Numerical simulation of electromagnetic wave diffraction on a finite number of slits in a flat screen
Abstract
The article presents an algorithm for modeling diffraction on slits made on a flat screen made of actual materials. As a result, the boundary conditions of Schukin-Leontovich lead to the mixed boundary value problem. According to the method of Y.V. Gandel and V.D. Dushkin the solution of the problem can be reduced to a system of paired integral equations with singular and logarithmic singularities. The author has created and debugged a PC program that performs the numerical solution of the arising problems, and a series of computational experiments has been performed. This work has been carried at School of Mathematics and Computer Sciences of V. N. Karazin Kharkiv National University within the state budget themes: "Modeling of the dynamics of folding systems with the method of identifying problem situations."
Downloads
References
/References
A. S. Il'insky, A. Ja. Slepjan, G. Ja. Slepjan, Propagation, diffraction and dissipation of electromagnetic waves. - London (UK): The IEE and Peter Peregrinous Ltd., 1993. - Electromagnetic Waves, Ser. 36. - 275 p.
T. L. Zinenko, A. I. Nosich, Wave Scattering and Absorption by Flat Gratings of Impedance Strips, IEEE Transactions on Antennas and Propagation. - V. 54, No. 7, JULY 2006. - P. 2088-2095.
V. F. Kravchenko, The electrodynamics of superconducting structures. The theory, algorithms and computational methods, Moscow: Fizmatlit, 2006. - 280 p.
O. V. Kostenko, Mathematical model of wave scattering by an impedance grating, Cybernetics and systems analysis. - V. 51, No. 3. - 2015. - P. 344-360.
Yu. Penkin, V. Katrych, M. Nesterenko, S. Berdnik, Coupling of Two Rectangular Waveguides Through a Slot With an Impedance Membrane, VII th International Conference on Mathematical Methods in ElectromagneticTheory. Kyiv, Ukraine 2 - 5 July - 2018, _ P. 140-143.
Yu. V. Gandel', V.F. Kravchenko, V.I. Pustovoit, Scattering of electromagnetic waves by a thin superconducting band, Doklady Math. - 1996. - 54, _ No. 3. _ P. 959-961.
Yu.V. Gandel, V.F. Kravchenko, N.N. Morozova, Solving the problem of electromagnetic wave diffraction by a superconducting thin stripes grating, Telecommunications and Radio Engineering (English translation of Elektrosvyaz and Radiotekhnika)._ 2001._ V. 56, No.2.- P. 15-17.
N. I. Akhiezer, Lectures on integral transforms. - Providence (R. I.): AMS, 1988. - 108 p.
Yu. V. Gandel', Boundary-Value Problems for the Helmholtz Equation and their Discrete Mathematical Models, Journal of Mathematical Sciences. - 2010. - V. 171, No.1. - Springer Science+Business Media, Inc. - P. 74-88.
Y.V. Gandel, V.D. Dushkin, The method of parametric representations of integral and pseudo-differential operators in diffraction problems on electrodynamics structures. - Proceedings of the International Conference Days on Diffraction DD 2012 (28 May-1 June 2012), St. Petersburg, 2012,- P.76-81.
I. K. Lifanov, Singular integral equations and discrete vortices. - Utrecht (the Netherlands): VSP VB, 1996. - 475 p.
Yu.V. Gandel, V.D. Dushkin, Mathematical models of two-dimensional diffraction problems: Singular integral equations and numerical methods of discrete singularities method. Academy of IT of the MIA of Ukraine, Kharkiv, _ 2012. -544p. (in Russian).
Yu.V. Gandel', V.D. Dushkin, Mathematical models based on SIE 2D diffraction problems on reflective multilayer periodic structures., Part I. The case of E-polarization, Scienti_c statements. Series: Mathematics. Physics. Belgorod State National Research University. _ V. 5 (100), _ 2. _ 2011. _P. 5-16. (in Russian).
V.A. Shcherbina, G.I. Zaginaylov, S.V. Zhuchenko, Numerical theory of excitation of axisymmetric open-ended finite length slow wave structure on the basis of the boundary singular integral equation method, VII th International Conference on Mathematical Methods in Electromagnetic Theory (MMET'98), Kharkov, Ukraine._ V. 1, _ 1998. _ P. 263-265.
G.I. Zaginaylov, V.D. Dushkin, V. Korostyshevski, P.V. Turbin, Modeling the beam excitation of planar waveguide with rectangular irregularities, Proceedings of the VII th International Conference on Mathematical Methods in Electromagnetic Theory (MMET'98); Kharkov, Ukraine; 2 June 1998 through 5 June 1998; _ V. 1, 1998_ P. 409-410.
Y.V. Gandel, V.D. Dushkin, G.I. Zaginaylov, New numerical-analytical approach in the theory of excitation of superdimensional electrodynamical structures Telecommunications and Radio Engineering (English translation of Elektrosvyaz and Radiotekhnika)._ 2000._ V. 54, 7, _ P. 36-48.
S.V. Zhuchenko, Numerical model diffraction of the plane electromagnetic wave onto axiallysymmetric parabolic reflector, Bulletin of V. Karazin Kharkiv National University, Series "Mathematical Modelling. Information Technology. Automated Control Systems _2013._ Issue 22. No.1063 _ P. 63-71. (in Russian).
V.D. Dushkin, Mathematical models of two-dimensional diffraction problems, Proceedings of the VI th International Conference on Mathematical Methods in Electromagnetic Theory (MMET'96); Lviv, V.1, 1996. - P. 483-486. DOI:10.1109/MMET.1996.565767
V.S. Bulygin, A.I. Nosich, Y.V. Gandel, Nystrom-type method in three dimensional electromagnetic diffraction by a _finite PEC rotationally symmetric surface, IEEE Transactions on Antennas and Propagation._ 60 (10), 2012._ P. 4710-4718.
S.V. Zhuchenko, Discrete mathematical model of electromagnenic wave 3D diffraction on axially symmetric reflector, Bulletin of V. Karazin Kharkiv National University, Series "Mathematical Modelling. Information Technology. Automated Control Systems"._ 2013._Issue 23. No. 1089 _ P. 50-68. (in Russian).
A. A. Nosich, Y. V. Gandel, Numerical analysis of quasioptical multi-reflector antennas in 2-D with the method of discrete singularities, IEEE Transactions on Antennas and Propagation. - 2007. - V. 57, no. 2. - P. 399-406.
S.V. Dukhopelnikov, Inhomogeneities in the antenna cavity and the diffractive properties of antennas of a special form Numerical analysis, Part 1, Bulletin of V. Karazin Kharkiv National University, Series "Mathematical Modelling. Information Technology. Automated Control Systems". _2016._ 32. _ P. 25-34.
A. S. Il'insky, A. Ja. Slepjan, G. Ja. Slepjan, Propagation, diffraction and dissipation of electromagnetic waves. London (UK): The IEE and Peter Peregrinous Ltd., Electromagnetic Waves, Ser. 36. - 275 p. 1993.
T. L. Zinenko, A. I. Nosich, “Wave Scattering and Absorption by Flat Gratings of Impedance Strips”, IEEE Trans. Antennas and Propagation, vol. 54, No. 7, pp. 2088-2095, JULY 2006. -.
V. F. Kravchenko, The electrodynamics of superconducting structures. The theory, algorithms and computational methods: Moscow: Fizmatlit, 2006.
O. V. Kostenko, “Mathematical model of wave scattering by an impedance grating,” Cybernetics and systems analysis, vol. 51, pp. 344-360, No. 3. 2015. -.
Yu. Penkin, V. Katrych, M. Nesterenko, S. Berdnik, “Coupling of Two Rectangular Waveguides Through a Slot With an Impedance Membrane,” VII th International Conference on Mathematical Methods in ElectromagneticTheory. Kyiv, Ukraine 2 - 5 July - 2018, pp. 140-143.
Yu. V. Gandel', V.F. Kravchenko, V.I. Pustovoit, “Scattering of electromagnetic waves by a thin superconducting band,” Doklady Math. - 1996. - 54, _ No. 3. pp. 959-961.
Yu.V. Gandel, V.F. Kravchenko, N.N. Morozova, “Solving the problem of electromagnetic wave diffraction by a superconducting thin stripes grating,” Telecommunications and Radio Engineering (English translation of Elektrosvyaz and Radiotekhnika). vol. 56, pp. 15-17, No.2.- 2001.
N. I. Akhiezer, Lectures on integral transforms. - Providence (R. I.): AMS, 1988.
Yu. V. Gandel', “Boundary-Value Problems for the Helmholtz Equation and their Discrete Mathematical Models,” Journal of Mathematical Sciences. vol. 171, pp. 74-88. No.1. Springer Science+Business Media, Inc. 2010.
Y.V. Gandel, V.D. Dushkin, The method of parametric representations of integral and pseudo-differential operators in diffraction problems on electrodynamics structures: Proceedings of the International Conference Days on Diffraction DD 2012 (28 May-1 June 2012), St. Petersburg, 2012,- pp.76-81.
I. K. Lifanov, Singular integral equations and discrete vortices. Utrecht (the Netherlands): VSP VB, 1996.
Yu.V. Gandel, V.D. Dushkin, Mathematical models of two-dimensional diffraction problems: Singular integral equations and numerical methods of discrete singularities method. Academy of IT of the MIA of Ukraine, Kharkiv, _ 2012. (in Russian).
Yu.V. Gandel', V.D. Dushkin, “Mathematical models based on SIE 2D diffraction problems on reflective multilayer periodic structures, Part I. The case of E-polarization, Scientific statements.” Series: Mathematics. Physics. Belgorod State National Research University. vol. 5 (100), pp. 5-16. 2 2011. (in Russian).
V.A. Shcherbina, G.I. Zaginaylov, S.V. Zhuchenko, Numerical theory of excitation of axisymmetric open-ended finite length slow wave structure on the basis of the boundary singular integral equation method: VII th International Conference on Mathematical Methods in Electromagnetic Theory (MMET'98), Kharkov, Ukraine. vol. 1, 1998. pp. 263-265.
G.I. Zaginaylov, V.D. Dushkin, V. Korostyshevski, P.V. Turbin, Modeling the beam excitation of planar waveguide with rectangular irregularities: Proceedings of the VII th International Conference on Mathematical Methods in Electromagnetic Theory (MMET'98); Kharkov, Ukraine; 2 June 1998 through 5 June 1998; vol. 1, 1998 pp. 409-410.
Y.V. Gandel, V.D. Dushkin, G.I. Zaginaylov, “New numerical-analytical approach in the theory of excitation of super dimensional electro dynamical structures,” Telecommunications and Radio Engineering (English translation of Elektrosvyaz and Radiotekhnika).vol. 54, 7, pp. 36-48, 2000.
S.V. Zhuchenko, Numerical model diffraction of the plane electromagnetic wave onto axially symmetric parabolic reflector: Bulletin of V. Karazin Kharkiv National University, Series "Mathematical Modelling. Information Technology. Automated Control Systems _Issue 22. No.1063 pp. 63-71, 2013. (in Russian).
V.D. Dushkin, “Mathematical models of two-dimensional diffraction problems,” Proceedings of the VI th International Conference on Mathematical Methods in Electromagnetic Theory (MMET'96); Lviv, V.1, 1996. DOI:10.1109/MMET.1996.565767, - pp. 483-486.
V.S. Bulygin, A.I. Nosich, Y.V. Gandel, “Nystrom-type method in three dimensional electromagnetic diffraction by a finite PEC rotationally symmetric surface,” IEEE Transactions on Antennas and Propagation. pp. 4710-4718, 60 (10), 2012.
S.V. Zhuchenko, “Discrete mathematical model of electromagnenic wave 3D diffraction on axially symmetric reflector,” Bulletin of V. Karazin Kharkiv National University, Series "Mathematical Modelling. Information Technology. Automated Control Systems", Issue 23. No. 1089, pp. 50-68, 2013. (in Russian).
A. A. Nosich, Y. V. Gandel, “Numerical analysis of quasioptical multi-reflector antennas in 2-D with the method of discrete singularities,” IEEE Transactions on Antennas and Propagation, vol. 57, - pp. 399-406, no. 2. 2007.
S.V. Dukhopelnikov, “Inhomogeneities in the antenna cavity and the diffractive properties of antennas of a special form Numerical analysis,” Part 1, Bulletin of V. Karazin Kharkiv National University, Series "Mathematical Modelling. Information Technology. Automated Control Systems". _pp. 25-34, 32, 2016.
