| 1. |
- Samokhin, Alexander, et al.
(författare)
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Stationary iteration methods for solving 3D electromagnetic scattering problems
- 2013
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Ingår i: Applied Mathematics and Computation. - : Elsevier BV. - 0096-3003 .- 1873-5649. ; 222, s. 107-122
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Tidskriftsartikel (refereegranskat)abstract
- Generalized Chebyshev iteration (GCI) applied for solving linear equations with nonselfadjoint operators is considered. Sufficient conditions providing the convergence of iterations imposed on the domain of localization of the spectrum on the complex plane are obtained. A minimax problem for the determination of optimal complex iteration parameters is formulated. An algorithm of finding an optimal iteration parameter in the case of arbitrary location of the operator spectrum on the complex plane is constructed for the generalized simple iteration method. The results are applied to numerical solution of volume singular integral equations (VSIEs) associated with the problems of the mathematical theory of wave diffraction by 3D dielectric bodies. In particular, the domain of the spectrum location is described explicitly for low-frequency scattering problems and in the general case. The obtained results are discussed and recommendations concerning their applications are given. (C) 2013 Elsevier Inc. All rights reserved.
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| 2. |
- Smirnov, A. P., et al.
(författare)
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FDTD Simulation of Waveguide with Non-uniform Dielectric Slab
- 2013
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Ingår i: PIERS 2013 STOCKHOLM. - 9781934142264 ; , s. 76-83
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Konferensbidrag (refereegranskat)abstract
- Scattering in the time domain of electromagnetic waves in the elongated waveguide with non-uniform dielectric slab is considered. Electromagnetic field components are computed and investigation of energy transport in the guide is performed by using Finite Difference Time Domain (FDTD) method for various frequency ranges. Computation for the non-stationary Maxwell equation system is performed by efficient 3D FDTD solver EMWSolver3D created by this paper authors. Simulation is performed for the H10-mode scattering from dielectric slab inclusions. Numerical computations for large-scale problems solution have been implemented on supercomputers of the last generation. The simulation of an empty waveguide without dielectric inclusions has shown that numerical dispersion arising during waves travelling in waveguide causes solution errors. Numerical phase velocity is shown to differ from the analytical phase velocity with the lapse of time that obstructs accurate finding of attenuation and propagation factors. In this respect method similar to Total Field/Scattered field has been proposed to specify waveguide mode with respect to numerical dispersion. The analytical solution of finite-difference equation for the H10-mode has been found for this purpose. Usage of the methods described above has allowed the authors to compute the values of waveguide attenuation and propagation factors for different configurations of dielectric slab.
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| 3. |
- Nakonechny, Alexander, et al.
(författare)
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Guaranteed estimation for inverse problems in electromagnetics and acoustics
- 2016
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Ingår i: Proceedings of the 2016 18th International Conference on Electromagnetics in Advanced Applications, ICEAA 2016. ; , s. 374-377
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Konferensbidrag (refereegranskat)abstract
- The analysis is performed and theorems are formulated concerning general form of guaranteed estimates of linear functionals from unknown data of Helmholtz transmission problems arising in electromagnetics and acoustics of inhomogeneous dielectric media.
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| 4. |
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| 5. |
- Shestopalov, Yury, 1953-, et al.
(författare)
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Analytical and numerical solution techniques for forward and inverse scattering problems in waveguides
- 2021
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Ingår i: Advances in Mathematical Methods for Electromagnetics. - Noida, Uttar Pradesh, India : IET: The Institution of Engineering and Technology. - 9781785613845 - 9781785613852 ; , s. 547-570
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Bokkapitel (refereegranskat)abstract
- Chapter: Investigations of the wave propagation in waveguides with inhomogeneous dielectric inclusions are performed using advanced analytical and numerical methods. A particular attention is paid to the analysis of benchmark problems: forward and inverse scattering by parallel-plane dielectric diaphragms and layered structures placed in a rectangular waveguide with perfectly conducting walls. A detailed study of the properties of transmitted fields using the theory of functions of one or several complex variables leads to the development of a technique aimed at reconstructing permittivity of the inclusions from the transmission coefficient. The unique solvability of this inverse problems is proved by establishing the domains where the transmission coefficient is a one-to-one function of permittivity and other problem parameters. The obtained results are used to improve FDTD numerical solution to the corresponding forward and inverse scattering problems for Maxwell’s equations in waveguides and create specifically developed codes. In general, the chapter contributes to the electromagnetic wave theory with several new findings and modified theoretical approaches.
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| 6. |
- Shestopalov, Yury, 1953-, et al.
(författare)
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Conclusion
- 2022
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Ingår i: Optical Waveguide Theory. - Singapore : Springer. - 9789811905834 - 9789811905841 ; , s. 259-260
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Bokkapitel (refereegranskat)abstract
- The book deals with the problems of the electromagnetic wave propagation in a wide class of waveguide structures: from planar waveguides to waveguides of arbitrary cross section (including the shielded ones). The settings for the Maxwell are reduced to boundary eigenvalue problems for the longitudinal components of the electromagnetic field in Sobolev spaces using a universal approach applicable to all the considered waveguide families. To determine and analyze the solution, variational formulations are used and the problems are reduced to the study of the spectra of OVF; many of them are polynomial operator pencils. The discreteness of the eigenwave spectra is proved and the distribution of characteristic numbers on the complex plane is described.
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| 7. |
- Shestopalov, Yury, 1953-, et al.
(författare)
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Determination of permittivity of an inhomogeneous dielectric body in a waveguide
- 2011
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Ingår i: Inverse Problems. - Philadelphia : Institute of Physics Publishing (IOPP). - 0266-5611 .- 1361-6420. ; 27, s. 095010-1-095010-12
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Tidskriftsartikel (refereegranskat)abstract
- The determination of permittivity of an inhomogeneous dielectric body located in a rectangular waveguide is considered. An iteration method for the numerical solution of the problem is proposed. Convergence of the method is proved. Numerical results for the determination of permittivity of a dielectric body are presented
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| 8. |
- Shestopalov, Yury, 1953-, et al.
(författare)
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Inverse problem method for permittivity reconstruction of two-layered media : numerical and experimental results
- 2014
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Ingår i: Progress in Electromagnetics Research Symposium. - : Electromagnetics Academy. - 9781934142288 ; , s. 2610-2613
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Konferensbidrag (refereegranskat)abstract
- This study employs the technique developed in [1-3] and deals with complex permittivity reconstruction of layered materials in the form of diaphragms (sections) in a single-mode waveguide of rectangular cross section from the transmission coefficient measured at different frequencies.
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| 9. |
- Shestopalov, Yury, 1953-, et al.
(författare)
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Inverse scattering in guides
- 2012
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Ingår i: Journal of Physics, Conference Series. - Philadelphia : Institute of Physics Publishing (IOPP). - 1742-6588 .- 1742-6596. ; 346, s. 012019-1-012019-13
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Tidskriftsartikel (refereegranskat)abstract
- We present statements and a method of solution to the inverse scattering problem of reconstructing permittivity of a dielectric inclusion in a 2D or 3D waveguide from thetransmission characteristics. The approach employs a volume singular integral equation (VSIE) method. The unique solvability of VSIE is established. The inverse problem is solved by themethod of iterations applied to VSIE; the convergence of the method is proved
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| 10. |
- Shestopalov, Yury, 1953-, et al.
(författare)
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Mathematical Aspects of the Theory of Wave Propagation in Metal-Dielectric Waveguides
- 2014
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Ingår i: General Assembly and Scientific Symposium (URSI GASS), 2014 XXXIth URSI. - : IEEE Press.
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Konferensbidrag (refereegranskat)abstract
- We consider fundamental issues of the mathematical theory of the wave propagation in waveguides with inclusions. Analysis is performed in terms of a boundary eigenvalue problem for the Maxwell equations which is reduced to an eigenvalue problem for an operator pencil. We prove that the spectrum of normal waves forms a nonempty set of isolated points localized in a strip with at most finitely many real points. We show the importance of these results for the theory of wave propagation in open guiding structures and consider in more detail the surface wave spectrum of the Goubau line.
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