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  • 1.
    Angermann, L.
    et al.
    Institut für MathematikTechnische Universität Clausthal, Clausthal-Zellerfeld, Germany.
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Smirnov, Y. G.
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.
    Yatsyk, V. V.
    O.Ya. Usikov Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, Kharkiv, Ukraine.
    A nonlinear multiparameter EV problem2018In: Progress In Electromagnetics Research Symposium: PIERS 2017, PIERS 2017: Nonlinear and Inverse Problems in Electromagnetics / [ed] Beilina L., Smirnov Y., Springer New York LLC , 2018, p. 55-70Conference paper (Refereed)
    Abstract [en]

    We investigate a generalization of one-parameter eigenvalue problems arising in the theory of wave propagation in waveguides filled with nonlinear media to more general nonlinear multi-parameter eigenvalue problems for a nonlinear operator. Using an integral equation approach, we derive functional dispersion equations (DEs) whose roots yield the desired eigenvalues. The existence of the roots of DEs is proved and their distribution is described.

  • 2.
    Angermann, Lutz
    et al.
    Clausthal University of Technology, Clausthal, Germany..
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Yatsyk, Vasyl
    O. Ya, Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine.
    Mathematical models for scattering and generation of plane wave packets on layered cubically polarisable structures2013In: Far East Journal of Applied Mathematics, ISSN 0972-0960, Vol. 81, no 1-2, p. 1-31Article in journal (Refereed)
    Abstract [en]

    The paper deals with different formulations of mathematical models for the analysis of processes of resonance scattering and generation of plane wave packets on isotropic, nonmagnetic, linearly polarised media with a nonlinear, layered dielectric structure of cubic polarisability. For each formulation, sufficient conditions for the existence and, partially, uniqueness of the corresponding solution are derived.

  • 3.
    Angermann, Lutz
    et al.
    Technische Universität Clausthal, Institut für Mathematik, Clausthal-Zellerfeld, Germany .
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Yatsyk, Vasyl V.
    O.Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine .
    Eigenmodes of linearised problems of scattering and generation of oscillations on cubically polarisable layers2015In: Inverse Problems and Applications / [ed] Larisa Beilina, Springer-Verlag New York, 2015, Vol. 120, p. 67-80Conference paper (Refereed)
    Abstract [en]

    In the frequency domain, the resonant properties of nonlinear structures are determined by the proximity of the scattering/generation frequencies of the nonlinear structures to the complex eigenfrequencies of the corresponding homogeneous linear spectral problems with the induced nonlinear permeability of the medium. Here the case of cubically polarisable, canalising, and decanalising layers is considered.

  • 4.
    Beilina, Larisa
    et al.
    Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg University, Gothenburg, Sweden.
    Bondestam Malmberg, John
    Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg University, Gothenburg, Sweden.
    Cristofol, Michel
    Institut de Mathematiques de Marseille, CNRS, UMR 7373, Ecole Centrale, Aix-Marseille University, Marseille, France.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Preface for the session "recent Progress in Electromagnetic Field Theory and New Trends in Inverse Problems"2017In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1863, article id 370001Article in journal (Refereed)
  • 5.
    Ivanchenko, I.
    et al.
    O. Ya. Usikov Institute for Radiophysics and Electronics of the NAS of Ukraine, Kharkiv, Ukraine.
    Khruslov, M.
    O. Ya. Usikov Institute for Radiophysics and Electronics of the NAS of Ukraine, Kharkiv, Ukraine.
    Popenko, N.
    O. Ya. Usikov Institute for Radiophysics and Electronics of the NAS of Ukraine, Kharkiv, Ukraine.
    Sheina, E.
    Lomonosov Moscow State University, Russia.
    Smirnov, A.
    Lomonosov Moscow State University, Russia.
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Reconstructing complex permittivity of local inhomogeneites in a radio-transparent dielectric matrix located in a waveguide2016In: 2016 22nd International Conference on Applied Electromagnetics and Communications (ICECOM), 2016Conference paper (Refereed)
    Abstract [en]

    The results are presented of the numerical solution to the forward problem of the electromagnetic wave scattering by inhomogeneous dielectric bodies in a waveguide and inverse problem of determining parameters of dielectric inclusions from the values of the transmission coefficient of the scattered electromagnetic wave. A comparison with the results of mesurements and analysis of the achieved threshold computational accuracy levels enable one to estimate and validate the simulation results and formulate the ways of improving the model and codes.

  • 6.
    Ivanchenko, I.
    et al.
    O. Ya. Usikov Institute for Radiophysics and Electronics of the NAS of Ukraine, Kharkiv, Ukraine.
    Khruslov, M.
    O. Ya. Usikov Institute for Radiophysics and Electronics of the NAS of Ukraine, Kharkiv, Ukraine.
    Popenko, N.
    O. Ya. Usikov Institute for Radiophysics and Electronics of the NAS of Ukraine, Kharkiv, Ukraine.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Rönnow, Daniel
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Electronics.
    Combined system of the microstrip antennas with different frequencies2016In: 2016 22nd International Conference on Applied Electromagnetics and Communications (ICECOM), 2016Conference paper (Refereed)
    Abstract [en]

    The combined system with microstrip antennas (f1=1.85GHz; f2=3.7GHz, f3=1.75GHz, f4= 3.5GHz) is presented. The measurements of the prototype characteristics have shown that elevation angle of peak directivity of the antennas is oriented to zenith. Simulated S11 at stated frequencies with the following minimum values of S11 = -34dB, f=1.85GHz; S11=-21dB, f=3.7GHz; S11 = -22dB, f=1.75GHz; S11=-19dB, f=3.5GHz are observed.

  • 7.
    Ivanchenko, Igor
    et al.
    O.Ya. Usikov Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, Kharkiv, Ukraine.
    Khruslov, Maksym
    O.Ya. Usikov Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, Kharkiv, Ukraine.
    Popenko, Nina
    O.Ya. Usikov Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, Kharkiv, Ukraine.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Tripathy, Malay Ranjan
    Amity University, Delhi, India.
    Derevyanchuk, Ekaterina
    Penza State University, Penza, Russian Federation.
    Determination of effective permittivity of metamaterial antenna cells2016In: 2016 10th European Conference on Antennas and Propagation: EuCAP 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, article id 7481369Conference paper (Refereed)
    Abstract [en]

    A numerical-analytical method of reconstructing complex frequency-dependent permittivities is proposed. Measurements of the transmission coefficient for three typical metamaterial antenna units are performed and the frequency-dependent effective complex permittivity of the units is reconstructed in a wide frequency range.

  • 8.
    Kushnin, R.
    et al.
    Riga Technical University, Latvia.
    Semenjako, J.
    Riga Technical University, Latvia.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Accelerated boundary integral method for solving the problem of scattering by multiple multilayered circular cylindrical posts in a rectangular waveguide2017In: 2017 Progress In Electromagnetics Research Symposium - Fall (PIERS - FALL), Electromagnetics Academy , 2017, p. 3263-3271Conference paper (Refereed)
    Abstract [en]

    An accelerated boundary integral method for the analysis of scattering of the dominant mode by multiple multi-layered full-height circular cylindrical posts in a rectangular waveguide is presented. After some transformations the surface integral equation is converted to a system of equations whose entries can be evaluated analytically yielding Schlömilch series. Slow convergence of these series is accelerated using the Ewald technique. The proposed method gives results that are comparable in terms of accuracy with other approaches, including those incorporated in solvers HFSS and CST Studio and outperforms them in terms of computation time, especially for posts with large electrical sizes. The efficiency of the proposed method is confirmed by the examples of H-plane cylinder bandpass filters design.

  • 9.
    Kushnin, R.
    et al.
    Riga Technical University, Latvia.
    Semenjako, J.
    Riga Technical University, Latvia.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Maximum-sensitivity method for minimizing uncertainty in the measurements of permittivity of a cylindrical dielectric sample in a rectangular waveguide2017In: 2017 Progress In Electromagnetics Research Symposium - Fall (PIERS - FALL), Electromagnetics Academy , 2017, p. 570-578Conference paper (Refereed)
    Abstract [en]

    A novel and efficient methodology is proposed for reducing measurement uncertainty associated with the dielectric constant of low-loss materials. The experimental setup consists of two H-plane cylindrical rods located in a rectangular waveguide. One of the rods has the unknown dielectric constant to be extracted, while the other dielectric rod whose dielectric constant is known in advance and serves as a tool for altering the shape of the dependence of the absolute value of the reflection coefficient on the dielectric constant in such a way that the resulting curve exhibits more rapid variations in the range of possible values of the dielectric constant of the post being characterized. The distance between the rods, radius of the optimizing rod, and position offset of the optimizing post serve as optimization parameters to be adjusted so that measurement uncertainty could be reduced which is confirmed by the results of numerical modeling. However, in the vicinity of the resonances, the method cannot be applied. © 2018 Electromagnetics Academy. All rights reserved.

  • 10.
    Kuzmina, E. A.
    et al.
    Institute of Information Technologies, Moscow Technological University (MIREA), 86 Vernadsky Avenue, Moscow, Russian Federation.
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Complex waves in a dielectric rod and goubau line2017In: 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA), Institute of Electrical and Electronics Engineers Inc. , 2017, p. 963-966, article id 8065417Conference paper (Refereed)
    Abstract [en]

    Existence of complex TM and TE waves in a dielectric waveguide of circular cross section and a Goubau line is proved by analyzing functional properties of the dispersion equations (DEs) using the theory of functions of several complex variables and validating the existence of complex roots of DE. The method proceeds from the analysis of general setting involving hybrid nonsymmetric azimuthally dependent real and complex waves.

  • 11. Kuzmina, E.
    et al.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Higher-order surface modes in the Goubau line2014In: Progress in Electromagnetics Research Symposium, Electromagnetics Academy , 2014, p. 2605-2609Conference paper (Refereed)
    Abstract [en]

    Existence of the higher-order surface waves of the Goubau line is proved and their structure is analyzed. An efficient computational approach is proposed based on numerical solution to initial-value problems obtained by the parameter differentiation. Several applications and further research directions are discussed.

  • 12.
    Kuzmina, Ekaterina
    et al.
    Moscow Technical University MIREA, Moscow, Russia.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Symmetric surface complex waves in Goubau Line2018In: Cogent Engineering, ISSN 2331-1916, Vol. 5, no 1, article id 1507083Article in journal (Refereed)
    Abstract [en]

    Existence of symmetric surface complex waves in a Goubau line—a perfectly conducting cylinder of circular cross-section covered by a concentric dielectric layer—is proved by constructing perturbation of the spectrum of symmetric real waves with respect to the imaginary part of the permittivity of the dielectric cover. Closed-form iteration procedures for calculating the roots of the dispersion equation (DE) in the complex domain supplied with efficient choice of initial approximation are developed. Numerical modeling is performed with the help of a parameter-differentiation method applied to the analytical and numerical solution of DEs.

  • 13.
    Kuzmina, Ekaterina
    et al.
    Moscow State Institute of Radio Engineering, Electronics and Automation, Technical University, Moscow, Russian Federation.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Waves in a lossy Goubau line2016In: 2016 10th European Conference on Antennas and Propagation: EuCAP 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, article id 7481368Conference paper (Refereed)
    Abstract [en]

    We consider a homogeneous Goubau line (GL) with a lossy cover. We analyze the dispersion equation for symmetric waves with respect to the problem parameters, find radially symmetric complex waves, and examine their behavior. We show that longitudinal wavenumbers of complex waves are regular perturbations of the propagation constants of eigenwaves of lossless GL, weakly depend om the imaginary part of permittivity of the cover, and that attenuation in GL is low at higher losses.

  • 14.
    Lagovsky, B. A.
    et al.
    Moscow Technological University, Moscow, Russia.
    Samokhin, A. B.
    Moscow Technological University, Moscow, Russia.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Increasing accuracy of angular measurements using UWB signals2017In: 2017 11th European Conference on Antennas and Propagation, EUCAP 2017, Institute of Electrical and Electronics Engineers (IEEE), 2017, p. 1083-1086Conference paper (Refereed)
    Abstract [en]

    We show that dispersion characteristics of antenna patterns should be taken into account when developing systems using UWB signals. The accuracy of measurement of angular coordinates of objects using UWB pulses is increased by optimizing their shape based on known characteristics of the antenna system and at least partially known characteristics of the investigated signal source. Optimization algorithms allow to minimize the width of the directional pattern for a given level of the useful signal.

  • 15.
    Lagovsky, B. A.
    et al.
    Moscow State Institute of Radio Engineering and Automation, Technical University, Moscow, Russian Federation.
    Samokhin, A. B.
    Moscow State Institute of Radio Engineering and Automation, Technical University, Moscow, Russian Federation.
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Pulse characteristics of antenna array radiating UWB signals2016In: 2016 10th European Conference on Antennas and Propagation: EuCAP 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, article id 7481624Conference paper (Refereed)
    Abstract [en]

    Dispersion properties of the mutual impedance of emitters significantly alter the shape and spectrum of ultra-wideband (UWB) signals which must be taken into account when forming the signal. In order to take into consideration mutual coupling of elements we propose to use pulse characteristics in the antenna performance analysis and calculations. This approach allows us to simplify calculations of UWB antenna systems and improve their accuracy.

  • 16.
    Lagovsky, B.
    et al.
    Moscow Technological University (MIREA), Moscow, Russian Federation.
    Samokhin, A.
    Moscow Technological University (MIREA), Moscow, Russian Federation.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Increasing effective angular resolution of measuring systems based on antenna arrays2016In: 2016 URSI International Symposium on Electromagnetic Theory (EMTS): Conference publications, IEEE conference proceedings, 2016, p. 432-434Conference paper (Refereed)
    Abstract [en]

    Resolution of goniometric systems on the basis of antenna arrays can be increased due to the secondary digital processing of the accepted signals. Necessary algorithms are created on the basis of solution to inverse problems.

  • 17. Lagovsky, Boris A.
    et al.
    Samokhin, Alexander B.
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Superresolution based on the methods of extrapolation2015In: PIERS 2015 Prague: Progress in Electromagnetics Research Symposium : Proceedings, Cambridge, MA: The Electromagnetics Academy , 2015, p. 1548-1551Conference paper (Refereed)
    Abstract [en]

    A new method of signal processing by smart antennas is proposed and justified. It allows to improve the accuracy of angle measurement and to restore the image of the object with superresolution. The method is based on the extrapolation of the signals received by each element of the antenna array, outside the aperture. This allows introducing new virtual elements and thus synthesizing significantly larger antenna array. The method is tested in numerical experiments using a mathematical model and the maximum effective angular resolution is found for different cases and objects. Algorithms based on the method of digital aperture synthesis provide angular superresolution 3-7 times greater than that according to the Rayleigh criterion for a signal/noise ratio of 12-13 dB.

  • 18.
    Nakonechny, A. G.
    et al.
    Taras Shevchenko National University of Kyiv, Ukraine.
    Podlipenko, Y. K.
    Taras Shevchenko National University of Kyiv, Ukraine.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Aposteriori estimates in inverse problems for the Helmholtz equation2017In: 2017 Progress In Electromagnetics Research Symposium - Fall (PIERS - FALL), Electromagnetics Academy , 2017, p. 3526-3531Conference paper (Refereed)
    Abstract [en]

    We consider the problem of estimation of the right-hand sides of the Helmholtz equation that models electromagnetic and acoustic wave fields when that initial data is uncertain. In the case when measurement errors depend on solutions, we construct algorithms of computation of the optimal estimates which are compatible with the measurement data. It is shown that approximate a posteriori estimates of the right-hand sides are expressed via solutions of linear algebraic equations.

  • 19.
    Nakonechny, Alexander G.
    et al.
    Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.
    Podlipenko, Yuri K.
    Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Guaranteed a posteriori estimates of right-hand sides in transmission problems for Helmholtz equations2017In: General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS), 2017 XXXIInd, Institute of Electrical and Electronics Engineers Inc. , 2017Conference paper (Refereed)
    Abstract [en]

    In this work we describe a method of obtaining guaranteed a posteriori estimates of unknown right-hand sides of the Helmholtz transmission problems from indirect measurements of a solution to this problem. The obtained results can be applied in various models of electromagnetics and acoustics that describe excitation of transparent bodies by sources of different kinds.

  • 20.
    Nakonechny, Alexander
    et al.
    T. Shevchenko Kyiv National University, Kyiv, Ukraine.
    Podlipenko, Yury
    T. Shevchenko Kyiv National University, Kyiv, Ukraine.
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Guaranteed estimation for inverse problems in electromagnetics and acoustics2016In: Proceedings of the 2016 18th International Conference on Electromagnetics in Advanced Applications, ICEAA 2016, 2016, p. 374-377, article id 7731403Conference paper (Refereed)
    Abstract [en]

    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.

  • 21.
    Podlipenko, Y. K.
    et al.
    Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.
    Nakonechny, A. G.
    Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Guaranteed estimation of solutions to Helmholtz problems from pointwise noisy observations2016In: Proceedings of the International Conference Days on Diffraction, DD 2016, 2016, p. 336-339, article id 7756869Conference paper (Refereed)
    Abstract [en]

    The theorems on a general form of guaranteed estimates of linear functionals from unknown solutions of Helmholtz transmission problems are formulated in the case of pointwise noisy observations of these solutions.

  • 22.
    Podlipenko, Y.
    et al.
    Taras Shevchenko National University, Kyiv, Ukraine.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Guaranteed estimation of solutions to transmission problems for Helmholtz equation with uncertain data from their indirect noisy observations2016In: 2016 URSI International Symposium on Electromagnetic Theory (EMTS), IEEE conference proceedings, 2016, p. 93-95Conference paper (Refereed)
    Abstract [en]

    We investigate the estimation problems of linear functionals from solutions to transmission problems for Helmholtz equation with inexact data. The right-hand sides of equations entering the statements of transmission problems and the statistical characteristics of observations errors are supposed to be unknown and belonging to the certain sets. It is shown that the linear mean square estimates of the above-mentioned functionals and estimation errors are expressed via solutions to the systems of transmission problems of the special type.

  • 23.
    Podlipenko, Y.
    et al.
    Kiev University, Kiev, Ukraine.
    Shestopalov, Yury V.
    arlstad University, Karlstad, Sweden.
    Guaranteed Estimates of Functionals from Solutions and Data of Interior Maxwell Problems Under Uncertainties2013In: Springer Proceedings in Mathematics & statistics, ISSN 2194-1017, E-ISSN 2194-1009, Vol. 52, p. 135-167Article in journal (Refereed)
    Abstract [en]

    We are looking for linear with respect to observations optimal estimates of solutions and right-hand sides of Maxwell equations called minimax or guaranteed estimates. We develop constructive methods for finding these estimates and estimation errors which are expressed in terms of solutions to special variational equations and prove that Galerkin approximations of the obtained variational equations converge to their exact solutions.

  • 24.
    Podlipenko, Yu K.
    et al.
    Faculty of Cybernetics, Taras Shevchenko National University of Kyiv, Kiev, Ukraine.
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Guaranteed estimation of solutions to Helmholtz transmission problems with uncertain data from their indirect noisy observations2017In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 52, no 9, p. 1129-1139Article in journal (Refereed)
    Abstract [en]

    We investigate the guaranteed estimation problem of linear functionals from solutions to transmission problems for the Helmholtz equation with inexact data. The right-hand sides of equations entering the statements of transmission problems and the statistical characteristics of observation errors are supposed to be unknown and belonging to certain sets. It is shown that the optimal linear mean square estimates of the above mentioned functionals and estimation errors are expressed via solutions to the systems of transmission problems of the special type. The results and techniques can be applied in the analysis and estimation of solution to forward and inverse electromagnetic and acoustic problems with uncertain data that arise in mathematical models of the wave diffraction on transparent bodies.

  • 25.
    Podlipenko, Yuri
    et al.
    T. Shevchenko Kyiv National University, Kyiv, Ukraine.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Mixed variational approach to finding guaranteed estimates from solutions and right-hand sides of the second-order linear elliptic equations under incomplete data2016In: Minimax Theory and its Applications, ISSN 2199-1413, Vol. 1, no 2, p. 197-244Article in journal (Refereed)
    Abstract [en]

    We investigate the problem of guaranteed estimation of values of linear continuous functionals defined on solutions to mixed variational equations generated by linear elliptic problems from indirect noisy observations of these solutions. We assume that right-hand sides of the equations, as well as the second moments of noises in observations are not known; the only available information is that they belong to given bounded sets in the appropriate functional spaces. We are looking for linear with respect to observations optimal estimates of solutions of aforementioned equations called minimax or guaranteed estimates. We develop constructive methods for finding these estimates and estimation errors which are expressed in terms ofsolutions to special mixed variational equations and prove that Galerkin approximations of the obtained variational equations converge to their exact solutions. We study also the problem of guaranteed estimation of right-hand sides of mixed variational equations.

  • 26.
    Samokhin, A. B.
    et al.
    Moscow Technological University (MIREA), Moscow, Russian Federation.
    Samokhina, A. S.
    Institute of Control Sciences, Moscow, Russian Federation.
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Fast algorithms for the solution of volume singular integral equations of electromagnetics2017In: 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA), Institute of Electrical and Electronics Engineers Inc. , 2017, p. 776-778, article id 8065364Conference paper (Refereed)
    Abstract [en]

    Fast algorithms for the solution of volume singular integral equations of electromagnetics are presented. Numerical results are demonstrated that confirm efficiency of the developed fast computational algorithms.

  • 27.
    Samokhin, Alexander
    et al.
    Moscow Technological University (MIREA), Moscow, Russia.
    Samokhina, Anna
    Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia.
    Shestopalov, Yury
    Moscow Technological University (MIREA), Moscow, Russia.
    Analysis and solution method for problems of electromagnetic wave scattering on dielectric and perfectly conducting structures2017In: Differential equations, ISSN 0012-2661, E-ISSN 1608-3083, Vol. 53, no 9, p. 1165-1173Article in journal (Refereed)
    Abstract [en]

    Problems of electromagnetic wave scattering on 3D dielectric structures in the presence of bounded perfectly conducting surfaces are reduced to a system of singular integral equations. We study this system mathematically and suggest a numerical solution method.

  • 28.
    Samokhin, Alexander
    et al.
    Moscow Technical University MIREA, Moscow, Russia.
    Samokhina, Anna
    Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Discretization Methods for Three-Dimensional Singular Integral Equations of Electromagnetism2018In: Differential equations, ISSN 0012-2661, E-ISSN 1608-3083, Vol. 54, no 9Article in journal (Refereed)
    Abstract [en]

      Theorems providing the convergence of approximate solutions of linear operator equations to the solution of the original equation are proved. The obtained theorems are used to rigorously mathematically justify the possibility of numerical solution of the 3D singular integral equations of electromagnetism by the Galerkin method and the collocation method.

  • 29.
    Samokhin, Alexander
    et al.
    Moscow State Technical University of Radio Engineering and Automation, Moscow, Russian Federation.
    Shestopalov, Yury V.
    Karlstad University, Karlstad, Sweden.
    Kobayashi, Kazuya
    Chuo University, Tokyo, Japan.
    Stationary iteration methods for solving 3D electromagnetic scattering problems2013In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 222, p. 107-122Article in journal (Refereed)
    Abstract [en]

    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.

  • 30.
    Sheina, E. A.
    et al.
    Lomonosov Moscow State University, Russian Federation.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Smirnov, A. P.
    Lomonosov Moscow State University, Russian Federation.
    Planning and processing of measurements in a waveguide aimed at determination of permittivity of dielectric inclusion2017In: 2017 Progress In Electromagnetics Research Symposium - Fall (PIERS - FALL), Electromagnetics Academy , 2017, p. 1866-1871Conference paper (Refereed)
    Abstract [en]

    The methods are developed for reconstructing permittivity of the inclusion in a rectangular waveguide with perfectly conducting walls by comparing the results of multifrequency measurements of the principal waveguide mode transmission coefficient with the data obtained from numerical solution to Maxwell's equations. Optimal schemes for experimentation and processing of the obtained data are proposed on the basis of comparison of experimental data with closed-form solutions for cases of empty waveguide and the waveguide containing a uniform diaphragm.

  • 31.
    Sheina, E. A.
    et al.
    Lomonosov Moscow State University, Russian Federation.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Smirnov, A. P.
    Lomonosov Moscow State University, Russian Federation.
    Ufimtsev, M. V.
    Lomonosov Moscow State University, Russian Federation.
    FDTD solution of reconstructing permittivity of a dielectric inclusion in a waveguide taking into account measurement inaccuracy2017In: Progress in Electromagnetics Research Symposium, Electromagnetics Academy , 2017, p. 3188-3195Conference paper (Refereed)
    Abstract [en]

    Wave propagation in a rectangular waveguide with perfectly conducting walls containing a parallel-plane dielectric diaphragm and a small inclusion is modeled using a numerical solution to Maxwell's equations. The methods are developed for reconstructing permittivity of the inclusion from the transmission coefficient of the principal waveguide mode taking into account experimental error. The results determined by these methods are compared with experimental data obtained for a homogeneous diaphragm.

  • 32.
    Sheina, E. A.
    et al.
    Lomonosov Moscow State University, Russian Federation.
    Smirnov, A. P.
    Lomonosov Moscow State University, Russian Federation.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Influence of standing waves on the solution of the inverse problem of reconstructing parameters of a dielectric inclusion in a waveguide2016In: 2016 URSI International Symposium on Electromagnetic Theory (EMTS), IEEE conference proceedings, 2016, p. 643-646Conference paper (Refereed)
    Abstract [en]

    We consider numerical determination of the dielectric media parameters of inclusions in a waveguide of rectangular cross-section from the transmission coefficient. We develop and apply computer codes implementing the FDTD algorithm for numerical solution of the nonstationary Maxwell equations with perfectly matched layer (PML) absorbing boundary conditions using the Berenger layout. We estimate parameter ranges providing the necessary accuracy for solving forward and inverse scattering problems for waveguides with inclusions. Aposteriori estimate of the amplitude of higher-order evanescent waves is obtained and their influence on the choice of parameters of the numerical method is determined.

  • 33.
    Sheina, E. A.
    et al.
    Lomonosov Moscow State University, Moscow, Russian Federation.
    Smirnov, A. P.
    Lomonosov Moscow State University, Moscow, Russian Federation.
    Shestopalov, Yury V.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Optimization of the boundary conditions and computational parameters for the FDTD solution of the inverse problem of reconstructing permittivity of a dielectric inclusion in a waveguide2016In: 2016 Progress In Electromagnetics Research Symposium, PIERS 2016 - Proceedings, 2016, p. 211-216, article id 773429Conference paper (Refereed)
    Abstract [en]

    Wave propagation in a waveguide of rectangular cross section with perfectly conducting wall containing an inhomogeneous dielectric insert in the form of a parallel-plane diaphragm with an inclusion is simulated numerically. The permittivity of the inclusion is a quantity to be restored from as little information about the scattered field as possible using FDTD numerical solution of Maxwell’s equations with nonlocal multimode scattering boundary conditions. The optimal number of higher-order evanescent waves and the size of the computational waveguide domain are found using the series of numerical experiments.

  • 34.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Complex waves in a dielectric waveguide2018In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 82, p. 16-19Article in journal (Refereed)
    Abstract [en]

    Existence of two families of symmetric complex waves in a dielectric waveguide of circular cross section is proved. Eigenvalues of the associated Sturm–Liouville problem on the half-line are determined. 

  • 35.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Methods for verifying solvability of the permittivity reconstruction in canonical waveguide inverse problems2017In: General Assembly and Scientific Symposium of the International Union of Radio Science (URSI GASS), 2017 XXXIInd, Institute of Electrical and Electronics Engineers Inc. , 2017, p. 1-2Conference paper (Refereed)
    Abstract [en]

    We present a summary of mathematical methods that enable one to study and reveal the properties of the transmission coefficient as a function of problem parameters aimed at solution to some canonical waveguide inverse problems. The results are based on application of the theory of functions of several complex variables and singularities of differentiable mappings and lead to substantial improvement of the available techniques for permittivity reconstruction of material samples in waveguides.

  • 36.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    On unique solvability of multi-parameter waveguide inverse problems2017In: 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA), Institute of Electrical and Electronics Engineers (IEEE), 2017, p. 372-376, article id 8065253Conference paper (Refereed)
    Abstract [en]

    This paper provides an introduction to mathematical methods of analytical-numerical solution to multi-parameter waveguide inverse problems of reconstructing permittivity of layered dielectric inclusions from the values of the transmission and reflection coefficients. Sufficient conditions of the unique solvability for a family of waveguide inverse problems are obtained.

  • 37.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Resonant states in forward and inverse waveguide scattering problems2015In: Proceedings of the 2015 International Conference on Electromagnetics in Advanced Applications: ICEAA 2015, IEEE Press, 2015, p. 31-34Conference paper (Refereed)
    Abstract [en]

    It is shown that the transmission coefficient of parallel-plane multi-sectional dielectric diaphragms in a waveguide of rectangular cross section has singularities in the complex plane of the longitudinal wavenumber of each section and the singularities are associated with resonant states of the transmission problem.

  • 38.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Singularities of the transmission coefficient and anomalous scattering by a dielectric slab2018In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 59, no 3, article id 033507Article in journal (Refereed)
    Abstract [en]

    We prove the existence and describe the distribution on the complex plane of the singularities, resonant states (RSs), of the transmission coefficient in the problem of the plane wave scattering by a parallel-plate dielectric slab in free space. It is shown that the transmission coefficient has isolated poles all with nonzero imaginary parts that form countable sets in the complex plane of the refraction index or permittivity of the slab with the only accumulation point at infinity. The transmission coefficient never vanishes and anomalous scattering, when its modulus exceeds unity, occurs at arbitrarily small loss of the dielectric filling the layer. These results are extended to the cases of scattering by arbitrary multi-layer parallel-plane media. Connections are established between RSs, spectral singularities, eigenvalues of the associated Sturm-Liouville problems on the line, and zeros of the corresponding Jost function.

  • 39.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Kuzmina, Ekaterina
    Moscow Technological University MIREA, Moscow, Russia.
    On Recent Findings in the Theory of Complex Waves in Open Metal-Dielectric Waveguides2018Conference paper (Refereed)
    Abstract [en]

    Theory of complex waves (see e.g. [1] and references therein) accumulated a big volume of results. However, its biggest drawback remains which brakes significantly the development of the theory: absence of rigorous proofs of the existence of complex waves. In this respect, studies of complex waves in open metal-dielectric waveguides has been essentially enhanced when two new families of symmetric (angle-independent) complex waves have been identified [2, 3] in a dielectric rod (DR) and Goubau line (GL) with homogeneous dielectric cover: surface complex waves occurring as perturbations of real surface waves caused by the presence of lossy dielectric, and pure complex waves which have no counterpart in the set of real waves. Existence of the latter family of complex waves has been shown using a special technique and the proof [3] of the existence of an infinite set of complex roots of the dispersion equation (DE) describing waves in DR and GL.

    In this work, a development of the analytical and numerical methods [2, 3] are considered for the analysis of the electromagnetic wave propagation in metal-dielectric waveguides with multi-layered dielectric filling. The first step constitutes extension of the results obtained for symmetric complex waves in DR and GLto the case of non-symmetric (angle-dependent) waves, and the second step, to multi-layered dielectric covers. Both steps are accomplished using specific forms of DEs obtained in [3]by construction analytical continuation of the functions involved in DEs to multi-sheet Riemann surfaces of the spectral parameter and applying appropriate generalization the techniques [4]forfinding complex roots of the DEs.

    Calculation ofnon-symmetric complex waves employs numerical solution of the DEs with the help of parameter differentiation in the complex domain using multi-parameter setting and analysis of implicit functions of several complex variables [5] and reduction [2, 3] to numerical solution of auxiliary Cauchy problems.

    1. A. S. Raevskiiand S. B. Raevskii, Complex Waves, Radiotekhnika, Moscow, 2010.

    2. E. Kuzmina and Y. Shestopalov, “Waves in a lossyGoubau line,”10th European Conf. on Antennas and Propagation (EuCAP), Davos, Switzerland, 2016, doi: 10.1109/EuCAP.2016.7481368.

    3. E. Kuzmina and Y. Shestopalov, “Complex waves in a dielectric rod and Goubau line,” 19th Int. Conf. on Electromagneticsin Advanced Applications (ICEAA), Verona, Italy, 2017, pp. 963-966, doi: 10.1109/ICEAA.2017.8065417.

    4. Y. Shestopalov, “Resonant states in waveguide transmission problems,”PIER B,64: pp.119-143, 2015, doi: 10.2528/PIERB15083001.

    5.Y. Shestopalov,“On unique solvability of multi-parameter waveguide inverse problems, ”19th Int. Conf. on Electromagnetics in Advanced Applications (ICEAA), Verona, Italy, 2017, pp. 372-376, doi: 10.1109/ICEAA.2017.8065253.

  • 40.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Kuzmina, Ekaterina
    Moscow Technical University MIREA, Moscow, Russia.
    Symmetric surface waves along a metamaterial dielectric waveguide and a perfectly conducting cylinder covered by a metamaterial layer2018In: Advanced Electromagnetics (AEM), E-ISSN 2119-0275, Vol. 7, no 2, p. 91-98Article in journal (Refereed)
    Abstract [en]

    Existence of symmetric complex waves in a metamaterial dielectric rod and a perfectly conducting cylinder of circular cross section covered by a concentric layer of metamaterial, a metamaterial Goubau line, is proved. Analytical investigation and numerical solution of dispersion equations reveal several important properties of running waves inher- ent to open metal-metamaterial waveguides which have not been reported for waveguides filled with standard media.

  • 41.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Kuzmina, Ekaterina
    Moscow State Technical University of Radio Engineering, Electronics and Automation, Moscow, Russia.
    Samokhin, Alexander
    Moscow State Technical University of Radio Engineering, Electronics and Automation, Moscow, Russia.
    On a Mathematical Theory of Open Metal-Dielectric Waveguides2014In: Forum for Electromagnetic Research Methods and Application Technologies (FERMAT), Vol. 5Article in journal (Refereed)
    Abstract [en]

    Existence of symmetric waves in open metal--dielectric waveguides, a dielectric rod and the Goubau line, is proven by analyzing the of functional properties of the dispersion equations (DEs) and parameter-differentiation method, applied to the analytical and numerical solution of the DEs. Various limiting cases are investigated. Reduction to singular Sturm--Liouville boundary eigenvalue problemson the half-line is performed. Principal and higher-order surface waves  are investigated

  • 42.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Menshikov, Y.
    Dnepropetrovsk University, Dnepropetrovsk, Ukraine.
    An approach to estimation of solutions to inverse problems of electromagnetics2016In: 2016 URSI International Symposium on Electromagnetic Theory (EMTS), IEEE conference proceedings, 2016, p. 780-782Conference paper (Refereed)
    Abstract [en]

    In this paper an approach is proposed which is based on a method of regularization for estimating the solution of inverse problems of electromagnetic with noisy measurements. The constraints on the solution of the inverse problem based on physical assumptions are taken into consideration. The solution is reduced to a nonlinear system with the given interval-type inaccuracy of the right-hand side. The developed approach enables one to take into account inaccuracy of the operator of the inverse problem. The method of the special mathematical model selection is described which improves the accuracy of estimations.

  • 43.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Sheina, Elena
    M. V. Lomonosov Moscow State University, Moscow, Russia.
    Smirnov, Alexander
    M. V. Lomonosov Moscow State University, Moscow, Russia.
    Development of Numerical Techniques for Forward and Inverse Waveguide Scattering Problems2018Conference paper (Refereed)
    Abstract [en]

    Development of the methods and algorithms [1, 2] are considered for the numerical solution to the forward problem of the electromagnetic wave scattering by inhomogeneous dielectric inclusions in a waveguide of rectangular cross section and inverse problem of reconstructing parameters of the dielectric inclusions from the values of the transmission coefficient of the scattered electromagnetic wave. The codes are developed implementing an FDTD method that employs the PML-layer technique. Numerical modeling and simulations are performed for the analysis of the wave propagation in waveguides of rectangular cross section loaded with parallel-plane layered media (layered dielectric diaphragms) and such diaphragms containing cubic dielectric inclusions. Validation is carried out of the results of calculations using closed-form solution [3] to the canonical single-layer structure.

    Progress in analytical - numerical investigations of the solutions to the forward and inverse waveguide problems are largely based on a recent discovery [4] of the singularities and extrema in the complex domain of the transmission coefficient of layered dielectric diaphragms. In fact, the knowledge of the location of singularity and extrema sets of the scattering matrix allows one to justify correct determination of real or complex permittivity of each layer of the diaphragm by specifying domains in the complex plane where the transmission coefficientis one-to-one; that is, the domains that do not contain singularities and where unique permittivity reconstruction is therefore possible. Forthe forward problem of the scattering of a normal waveguide mode by a single-and three-layer diaphragms with a dielectric cube, it is shown [1, 2] that variation in the values of the transmission coefficient can be up to two orders of magnitude less than that of the permittivity of the inclusion. Taking into account this result and the presence of singularities, improvements are proposed of the numerical method, algorithms and codes implementing the calculations. The results of modeling and computations are validated by comparing with experimental and measurement data [3]. The requirements are formulated that should be imposed on the accuracy of computations and measurements necessary to reconstruct numerically permittivity of the inclusion from the amplitude and phase of the transmitted wave with the prescribed accuracy.

    1. E. Sheina, A. Smirnov,Y. Shestopalov,and M.Ufimtsev,“FDTD solution of reconstructing permittivity of a dielectric inclusion in a waveguide taking into account measurement inaccuracy,”Progress in Electromagnetics Research Symposium (PIERS),St Petersburg, Russia, 2017, pp. 3188-3195, doi:10.1109/PIERS.2017.8262306.

    2.E. Sheina, A. Smirnov, and Y. Shestopalov, “Influence of standing waves on the solution of the inverse problem ofreconstructing parameters of a dielectric inclusion in a waveguide,”URSI Int. Symposium on Electromagnetic Theory (EMTS), Espoo, Finland, 2016,pp. 643-646, doi:10.1109/URSI-EMTS.2016.7571479.

    3. Yu. G. Smirnov, Yu. V. Shestopalov, and E. D. Derevyanchuk, “Inverse problem method for complex permittivity reconstruction of layered media in a rectangular waveguide,”Physica Status Solidi(C), 11,5-6, 2014,pp. 969–974, doi:10.1002/pssc.201300697.

    4. Y. Shestopalov, “Resonant states in waveguide transmission problems,”PIER B,64: pp.119-143, 2015, doi: 10.2528/PIERB15083001.

  • 44.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Smirnov, Y. G.
    Penza State University, Penza, Russian Federation.
    Derevyanchuk, E. D.
    Penza State University, Penza, Russian Federation.
    Tensor permittivity and permeability reconstruction of a one-sectional diaphragm in a rectangular waveguide2016In: 2016 URSI International Symposium on Electromagnetic Theory (EMTS), IEEE conference proceedings, 2016, p. 353-355Conference paper (Refereed)
    Abstract [en]

    This work is devoted to the solution of the inverse problem of reconstructing electromagnetic characteristics of anisotropic parallel-plane dielectric diaphragms. We consider a one-sectional diaphragm in a rectangular waveguide filled with anisotropic media having a diagonal permittivity and permeability tensors and propose a method of reconstructing the permittivity and permeability tensors from the values of the transmission coefficient at different frequencies.

  • 45.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Smirnov, Yury
    Penza State University, Penza, Ryssland.
    Advanced mathematical techniques  for the analysis of inverse scattering  in waveguides2014In: Proceedings of the 7th International Conference Inverse Problems: Modeling and Simulation (IPMS 2014): Ölüdeniz, Fethiye, Turkey, May 22–30,2014 / [ed] A. Hasanov, 2014, p. 32-Conference paper (Refereed)
  • 46.
    Shestopalov, Yury
    et al.
    Karlstad University, Karlstad, Sweden.
    Smirnov, Yury
    Penza State University, Penza,, Russian Federation.
    Determination of permittivity of an inhomogeneous dielectric body in a waveguide2011In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 27, no 9, article id 095010Article in journal (Refereed)
    Abstract [en]

    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.

  • 47.
    Shestopalov, Yury
    et al.
    Karlstad University, Karlstad, Sweden.
    Smirnov, Yury
    Penza State University, Penza, Ryssland.
    Eigenwaves in Waveguides with Dielectric Inclusions : Spectrum2014In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 93, no 2, p. 408-427Article in journal (Refereed)
    Abstract [en]

    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 formulate the definition of eigenwaves and associated waves using the system of eigenvectors and associated vectors of the pencil and prove that the spectrum of normal waves forms a non-empty set of isolated points localized in a strip with at most finitely many real points.

  • 48.
    Shestopalov, Yury
    et al.
    Karlstads universitet.
    Smirnov, Yury
    Penza State University, Penza, Ryssland.
    Eigenwaves in waveguides with dielectric inclusions: completeness2014In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 93, no 9, p. 1824-1845Article in journal (Refereed)
    Abstract [en]

    We formulate the definition of eigenwaves and associated waves in a nonhomogeneously filled waveguide using the system of eigenvectors and associated vectors of a pencil and prove its double completeness with a finite defect or without a defect. Then, we prove the completeness of the system of transversal components of eigenwaves and associated waves as well as the ‘mnimality’ of this system and show that this system is generally not a Schauder basis. This work is a continuation of the paper Eigenwaves in waveguides with dielectric inclusions: spectrum. Appl. Anal. 2013. doi:10.1080/00036811.2013.778980 by Y. Smirnov and Y. Shestopalov. Therefore, we omit the problem statements and all necessary basic definitions given in the previous paper.

  • 49.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Smirnov, Yury
    Penza State University, Penza, Ryssland.
    Derevyanchuk, Ekaterina
    Penza State University, Penza, Russia.
    Inverse problem method for permittivity reconstruction of two-layered media: numerical and experimental results2014In: Progress in Electromagnetics Research Symposium: , Electromagnetics Academy , 2014, p. 2610-2613Conference paper (Refereed)
    Abstract [en]

    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.

  • 50.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Smirnov, Yury G.
    Penza State University, Russian Federation .
    Derevyanchuk, Ekaterina D.
    Penza State University, Russian Federation .
    Permittivity reconstruction of a diaphragm in a rectangular waveguide: Unique solvability of benchmark inverse problems2015In: PIERS 2015 Prague: Progress in Electromagnetics Research Symposium : Proceedings, Cambridge, MA: The Electromagnetics Academy , 2015, p. 1528-1532Conference paper (Refereed)
    Abstract [en]

    This work is devoted to the analysis of inverse problems of permittivity reconstruction of diaphragms loaded in a rectangular waveguide including justification of the solution to a benchmark inverse problem of reconstructing permittivity of a one-sectional diaphragm. We perform comparison of theoretical and numerical results based on the measurement data to validate the efficiency of the proposed technique. The obtained solutions can be implemented in practical measurements for investigation of new artificial materials and media and can be applied in optics, nanotechnology, and design of microwave devices.

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