Abstract:
We consider boundary-value problems of mathematical diffraction theory and discuss the possibility of reducing them to boundary hypersingular integral equations and solving them numerically. The analytic technique of parametric representations of pseudodifferential and integral operators and the numerical method of discrete singularities are essentially used. We discuss the reasoning in applying this approach to constructing mathematical models of wave diffraction problems and solving them numerically.
Citation:
Yu. V. Gandel', “Boundary-value problems for the Helmholtz equation and their discrete mathematical models”, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 2, CMFD, 36, PFUR, M., 2010, 36–49; Journal of Mathematical Sciences, 171:1 (2010), 74–88
\Bibitem{Gan10}
\by Yu.~V.~Gandel'
\paper Boundary-value problems for the Helmholtz equation and their discrete mathematical models
\inbook Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17--24, 2008). Part~2
\serial CMFD
\yr 2010
\vol 36
\pages 36--49
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd154}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2752648}
\transl
\jour Journal of Mathematical Sciences
\yr 2010
\vol 171
\issue 1
\pages 74--88
\crossref{https://doi.org/10.1007/s10958-010-0127-3}
Linking options:
https://www.mathnet.ru/eng/cmfd154
https://www.mathnet.ru/eng/cmfd/v36/p36
This publication is cited in the following 22 articles:
Ludmila Illyashenko, 2023 IEEE XXVIII International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED), 2023, 37
George Koshovy, Andrew Koshovy, Oksana Ahapova, “Investigation of Problems of Electromagnetic Wave Scattering by Conductive Strip Gratings Using Integral Equation Method”, Radioelectron.Commun.Syst., 66:9 (2023), 439
Andrew G. Koshovy, GeorgeI. Koshovy, Oksana O. Ahapova, 2022 IEEE 2nd Ukrainian Microwave Week (UkrMW), 2022, 490
Mstislav E. Kaliberda, Leonid M. Lytvynenko, Sergey A. Pogarsky, “Method of singular integral equations in scattering by double-layer infinite strip grating with several strips removed in every layer”, Journal of Electromagnetic Waves and Applications, 35:11 (2021), 1433
Mstislav E. Kaliberda, Leonid M. Lytvynenko, Sergey A. Pogarsky, “Scattering of eigenmodes of planar dielectric waveguide with PEC wall by graphene strip grating at THz”, Waves in Random and Complex Media, 2021, 1
V. D. Dushkin, V. N. Melnik, “MATHEMATICAL MODEL OF WAVE DIFFRACTION BY THE SYSTEM OF STRIPES WITH DIFFERENT VALUES OF SURFACE IMPEDANCE”, JNAM, 2021, no. 1 (135), 131
M. E. Kaliberda, L. M. Lytvynenko, S. A. Pogarsky, “OPERATOR METHOD IN THE PROBLEM OF AN H-POLARIZED PLANE WAVE DIFFRACTION BY A DOUBLE-LAYER INFINITE PERIODIC STRIP GRATING IN THE ABSENCE OF ONE STRIP IN EVERY LAYER”, Radio phys. radio astron., 25:2 (2020), 136
Vladimir D. Dushkin, Stanislav V. Zhuchenko, Oleksii V. Kostenko, 2020 IEEE Ukrainian Microwave Week (UkrMW), 2020, 625
“Discrete mathematical model of the scattering process of E-polarized wave on a periodic impedance grating”, MAMM, 2019, no. 90
Mstislav E. Kaliberda, Leonid M. Lytvynenko, Sergey A. Pogarsky, “Electromagnetic interaction of two semi-infinite coplanar gratings of flat PEC strips with arbitrary gap between them”, Journal of Electromagnetic Waves and Applications, 33:12 (2019), 1557
Mstislav E. Kaliberda, Leonid M. Lytvynenko, Sergey A. Pogarsky, “Singular integral equations in diffraction problem by an infinite periodic strip grating with one strip removed: E–polarization case”, Journal of Electromagnetic Waves and Applications, 32:3 (2018), 332
Mstislav E. Kaliberda, Leonid M. Lytvynenko, Sergey A. Pogarsky, “Modeling of Graphene Planar Grating in the THz Range by the Method of Singular Integral Equations”, Frequenz, 72:5-6 (2018), 277
Khalilov E.H., “Substantiation of the Collocation Method For One Class of Systems of Integral Equations”, Ukr. Math. J., 69:6 (2017), 955–969
Mstislav E. Kaliberda, Sergey A. Pogarsky, Leonid M. Lytvynenko, 2017 IEEE First Ukraine Conference on Electrical and Computer Engineering (UKRCON), 2017, 84
M. E. Kaliberda, L. M. Lytvynenko, S. A. Pogarsky, “THE E-POLARIZED WAVE DIFFRACTION BY INFINITE PERIODICAL STRIP GRATING WITHOUT SINGLE STRIP”, Radio phys. radio astron., 21:3 (2016), 189
Mstislav E. Kaliberda, Leonid M. Lytvynenko, Sergey A. Pogarsky, “Singular integral equations in diffraction problem by an infinite periodic strip grating with one strip removed”, Journal of Electromagnetic Waves and Applications, 30:18 (2016), 2411
Yu. V. Gandel', V. D. Dushkin, “Mathematical Model of Scattering of Polarized Waves on Impedance Strips Located on a Screened Dielectric Layer”, J Math Sci, 212:2 (2016), 156
Sergiy Steshenko, Maxim Zhadobov, Ronan Sauleau, Anatoliy A. Kirilenko, Artem V. Boriskin, “Beam-Forming Capabilities of Waveguide Feeds Assisted by Corrugated Flanges”, IEEE Trans. Antennas Propagat., 63:12 (2015), 5548
Kateryna Nesvit, The 8th European Conference on Antennas and Propagation (EuCAP 2014), 2014, 2773
Kateryna V. Nesvit, 2012 Proceedings of the International Conference Days on Diffraction, 2012, 183
Citation in format AMSBIB
Contact us: