necessary boundary conditions. And this is the novelty and difference of the approach developed in this work from the methods known in the scientific literature. We develop a theory of an operator equation with a small parameter and a numerical method based on Chebyshev polynomials with weights that take into account the behavior at the boundary. The efficiency of the numerical method is shown.
Keywords: equation with a small parameter, positive definite operator, completely continuous operator, Hilbert space.
Mots-clés : inverse diffraction problem 
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     title = {Synthesis of surface {H-polarized} currents on an unclosed cylindrical surface},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {135--141},
     year = {2019},
     volume = {12},
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     url = {http://geodesic.mathdoc.fr/item/VYURU_2019_12_4_a11/}
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S. I. Eminov; S. Yu. Petrova. Synthesis of surface H-polarized currents on an unclosed cylindrical surface. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 4, pp. 135-141. http://geodesic.mathdoc.fr/item/VYURU_2019_12_4_a11/

[1] Bakhrakh L. D., Kremenetskiy S. D., Synthesis of Radiating Systems (Theory and Methods of Calculation, Sovetskoe radio, M., 1974 (in Russian)

[2] Zakharov E. V., Pimenov Yu. V., Numerical Analysis of Radio Wave Diffraction, Radio i svyaz', M., 1982 (in Russian) | MR

[3] Katsenelenbaum B. Z., Electromagnetic Field Approximability Problems, Nauka, M., 1996 (in Russian)

[4] Ivanov V. K., Vasin V. V., Tanana V. P., The Theory of Linear Ill-Posed Problems and Its Applications, Nauka, M., 1978 (in Russian)

[5] Sochilin A. V., Eminova V. S., Eminov I. S., “The Galerkin Method in the Problem of Diffraction of the H-Polarization on a Cylindrical Surface”, Non-linear World, 2014, no. 6, 26–31 (in Russian)

[6] Mikhlin S. G., Linear Partial Differential Equations, Nauka, M., 1977

[7] Eminova V. S., Eminov S. I., “Justification of the Galerkin Method for Hypersingular Equations”, Journal of Computational Mathematics and Mathematical Physics, 56:3 (2016), 432–440 (in Russian) | DOI | MR | Zbl

[8] Sakhnovich L. A., “Equations with a Difference Kernel on a Finite Interval”, Russian Mathematical Surveys, 35:4 (1980), 69–129 (in Russian) | MR | Zbl

[9] Rudin W., Functional Analysis, McGRAW-Hill Book Company, N.Y., 1973 | MR | Zbl

[10] Sukacheva T. G., Matveeva O. P., “Taylor Problem for the Zero-Order Model of an Incompressible Viscoelastic Fluid”, Differential Equations, 51:6 (2015), 783–791 | DOI | MR | Zbl