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Application of the Collocation Method for Solving the Problem of Diffraction of an Electromagnetic Wave by a Rectangular Metal Plate

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Abstract

The classical problem of the electromagnetic wave diffraction by a rectangular perfectly conducting metal plate is considered. The solution of the problem is reduced to the solving integral equations for the tangential components of the magnetic intensity vector on the metal surface. The collocation method is applied to the equation with the representation of the sought functions in the form of a series in the Chebyshev polynomials of the 1st and 2nd kind. Numerical experiments have been carried out for a different number of terms of the Fourier series of the sought functions and a different number of collocation points. Graphs comparing the results obtained for various parameters are presented. It is shown that an increase in the number of collocation points leads to a greater stability of the solution. It is concluded that there is no clear-cut convergence of the solution with this choice of collocation points.

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Notes

  1. It should be noted that formula (2.3.5.7) in some copies of the monograph [24] contains a typo: instead of the correct \(\Gamma^{-1}(\rho)\) is printed by \(\Gamma(\rho)\).

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Authors and Affiliations

  1. Institute of Computational Mathematics and Information Technologies, Kazan Federal University, 420008, Kazan, Tatarstan, Russia

    A. Markina, D. Tumakov & D. Giniyatova

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  1. A. Markina
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  2. D. Tumakov
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  3. D. Giniyatova
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Correspondence to A. Markina, D. Tumakov or D. Giniyatova.

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(Submitted by E. E. Tyrtyshnikov)

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Markina, A., Tumakov, D. & Giniyatova, D. Application of the Collocation Method for Solving the Problem of Diffraction of an Electromagnetic Wave by a Rectangular Metal Plate. Lobachevskii J Math 42, 1355–1369 (2021). https://doi.org/10.1134/S1995080221060184

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