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  • 51.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Methods for verifying solvability of the permittivity reconstruction in canonical waveguide inverse problems2017Ingår i: 2017 XXXIIND GENERAL ASSEMBLY AND SCIENTIFIC SYMPOSIUM OF THE INTERNATIONAL UNION OF RADIO SCIENCE (URSI GASS), Institute of Electrical and Electronics Engineers (IEEE), 2017, s. 1-2Konferensbidrag (Refereegranskat)
    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.

  • 52.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektroteknik, matematik och naturvetenskap, Matematik.
    On a Method of Solution to Dispersion Equations in Electromagnetics2019Ingår i: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli, 2019, artikel-id 8738297Konferensbidrag (Refereegranskat)
    Abstract [en]

    A possible general approach to the analysis of dispersion equations (DEs) of electromagnetics is presented. The method takes into account the known explicit forms of DEs describing eigenoscillations and normal waves in layered structures and is based on the development of the notion of generalized cylindrical polynomials. The approach enables one to complete rigorous proofs of existence and determine domains of localization of the DE roots and validate iterative numerical solution techniques.

  • 53.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    On a Perspective of Discovering Wave Interaction in Canonical Open Metal-Dielectric Waveguides2018Ingår i: Proceedings of 2018 International Conference on Electromagnetics in Advanced Application (ICEAA), Piscataway, New Jersey, USA: IEEE conference proceedings, 2018, s. 72-75, artikel-id 8520368Konferensbidrag (Refereegranskat)
    Abstract [en]

    A possibility of the wave interaction is demonstrated for canonical types of open metal-dielectric waveguides: a dielectric rod of circular cross section and a perfectly conducting circular cylinder covered by a concentric layer of dielectric, a Goubau line. The results and technique that apply rigorous analysis of dispersion equations and determination of Morse critical points admit extension to other types of guiding structures.

  • 54.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    On a spectrum of complex waves in open metal-dielectric waveguides [О спектре комплексных волн в открытых металлических диэлектрических волноводах]2018Ingår i: Современные методы теории краевых задач: материалы международной конференции, посвящённой 90-летию Владимира Александровича Ильина (2-6 мая 2018 г., Москва): Понтрягинские чтения - XXIX / [ed] Budak Alexander Borisovich [Будак Александр Борисович], Moscow: Moscow State University Press , 2018, s. 243-244Konferensbidrag (Refereegranskat)
  • 55.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    On unique solvability of multi-parameter waveguide inverse problems2017Ingår i: 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA), Institute of Electrical and Electronics Engineers (IEEE), 2017, s. 372-376, artikel-id 8065253Konferensbidrag (Refereegranskat)
    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.

  • 56.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektroteknik, matematik och naturvetenskap, Matematik.
    RCS Resonances for Canonical Structures2019Ingår i: 2019 IEEE International Conference on Microwaves, Antennas, Communications and Electronic Systems, COMCAS 2019, IEEE, 2019Konferensbidrag (Refereegranskat)
    Abstract [en]

    A brief survey is presented on the methods aimed at rigorous validation of the occurrence of complex RCS resonances for canonical structures: dielectric and perfectly conducting cylinders covered by layered media possessing circular symmetry. It is shown that the resonances are associated with singularities of the scattered field in the complex domain. © 2019 IEEE.

  • 57.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Resonant states in forward and inverse waveguide scattering problems2015Ingår i: Proceedings of the 2015 International Conference on Electromagnetics in Advanced Applications: ICEAA 2015, IEEE Press, 2015, s. 31-34Konferensbidrag (Refereegranskat)
    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.

  • 58.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Singularities of the transmission coefficient and anomalous scattering by a dielectric slab2018Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 59, nr 3, artikel-id 033507Artikel i tidskrift (Refereegranskat)
    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.

  • 59.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektroteknik, matematik och naturvetenskap, Matematik.
    Trigonometric and cylindrical polynomials and their applications in electromagnetics2019Ingår i: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504XArtikel i tidskrift (Refereegranskat)
    Abstract [en]

    Development of the theory of trigonometric polynomials (TPs) is considered that involves generalization of the notion of TP and extension of the methods and results to cylindrical polynomials (CPs). On the basis of the proposed augmentation of TPs and CPs, a general approach is presented to the analysis of guided waves and resonances in electromagnetics and beyond. The method employs the known explicit forms of dispersion equations (DEs) describing eigenoscillations and normal waves in layered structures and is based on the development of the theory of generalized TPs and CPs performed in the study. The approach enables one to complete rigorous proofs of existence and determine domains of localization of the TP and CP zeros and the DE roots and validate iterative numerical solution techniques.

  • 60.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektroteknik, matematik och naturvetenskap, Matematik.
    Aboltins, A
    Litvinenko, A
    Mathematical methods for inverse waveguide problems2019Ingår i: 2019 IEEE Microwave Theory and Techniques in Wireless Communications  (MTTW). Proceedings, 2019Konferensbidrag (Refereegranskat)
    Abstract [en]

    An introduction is given to mathematical methods for inverse waveguide  problems. Applications are considered to the solution of the inverse  waveguide problems of reconstructing permittivity of layered dielectric  inclusions. It is shown that the existence and uniqueness can be justified by  establishing one-to-one correspondence between the sought quantities and the  measured noisy data.

  • 61.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Kuzmina, Ekaterina
    Russian Technological University MIREA, Moscow, Russia.
    On a rigorous proof of the existence of complex waves in a dielectric waveguide of circular cross section2018Ingår i: Progress in Electromagnetics Research B, ISSN 1937-6472, E-ISSN 1937-6472, Vol. 82, s. 137-164Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Existence of symmetric complex waves in a dielectric rod (DR) - a dielectric waveguide of circular cross section - 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. A closed-form iteration procedure for calculating the roots in the complex domain supplied with efficient choice of initial approximation is proposed. Numerical modeling is performed with the help of a parameter-differentiation method applied to the analytical and numerical solution of DEs.

  • 62.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektroteknik, matematik och naturvetenskap, Matematik.
    Kuzmina, Ekaterina
    Moscow Technological University MIREA, Moscow, Russia.
    On Recent Findings in the Theory of Complex Waves in Open Metal-Dielectric Waveguides2018Ingår i: 2018 2ND URSI Atlantic Radio Science Meeting (AT-RASC), IEEE, 2018Konferensbidrag (Refereegranskat)
    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.

  • 63.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    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 layer2018Ingår i: Advanced Electromagnetics (AEM), E-ISSN 2119-0275, Vol. 7, nr 2, s. 91-98Artikel i tidskrift (Refereegranskat)
    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.

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  • 64.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    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 Waveguides2014Ingår i: Forum for Electromagnetic Research Methods and Application Technologies (FERMAT), Vol. 5Artikel i tidskrift (Refereegranskat)
    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

  • 65.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Menshikov, Y.
    Dnepropetrovsk University, Dnepropetrovsk, Ukraine.
    An approach to estimation of solutions to inverse problems of electromagnetics2016Ingår i: 2016 URSI International Symposium on Electromagnetic Theory (EMTS), IEEE conference proceedings, 2016, s. 780-782Konferensbidrag (Refereegranskat)
    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.

  • 66.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Samokhin, Alexander
    Russian Technological University MIREA.
    Lagovsky, Boris
    Russian Technological University MIREA.
    Increasing the Range of UWB Radars2018Ingår i: IET Conference Publications 2018, Piscataway, New Jersey, USA: IEEE, 2018, Vol. CP741, artikel-id 1570403971Konferensbidrag (Refereegranskat)
    Abstract [en]

    The use of UWB radars makes it possible to detect, recognize, and carry out measurements of coordinate and velocities of hardly noticeable radar targets. The variational problems of searching for the maximum range of UWB-radar operation using optimization of the shape and duration of UWB-pulses are justified and solved.

  • 67.
    Shestopalov, Yury
    et al.
    Russian Technological University MIREA, Moscow, 119454 Russia.
    Samokhin, Alexander
    Russian Technological University MIREA, Moscow, 119454 Russia.
    Samokhina, Anna
    Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997 Russia.
    Iterative Gradient Descent Methods for Solving Linear Equations2019Ingår i: Computational Mathematics and Mathematical Physics, ISSN 0965-5425, E-ISSN 1555-6662, Vol. 59, nr 8, s. 1267-1274Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The paper presents the results on the use of gradient descent algorithms for constructing iterative methods for solving linear equations. A mathematically rigorous substantiation of the conver- gence of iterations to the solution of the equations is given. Numerical results demonstrating the effi- ciency of the modified iterative gradient descent method are presented.

  • 68.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektroteknik, matematik och naturvetenskap, Matematik.
    Shakhverdiev, Azizaga
    Russian State Geological Prospecting University, Moscow, 117997 Russia.
    Qualitative Analysis of Quadratic Polynomial Dynamical Systems Associated with the Modeling and Monitoring of Oil Fields2019Ingår i: Lobachevskii Journal of Mathematics, ISSN 1995-0802, E-ISSN 1818-9962, Vol. 40, nr 10, s. 1695-1710Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The behavior and properties of solutions of two-dimensional quadratic polynomial dynamical system on the phase plane of variables and time are considered. A complete qualitative theory is constructed which includes the analysis of all singular points and the features of solutions depending on all parameters of the problem. A main result is that, with the discriminant criteria created on the basis of the growth model constructed in the present study, it is possible to formulate practical recommendations for regulating and monitoring the process of waterflooding and the development of an oil field.

  • 69.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektroteknik, matematik och naturvetenskap, Matematik.
    Shakhverdiev, Azizaga
    S. Ordzhonikidze Russian State Geological Prospecting University, Moscow, Russia.
    Mandrik, I.E.
    LUKOIL, PJSC, Moscow, Russia.
    Arefiev, S.V.
    LUKOIL, Western Siberia, Kogalym, Russia.
    Alternative conception of the monitoring and optimization of water flooding of oil reservoirs  under instability of displacement front2019Ingår i: Oil industry (Neftyanoye khozyaystvo), ISSN 0028-2448, nr 12, s. 118-123Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The theory of Buckley and Leverett does not take into account the loss of stability of the displacement front whch provokes a stepwise change and the triple value of water saturation. Traditionally a mathematically simplified approach was proposed: a differentiable approximation to eliminate the ' jump' in water saturation. Such a simplified solution led to negative consequences well-know from the water flooding practice, recognized by experts as 'viscous instability of the displacement front' and 'fractal geometry of the displacement front'.The core of the issue is to attempt to predict the beginning of the stability loss of the front of oil displacement by water and to prevent its negative effect on the water flooding process under difficult conditions of interaction of hydro-thermodynamic, capillary, molecular, inertial, and gravitational forces. In this study, catastrophe theory methods applied for the analysis of nonlinear polynomial dynamical systems are used as a novel approach. namely, a mathematical growth model is developed and an inverse problem is formulated so that the initial coefficients of the system of differential equations for a two-phase flow can be determined using this model. A unified control parameter has been selected which enables one to propose and validate a discriminant criterion for  oil and water growth models for monitoring and optimization.

  • 70.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    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 Problems2018Ingår i: 2018 2ND URSI Atlantic Radio Science Meeting (AT-RASC), IEEE, 2018Konferensbidrag (Refereegranskat)
    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.

  • 71.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    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 waveguide2016Ingår i: 2016 URSI International Symposium on Electromagnetic Theory (EMTS), IEEE conference proceedings, 2016, s. 353-355Konferensbidrag (Refereegranskat)
    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.

  • 72.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smirnov, Yury
    Penza State University, Penza, Ryssland.
    Advanced mathematical techniques  for the analysis of inverse scattering  in waveguides2014Ingår i: Proceedings of the 7th International Conference Inverse Problems: Modeling and Simulation (IPMS 2014): Ölüdeniz, Fethiye, Turkey, May 22–30,2014 / [ed] A. Hasanov, 2014, s. 32-Konferensbidrag (Refereegranskat)
  • 73.
    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 waveguide2011Ingår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 27, nr 9, artikel-id 095010Artikel i tidskrift (Refereegranskat)
    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.

  • 74.
    Shestopalov, Yury
    et al.
    Karlstad University, Karlstad, Sweden.
    Smirnov, Yury
    Penza State University, Penza, Ryssland.
    Eigenwaves in Waveguides with Dielectric Inclusions : Spectrum2014Ingår i: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 93, nr 2, s. 408-427Artikel i tidskrift (Refereegranskat)
    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.

  • 75.
    Shestopalov, Yury
    et al.
    Karlstads universitet.
    Smirnov, Yury
    Penza State University, Penza, Ryssland.
    Eigenwaves in waveguides with dielectric inclusions: completeness2014Ingår i: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 93, nr 9, s. 1824-1845Artikel i tidskrift (Refereegranskat)
    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.

  • 76.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    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 results2014Ingår i: Progress in Electromagnetics Research Symposium: , Electromagnetics Academy , 2014, s. 2610-2613Konferensbidrag (Refereegranskat)
    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.

  • 77.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    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 problems2015Ingår i: PIERS 2015 Prague: Progress in Electromagnetics Research Symposium : Proceedings, Cambridge, MA: The Electromagnetics Academy , 2015, s. 1528-1532Konferensbidrag (Refereegranskat)
    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.

  • 78.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smirnov, Yury
    Penza State University, Penza, Russia.
    Il’inski, Anatolij
    Moscow MV Lomonosov State University, Moscow, Russia.
    Recent Progress in the Analysis of Mode Spectrum in Waveguides with Inclusions2015Ingår i: 2015 1st URSI Atlantic Radio Science Conference (URSI AT-RASC) / [ed] IEEE, New York: Institute of Electrical and Electronics Engineers (IEEE), 2015Konferensbidrag (Refereegranskat)
  • 79.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smirnov, Yury
    Penza State University, Penza, Ryssland.
    Kuzmina, Ekaterina
    Moscow State Technical University of Radio Engineering, Electronics and Automation, Moscow, Russia.
    Mathematical Aspects of the Theory of Wave Propagation in Metal-Dielectric Waveguides2014Ingår i: General Assembly and Scientific Symposium (URSI GASS), 2014 XXXIth URSI: Beijing, China,  August 16–23, 2014, IEEE Press, 2014Konferensbidrag (Refereegranskat)
    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 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.

  • 80.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smirnov, Yury
    Penza State University, Penza, Ryssland.
    Smolkin, Eugene
    Penza State University, Russia.
    New Propagation Regimes of Symmetric Hybrid Waves in a Nonlinear Metal-Dielectric Waveguide2018Ingår i: IET Conference Publications 2018, Piscataway, New Jersey, USA: IEEE, 2018, Vol. CP741, artikel-id 1570402136Konferensbidrag (Refereegranskat)
    Abstract [en]

    The propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear metal-dielectric waveguide is considered. The physical setting is reduced to a transmission eigenvalue problem for a system of ordinary differential equations which is new type of nonlinear eigenvalue problem where spectral parameters are the wave propagation constants. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 81.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smith, Paul
    Macquarie University, Sydney, Australia.
    Vinogradova, Elena
    Macquarie University, Sydney, Australia.
    The effect of inserts upon propagation modes in a waveguide2018Ingår i: Proceedings of 2018 International Conference on Electromagnetics in Advanced Application (ICEAA), Piscataway, New Jersey, USA: IEEE, 2018, s. 315-318, artikel-id 8520404Konferensbidrag (Refereegranskat)
    Abstract [en]

    When a perfectly electrically conducting (PEC) waveguide is perturbed by the insertion of a PEC structure aligned with its axis, its propagation constants are perturbed. The underlying boundary value problem may be converted to a homogeneous Fredholm matrix equation in which the propagation constants are found from the roots of the determinant of the matrix; stable and numerically efficient processes may be employed to find the propagation constants. There is no constraint on the size or shape of the inserts. As well as determining the empty waveguide parameters, this approach provides an estimate of the perturbation to the propagation constants of the empty waveguide.

  • 82.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smolkin, Eugene
    Penza State University, Russia.
    Kuzmina, Ekaterina
    Moscow Technologiical University MIREA, Moscow, Russia.
    Spectra of Nonselfadjoint Eigenvalue Problems for Elliptic Systems in Mathematical Models of the Wave Propagation in Open Waveguides2018Ingår i: Lobachevskii Journal of Mathematics, ISSN 1995-0802, E-ISSN 1818-9962, Vol. 39, nr 8, s. 1117-1129Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Statements and analysis are presented of nonselfadjoint eigenvalue problems for ellipticequations and systems, including singular Sturm–Liouville problems on the line, that arise inmathematical models of the wave propagation in open metal-dielectric waveguides. Existence ofreal and complex spectra are proved and their distribution is investigated for canonical structurespossessing circular symmetry of boundary contours.

  • 83.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektroteknik, matematik och naturvetenskap, Matematik.
    Smolkin, Eugene
    Smirnov, Yury
    Department of Mathematics and Supercomputing, Penza State University, Krasnaya Str. 40, Penza, 440026, Russia.
    On the existence of the nonlinear leaky TE-polarized waves in a metal–dielectric cylindrical waveguide2019Ingår i: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 91, artikel-id 102378Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider propagation of leaky waves in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green’s function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear leaky waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. Conditions under which a finite number of waves can propagate are obtained and the intervals of localization of the corresponding propagation constants are determined. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. In numerical experiments, two types of nonlinearities are considered and compared: Kerr nonlinearity and nonlinearity with saturation. New propagation regimes are discovered.

  • 84.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smolkin, Eugene
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.
    Snegur, M.
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.
    TE-polarized Wave Diffraction by a Cylinder Covered with Nonlinear Dielectric Layer2018Ingår i: Proceedings of 2018 IEEE Asia-Pacific Conference on Antennas and Propagation (APCAP), 2018, s. 321-322Konferensbidrag (Refereegranskat)
    Abstract [en]

    The problem of diffraction of TE polarized EM waves by an open dielectric waveguide with a nonlinear inhomogeneous filling is under consideration. In such problems a nonlinear eigenvalue problem for a system of differential equations is arised. For the numerical solution a method based on the solution of the auxillary Cauchy problem is proposed. Numerical results are presented.

  • 85.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektroteknik, matematik och naturvetenskap, Matematik.
    Smolkin, Eugene
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.
    Snegur, Maxim
    Department of Mathematics and Supercomputing, Penza State University, Penza, Russi.
    New Propagation Regimes of TE Waves in a Waveguide filled with a Nonlinear Dielectric Metamaterial2019Ingår i: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli: IEEE, 2019, artikel-id 8738241Konferensbidrag (Refereegranskat)
    Abstract [en]

    We consider propagation of surface TE waves in a circular metal-dielectric waveguide filled with nonlinear (Kerr nonlinearity) metamaterial medium. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the waveguide. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 86.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektroteknik, matematik och naturvetenskap, Matematik.
    Smolkin, Eugene
    Snegur, Maxim
    New propagation regimes of TM waves in a waveguide filled with a nonlinear dielectric metamaterial2019Ingår i: 2019 URSI International Symposium on Electromagnetic Theory, EMTS 2019, IEEE , 2019Konferensbidrag (Refereegranskat)
    Abstract [en]

    We consider propagation of surface TM waves in a circular metal-dielectric waveguide filled with nonlinear (Kerr nonlinearity) metamaterial medium. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the surface waves. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 87.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smolkin, Eugene
    Penza State University, Russia.
    Snegur, Maxim
    Penza State University, Russia.
    Numerical Study of Multilayer Nonlinear Inhomogeneous Goubau Lines2018Ingår i: Proceedings of the 2018 International Conference on Electromagnetics in Advanced Application (ICEAA), Piscataway, New Jersey, USA: IEEE conference proceedings, 2018, s. 126-129, artikel-id 8520464Konferensbidrag (Refereegranskat)
    Abstract [en]

    We consider propagation of surface TE waves in a circular metal-dielectric waveguide filled with nonlinear (Kerr nonlinearity) multilayered inhomogeneous medium. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the waveguide. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 88.
    Shestopalov, Yury
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektroteknik, matematik och naturvetenskap, Matematik.
    Smolkin, Eugene
    Penɀa State University, Penza, Russia.
    Snegur, Maxim
    Penɀa State University, Penza, Russia.
    Numerical study of nonlinear metamaterial rod2019Ingår i: 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2019, s. 0162-0164Konferensbidrag (Refereegranskat)
    Abstract [en]

    We consider propagation of leaky and surface TE waves in the rod filled with nonlinear metamaterial medium. The physical setting is reduced to a transmission eigenvalue problem for an ordinary differential equation. The eigenvalues of the problem are the wave propagation constants. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

  • 89.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Recent advances in the spectral theory of open structures: Existence and distribution of the spectra of running waves for a class of open waveguides2016Ingår i: Proceedings of the 2016 18th International Conference on Electromagnetics in Advanced Applications, ICEAA 2016, 2016, s. 370-373, artikel-id 7731402Konferensbidrag (Refereegranskat)
    Abstract [en]

    We give a general description of mathematical background and a resume of the results about existence and distribution of the spectra of running waves in open waveguides, including metal-dielectric waveguides with arbitrary cylindrical in-homogeneities, layered concentric dielectric waveguides of circular cross section and Goubau lines with layered dielectric covers. The newly obtained results are reported concerning singularities (resonant states) of the transmission coefficient in the problems of the wave scattering by parallel-plate dielectric slabs in a waveguide and free space. The findings are based on recent advances in the spectral theory of open structures.

  • 90.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Resonant states in waveguide transmission problems2015Ingår i: Progress in Electromagnetics Research B, ISSN 1937-6472, E-ISSN 1937-6472, Vol. 64, nr 1, s. 119-143Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove the existence of complex eigenfrequencies of open waveguide resonators in the form of parallel-plate waveguides and waveguides of rectangular crosssection containing layered dielectric inclusions. It is shown that complex eigenfrequencies are finite-multiplicity poles of the analytical continuation of the operator of the initial diffraction problem and its Green's function to a multi-sheet Riemann surface, and also of the transmission coefficient extended to the complex plane of some of the problem parameters. The eigenfrequencies are associated with resonant states (RSs) and eigenvalues of distinct families of Sturm-Liouville problems on the line; they form countable sets of points in the complex plane with the only accumulation point at infinity and depend continuously on the problem parameters. The set of complex eigenfrequencies is similar in its structure to the set of eigenvalues of a Laplacian in a rectangle. The presence of a resonance domain in the form of a parallel-plane layered dielectric insert removes the continuous frequency spectrum and gives rise to a discrete set of points shifted to (upper half of) the complex plane.

  • 91.
    Shestopalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Resonant states in waveguide transmission problems2015Ingår i: 2015 1st URSI Atlantic Radio Science Conference (URSI AT-RASC), New York: Institute of Electrical and Electronics Engineers (IEEE), 2015Konferensbidrag (Refereegranskat)
    Abstract [en]

    We prove the existence of complex eigenfrequencies of open waveguide resonators in the form of parallel-plate waveguides and waveguides of rectangular crosssection containing layered dielectric inclusions. It is shown that complex eigenfrequencies are finite-multiplicity poles of the analytical continuation of the operator of the initial diffraction problem and its Green's function to a multi-sheet Riemann surface, and also of the transmission coefficient extended to the complex plane of some of the problem parameters. The eigenfrequencies are associated with resonant states (RSs) and eigenvalues of distinct families of Sturm-Liouville problems on the line; they form countable sets of points in the complex plane with the only accumulation point at infinity and depend continuously on the problem parameters. The set of complex eigenfrequencies is similar in its structure to the set of eigenvalues of a Laplacian in a rectangle. The presence of a resonance domain in the form of a parallel-plane layered dielectric insert removes the continuous frequency spectrum and gives rise to a discrete set of points shifted to (upper half of) the complex plane.

  • 92.
    Shestopalov, Yury V.
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Podlipenko, Yuri
    T. Shevchenko Kyiv National University, Kyiv, Ukraine.
    Nakonechnyi, Olexandr
    T. Shevchenko Kyiv National University, Kyiv, Ukraine.
    Estimation of Parameters of Boundary Value Problems for Linear Ordinary Differential Equations with Uncertain Data2014Ingår i: Advances in Pure Mathematics, ISSN 2160-0368, E-ISSN 2160-0384, Vol. 4, nr 4, s. 118-146Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed here that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax mean square or guaranteed estimates. We establish that the minimax mean square estimates are expressed via solutions of some systems of differential equations of special type and determine estimation errors.

  • 93.
    Shestopalov, Yury V.
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smirnov, Yu.G.
    Penza State University, Penza, Russia.
    Derevyanchuk, E. D.
    Penza State University, Penza, Russia.
    Tensor permittivity reconstruction of multi-sectional diaphragm in a rectangular waveguide2016Ingår i: Proceedings of the 2016 18th International Conference on Electromagnetics in Advanced Applications, ICEAA 2016, 2016, s. 407-409, artikel-id 7731412Konferensbidrag (Refereegranskat)
    Abstract [en]

    This work is devoted to the development of a numerical-analytical method for solving the inverse problem of reconstructing tensor permittivity of a multi-sectional diaphragm in a rectangular waveguide. Numerical results are presented that confirm the efficiency of the proposed technique.

  • 94.
    Shestopalov, Yury V.
    et al.
    Karlstad University, Karlstad, Sweden.
    Smirnov, Yuri
    Penza State University, Penza, Russian Federation.
    Inverse scattering in guides2012Ingår i: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 346, nr 1, artikel-id 012019Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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 the transmission characteristics. The approach employs a volume singular integral equation (VSIE) method. The unique solvability of VSIE is established. The inverse problem is solved by the method of iterations applied to VSIE; the convergence of the method is proved.

  • 95.
    Shestopalov, Yury V.
    et al.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Smirnov, Yurij G.
    Penza State University, Penza, Russian Federation.
    Derevyanchuk, E. D.
    Penza State University, Penza, Russian Federation.
    Numerical-analytical method for reconstructing tensor permittivity and permeability of a diaphragm in a rectangular waveguide2016Ingår i: 2016 Progress In Electromagnetics Research Symposium, PIERS 2016 - Proceedings, 2016, s. 217-221, artikel-id 7734296Konferensbidrag (Refereegranskat)
    Abstract [en]

    A numerical-analytical method is developed for reconstructing tensor permittivity and permeability of a dielectric diaphragm in a rectangular waveguide. The techniques and obtained solutions can be implemented in practical measurements for the investigation of new artificial materials and media and can be applied in optics, nanotechnology, and design of microwave devices.

  • 96.
    Smirnov, A. P.
    et al.
    Lomonosov Moscow State University, Russia.
    Semenov, A. N.
    Lomonosov Moscow State University, Russia.
    Sheina, E. A.
    Lomonosov Moscow State University, Russia.
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Absorbing boundary conditions for FDTD analysis of rectangular waveguide with non-uniform dielectric inclusions2015Ingår i: 2015 1st URSI Atlantic Radio Science Conference (URSI AT-RASC), New York: Institute of Electrical and Electronics Engineers (IEEE), 2015Konferensbidrag (Refereegranskat)
    Abstract [en]

    When the finite-difference time-domain method is used for analysis of waveguide structures, incident waves are needed for calculating electromagnetic parameters and effective absorbing boundary conditions are required for terminating open waveguide structures.

  • 97.
    Smirnov, A. P.
    et al.
    Moscow MV Lomonosov State Univ, Moscow, Russia..
    Semenov, A. N.
    Moscow MV Lomonosov State Univ, Moscow, Russia..
    Shestopalov, Yury
    FDTD Simulation of Waveguide with Non-uniform Dielectric Slab2013Ingår i: PIERS 2013 STOCKHOLM: PROGRESS IN ELECTROMAGNETICS RESEARCH SYMPOSIUM, 2013, s. 76-83Konferensbidrag (Refereegranskat)
    Abstract [en]

    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.

  • 98. Smirnov, A. P.
    et al.
    Semenov, A. N.
    Shestoplalov, Yury V.
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Numerical analyze of waveguide transmission coefficient with non-uniform dielectric slab2014Ingår i: Progress in Electromagnetics Research Symposium, Electromagnetics Academy , 2014, s. 2619-2621Konferensbidrag (Refereegranskat)
    Abstract [en]

    Propagation in the time domain of electromagnetic waves in a rectangular waveguide with a 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 in different frequency ranges. Parallel high performance FDTD solver, based on Maxwell equations approximation in integral form on Yee lattice and developed by the paper authors is used. A method for calculating the transmission coefficient with respect to all the problem parameters is proposed. The method is based on the analysis of the amplitude of the scattered wave derived from FDTD numerical solution. The pure scattered field method is proposed to specify the waveguide mode with respect to numerical dispersion. Computations for nonstationary Maxwell equations system are performed for the H10-mode scattering from a dielectric slab placed in the waveguide. Multiple numerical computations for the corresponding large-scale problems have been performed on Lomonosov Moscow State University IBM BlueGene/P supercomputer. Using the methods described above, we compute the values of the waveguide transmission, attenuation and propagation factors in a wide range of permittivity and different positions of the dielectric slab inclusions. Continuous curves on the complex plane describing the dependence of the transmission coefficient on the dielectric constant are obtained. The comparison of the transmission coefficient calculated by the present approach and the volume integral equation method is performed.

  • 99.
    Smirnov, A. P.
    et al.
    Lomonosov Moscow State University, Russian Federation .
    Sheina, E. A.
    Lomonosov Moscow State University, Russian Federation .
    Shestopalov, Yury
    Högskolan i Gävle, Akademin för teknik och miljö, Avdelningen för elektronik, matematik och naturvetenskap, Matematik.
    Semenov, A. N.
    Lomonosov Moscow State University, Russian Federation .
    Numerical simulation of a nonuniform dielectric inclusion in a waveguide aimed at reconstructing its permittivity2015Ingår i: Proceedings of the 2015 International Conference on Electromagnetics in Advanced Applications: ICEAA 2015, IEEE Press, 2015, s. 419-421Konferensbidrag (Refereegranskat)
    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 nonstationary Maxwell’s equations with perfectly matched layer (PML) absorbing boundary conditions using the Berenger layout and estimate parameter ranges providing the prescribed accuracy for solving forward and inverse scattering problems for waveguides with inclusions.

  • 100.
    Smirnov, A.
    et al.
    Lomonosov Moscow State University, Moscow, Russian Federation.
    Semenov, A.
    Lomonosov Moscow State University, Moscow, Russian Federation.
    Shestopalov, Yury V.
    Karlstad University, Karlstad, Sweden.
    Modeling of Electromagnetic Wave Propagation in Guides with Inhomogeneous Dielectric Inclusions2013Ingår i: Springer Proceedings in Mathematics & statistics, ISSN 2194-1017, E-ISSN 2194-1009, Vol. 52, s. 113-118Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider scattering in the time domain of electromagnetic waves from inhomogeneous dielectric inclusions in a 3D waveguide of rectangular cross section. All electromagnetic field components are calculated, and transport of energy in the guide is investigated using finite difference time domain (FDTD) method in different frequency ranges. An efficient 3D FDTD EMWSolver3D solver for the nonstationary Maxwell equation system is used. The model computations are performed for the H10-mode scattering from parallelepiped-shaped dielectric inclusions. Attenuation and propagation factors are calculated for the transmitted modes and field distributions are visualized. The present method can be used for a wide class of waveguide problems that meet substantial difficulties as far as numerical solution by conventional FDTD methods is concerned due to complex geometries or computational requirements. The solver employs algorithms of parallel computations and is implemented on supercomputers of last generation for solving large-scale problems with characteristic matrix dimensions achieving 1012.

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