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Publications (10 of 94) Show all publications
Shestopalov, Y. & Smirnov, Y. (2014). Eigenwaves in waveguides with dielectric inclusions: completeness. Applicable Analysis, 93(9), 1824-1845.
Open this publication in new window or tab >>Eigenwaves in waveguides with dielectric inclusions: completeness
2014 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 93, no 9, 1824-1845 p.Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Taylor & Francis, 2014
Keyword
eigenwave, waveguide, pencil, spectrum, completeness, basis
National Category
Mathematics
Identifiers
urn:nbn:se:kau:diva-41585 (URN)10.1080/00036811.2013.850494 (DOI)000339059500003 ()
Available from: 2016-04-25 Created: 2016-04-11 Last updated: 2017-11-30Bibliographically approved
Shestopalov, Y. & Smirnov, Y. (2014). Eigenwaves in waveguides with dielectric inclusions: spectrum. Applicable Analysis, 93(2), 408-427.
Open this publication in new window or tab >>Eigenwaves in waveguides with dielectric inclusions: spectrum
2014 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 93, no 2, 408-427 p.Article in journal (Refereed) Published
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.

Keyword
eigenwave, waveguide, pencil, spectrum, dielectric, inclusion, 45E99, 31B20, 83C50, 74S10
National Category
Mathematics
Identifiers
urn:nbn:se:kau:diva-41553 (URN)10.1080/00036811.2013.778980 (DOI)000331601900012 ()
Available from: 2016-04-25 Created: 2016-04-11 Last updated: 2017-11-30Bibliographically approved
Podlipenko, Y. & Shestopalov, Y. (2013). Guaranteed Estimates of Functionals from Solutions and Data of Interior Maxwell Problems Under Uncertainties. Springer Proceedings in Mathematics & statistics, 52, 135-167.
Open this publication in new window or tab >>Guaranteed Estimates of Functionals from Solutions and Data of Interior Maxwell Problems Under Uncertainties
2013 (English)In: Springer Proceedings in Mathematics & statistics, ISSN 2194-1017, E-ISSN 2194-1009, Vol. 52, 135-167 p.Article in journal (Refereed) Published
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. © Springer International Publishing Switzerland 2013.

Keyword
Estimation, Constructive methods; Estimation errors; Exact solution; Functionals; Galerkin approximations; Optimal estimates; Right-hand sides; Variational equations, Uncertainty analysis
National Category
Other Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-44270 (URN)10.1007/978-3-319-00660-4_10 (DOI)2-s2.0-84885690338 (Scopus ID)
Available from: 2016-07-01 Created: 2016-07-01 Last updated: 2017-11-28Bibliographically approved
Beilina, L. & Shestopalov, Y. (Eds.). (2013). Inverse problems and large-scale computations. Springer, 52.
Open this publication in new window or tab >>Inverse problems and large-scale computations
2013 (English)Conference proceedings (editor) (Refereed)
Place, publisher, year, edition, pages
Springer, 2013
Series
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1017, E-ISSN 2194-1009 ; 52
National Category
Other Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-44272 (URN)10.1007/978-3-319-00660-4 (DOI)2-s2.0-84892763521 (Scopus ID)978-3-319-00659-8 (ISBN)978-3-319-00660-4 (ISBN)
Available from: 2016-07-01 Created: 2016-07-01 Last updated: 2017-10-30Bibliographically approved
Karchevskiy, E. & Shestopalov, Y. (2013). Mathematical and numerical analysis of dielectric waveguides by the integral equation method. Paper presented at PIERS 2013 - Conference of Progress in Electromagnetics Research Symposium, Stockholm, 12-15 August 2013. Progress in Electromagnetics Research Symposium, 388-393.
Open this publication in new window or tab >>Mathematical and numerical analysis of dielectric waveguides by the integral equation method
2013 (English)In: Progress in Electromagnetics Research Symposium, ISSN 1559-9450, 388-393 p.Article in journal (Refereed) Published
Abstract [en]

The eigenvalue problems for generalized natural modes of an inhomogeneous dielectric waveguide without a sharp boundary and a step-index dielectric waveguide with a smooth boundary of cross-section are formulated as problems for the set of time-harmonic Maxwell equations with partial radiation conditions at infinity in the cross-sectional plane. The original problems are reduced by the integral equation method to nonlinear spectral problems with Fredholm integral operators. Properties of the spectrum are investigated. The Galerkin and collocation methods for the calculations of generalized natural modes are proposed and convergence of the methods is proved. Some results of numerical experiments are discussed.

Place, publisher, year, edition, pages
Cambridge, USA: Electromagnetics Academy, 2013
Keyword
Collocation method; Eigenvalue problem; Fredholm integral; Inhomogeneous dielectrics; Integral equation methods; Numerical experiments; Partial radiation conditions; Time-harmonic maxwell equations, Eigenvalues and eigenfunctions; Integral equations, Dielectric waveguides
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-43866 (URN)2-s2.0-84884766642 (Scopus ID)
Conference
PIERS 2013 - Conference of Progress in Electromagnetics Research Symposium, Stockholm, 12-15 August 2013
Available from: 2016-06-30 Created: 2016-06-30 Last updated: 2017-11-28Bibliographically approved
Smirnov, A., Semenov, A. & Shestopalov, Y. (2013). Modeling of Electromagnetic Wave Propagation in Guides with Inhomogeneous Dielectric Inclusions. In: Larisa Beilina, Yury V. Shestopalov (Ed.), Inverse Problems and Large-Scale Computations: . Paper presented at Second Annual Workshop on Inverse Problems and the Workshop on Large-Scale Modeling, Sunne, Sweden, May 1-6 2012. (pp. 113-118). Springer, 52.
Open this publication in new window or tab >>Modeling of Electromagnetic Wave Propagation in Guides with Inhomogeneous Dielectric Inclusions
2013 (English)In: Inverse Problems and Large-Scale Computations / [ed] Larisa Beilina, Yury V. Shestopalov, Springer, 2013, Vol. 52, 113-118 p.Conference paper, Published paper (Refereed)
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.

Place, publisher, year, edition, pages
Springer, 2013
Series
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1017, E-ISSN 2194-1009 ; 52
Keyword
Acoustics; Electromagnetic fields; Electromagnetic wave propagation; Electromagnetic waves; Finite difference time domain method; Supercomputers; Three dimensional; Waveguides, Characteristic matrices; Computational requirements; Dielectric inclusions; Electromagnetic field components; Finite-difference time-domain (FDTD) methods; Inhomogeneous dielectrics; Parallel Computation; Rectangular cross-sections, Time domain analysis
National Category
Other Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-44269 (URN)10.1007/978-3-319-00660-4_8 (DOI)2-s2.0-84892698056 (Scopus ID)978-3-319-00660-4 (ISBN)
Conference
Second Annual Workshop on Inverse Problems and the Workshop on Large-Scale Modeling, Sunne, Sweden, May 1-6 2012.
Available from: 2016-07-01 Created: 2016-07-01 Last updated: 2017-10-30Bibliographically approved
Derevyanchuk, E., Smirnov, Y. & Shestopalov, Y. (2013). Permittivity determination of thin multi-sectional diaphragms in a rectangular waveguide. In: Proceedings of the International Conference Days on Diffraction 2013: . Paper presented at 2013 International Conference Days on Diffraction, St. Petersburg, 27-31 May 2013 (pp. 32-35). , Article ID 6712799.
Open this publication in new window or tab >>Permittivity determination of thin multi-sectional diaphragms in a rectangular waveguide
2013 (English)In: Proceedings of the International Conference Days on Diffraction 2013, 2013, 32-35 p., 6712799Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we consider the inverse problem of the permittivity determination of thin multisectional diaphragm in a rectangular waveguide. We perform a detailed analysis for one-, two- and three-sectional thin diaphragms. Numerical results are presented.

Keyword
Diffraction; Inverse problems; Permittivity; Rectangular waveguides, Numerical results; Thin diaphragms, Diaphragms
National Category
Other Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-44290 (URN)10.1109/DD.2013.6712799 (DOI)2-s2.0-84893951479 (Scopus ID)
Conference
2013 International Conference Days on Diffraction, St. Petersburg, 27-31 May 2013
Available from: 2016-07-01 Created: 2016-07-01 Last updated: 2016-07-01Bibliographically approved
Smirnov, Y. G. G., Shestopalov, Y. & Derevyanchuk, E. D. (2013). Reconstruction of Permittivity and Permeability Tensors of Anisotropic Materials in a Rectangular Waveguide from the Reflection and Transmission Coefficients at Different Frequencies. In: PIERS 2013 STOCKHOLM: Progress In Electromagnetics Research Symposium. Paper presented at Progress In Electromagnetics Research Symposium, AUG 12-15, 2013, Stockholm, SWEDEN (pp. 290-295). .
Open this publication in new window or tab >>Reconstruction of Permittivity and Permeability Tensors of Anisotropic Materials in a Rectangular Waveguide from the Reflection and Transmission Coefficients at Different Frequencies
2013 (English)In: PIERS 2013 STOCKHOLM: Progress In Electromagnetics Research Symposium, 2013, 290-295 p.Conference paper, Published paper (Refereed)
Abstract [en]

This paper is devoted to the study of inverse problem of the permittivity and permeability tensor reconstruction of anisotropic materials in the form of diaphragms (sections) in a single-mode waveguide of rectangular cross section from the transmission and reflection coefficients measured. Results of numerical modeling are presented for different types of anisotropic materials. The developed solution techniques for the inverse problem under study can be applied in optics, nanotechnology, and design of microwave devices.

Series
Progress in Electromagnetics Research Symposium, ISSN 1559-9450
National Category
Other Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-38686 (URN)000361384200059 ()978-1-934142-26-4 (ISBN)
Conference
Progress In Electromagnetics Research Symposium, AUG 12-15, 2013, Stockholm, SWEDEN
Available from: 2015-11-23 Created: 2015-11-23 Last updated: 2016-06-09Bibliographically approved
Samokhin, A., Shestopalov, Y. & Kobayashi, K. (2013). Stationary iteration methods for solving 3D electromagnetic scattering problems. Applied Mathematics and Computation, 222, 107-122.
Open this publication in new window or tab >>Stationary iteration methods for solving 3D electromagnetic scattering problems
2013 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 222, 107-122 p.Article in journal (Refereed) Published
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. (C) 2013 Elsevier Inc. All rights reserved.

Keyword
Generalized Chebyshev iteration, Optimal iteration parameters, Localization of the spectrum, Volume singular integral equations
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-38586 (URN)10.1016/j.amc.2013.07.019 (DOI)000326877300011 ()
Available from: 2015-11-30 Created: 2015-11-23 Last updated: 2017-12-01Bibliographically approved
Fuchs, J., Stolin, A., Abramov, V., Paal, E., Shestopalov, Y. & Silvestrov, S. (Eds.). (2012). Algebra, Geometry, and Mathematical Physics 2010. Institute of Physics Publishing (IOPP).
Open this publication in new window or tab >>Algebra, Geometry, and Mathematical Physics 2010
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2012 (English)Conference proceedings (editor) (Refereed)
Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2012
Series
Journal of Physics: Conference Series, ISSN 1742-6588 ; 346
National Category
Mathematics
Identifiers
urn:nbn:se:kau:diva-15463 (URN)10.1088/1742-6596/346/1/011001 (DOI)
Available from: 2012-11-08 Created: 2012-11-08 Last updated: 2016-06-09Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-2691-2820

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