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Publications (10 of 98) 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, p. 1824-1845Article 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
Keywords
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, p. 408-427Article 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.

Keywords
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
Smirnov, A. P., Semenov, A. N. & Shestopalov, Y. (2013). FDTD Simulation of Waveguide with Non-uniform Dielectric Slab. In: PIERS 2013 STOCKHOLM: PROGRESS IN ELECTROMAGNETICS RESEARCH SYMPOSIUM. Paper presented at Progress In Electromagnetics Research Symposium, AUG 12-15, 2013, Stockholm, SWEDEN (pp. 76-83).
Open this publication in new window or tab >>FDTD Simulation of Waveguide with Non-uniform Dielectric Slab
2013 (English)In: PIERS 2013 STOCKHOLM: PROGRESS IN ELECTROMAGNETICS RESEARCH SYMPOSIUM, 2013, p. 76-83Conference paper, Published paper (Refereed)
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.

Series
Progress in Electromagnetics Research Symposium, ISSN 1559-9450
National Category
Other Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-38685 (URN)000361384200012 ()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: 2019-12-02Bibliographically 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, p. 135-167Article 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.

Keywords
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
Podlipenko, Y. & Shestopalov, Y. (2013). Guaranteed Estimates of Linear Continuous Functionals of Solutions and Right-hand Sides of the Helmholtz Equation in the Domains with Infinite Boundaries under Uncertainties. In: PIERS 2013 STOCKHOLM: PROGRESS IN ELECTROMAGNETICS RESEARCH SYMPOSIUM. Paper presented at Progress In Electromagnetics Research Symposium, AUG 12-15, 2013, Stockholm, SWEDEN (pp. 65-69).
Open this publication in new window or tab >>Guaranteed Estimates of Linear Continuous Functionals of Solutions and Right-hand Sides of the Helmholtz Equation in the Domains with Infinite Boundaries under Uncertainties
2013 (English)In: PIERS 2013 STOCKHOLM: PROGRESS IN ELECTROMAGNETICS RESEARCH SYMPOSIUM, 2013, p. 65-69Conference paper, Published paper (Refereed)
Abstract [en]

We consider the construction of guaranteed estimates of linear continuous function als of the unknown solutions and right-hand sides of the Helmholtz equation; the boundary value problems under study are associated with the wave diffraction by a bounded body D situated in a domain Omega is an element of R-n, n = 2, 3, whose boundary partial derivative Omega stretches to infinity (e.g., a wedge or a layer) and Green's function Phi(k) (x, y), (x, y is an element of Omega, x not equal y) corresponding to wave number k with k > 0 and boundary condition (I)k (x, y)vertical bar y is an element of Omega = 0 is known [4]. Here, for a function u(y) defined in (Omega) over bar Bu(y)vertical bar(y is an element of partial derivative Omega) + beta partial derivative u(y)/partial derivative y vertical bar(y is an element of partial derivative Q), alpha, beta = 0, 1, alpha + beta = 1, v is outward normal to aft We assume that right-hand sides of the equations entering the problem statement are not known; the only available information is that they belong to a bounded set of the space of square-integrable functions. In order to solve these estimation problems we need additional data: observations in the form of certain linear transformations of the solution distorted by noise. The latter are realizations of the random fields with the unknown second moment functions belonging to a given bounded set in the appropriate functional space. The approach set forth in and developed in this study allows us to obtain optimal estimates of the unknown solution or righthand sides of the equations and linear functionals, i.e., estimates sought in the class of functionals linear with respect to observations for which the maximal mean-square estimation error taken over all elements belonging to the aforementioned sets takes minimal value. Such estimates are called minimax or guaranteed estimates. We obtain representations for these estimates and estimation errors in terms of solutions to certain integro-differential or integral equations in bounded subdomains of domain Omega \ D.

Series
Progress in Electromagnetics Research Symposium, ISSN 1559-9450
National Category
Other Mathematics
Research subject
Mathematics; Mathematics
Identifiers
urn:nbn:se:kau:diva-38684 (URN)000361384200010 ()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: 2019-12-02Bibliographically 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, p. 388-393Article 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
Keywords
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, p. 113-118Conference 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
Keywords
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
Tomasek, P. & Shestopalov, Y. (2013). Parameter Optimization of Waveguide Filters Employing Analysis of Closed-form Solution. In: PIERS 2013  Stockholm: Progress In Electromagnetics Research Symposium. Paper presented at Progress in Electromagnetics Research Symposium, August 12-15, 2013, Stockholm, Sweden (pp. 296-299). Cambridge, MA: Electromagnetics Academy
Open this publication in new window or tab >>Parameter Optimization of Waveguide Filters Employing Analysis of Closed-form Solution
2013 (English)In: PIERS 2013  Stockholm: Progress In Electromagnetics Research Symposium, Cambridge, MA: Electromagnetics Academy , 2013, p. 296-299Conference paper, Published paper (Refereed)
Abstract [en]

This work aims at computation and optimization of transmission coefficients of waveguide filters formed by one- or multi-sectional diaphragms in a waveguide of rectangular cross-section. An approach for designing band-stop and band-pass filters is proposed employing analysis of closed-form solutions and numerical multi-parameter optimization.

Place, publisher, year, edition, pages
Cambridge, MA: Electromagnetics Academy, 2013
Series
Progress in Electromagnetics Research Symposium, ISSN 1559-9450
National Category
Other Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-38687 (URN)000361384200060 ()978-1-934142-26-4 (ISBN)
Conference
Progress in Electromagnetics Research Symposium, August 12-15, 2013, Stockholm, Sweden
Available from: 2015-11-23 Created: 2015-11-23 Last updated: 2019-12-02Bibliographically approved
Smirnov, Y. .., Shestopalov, Y. & Derevyanchuk, E. (2013). Permittivity determination of multi-sectional diaphragm with metamaterial layers in rectangular waveguide. In: : . Paper presented at Conference of Progress in Electromagnetics Research Symposium, PIERS 2013 Taipei ; Conference Date: 25 March 2013 Through 28 March 2013 (pp. 135-139).
Open this publication in new window or tab >>Permittivity determination of multi-sectional diaphragm with metamaterial layers in rectangular waveguide
2013 (English)Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we consider the inverse problem of the permittivity determination of a multi-sectional diaphragm with metamaterial layers. Based on the developed recursive method of the solution to the inverse problem we perform a detailed analysis for a three-sectional diaphragm. Copyright © 2013 The Electromagnetics Academy.

Keywords
Recursive methods, Inverse problems; Metamaterials; Permittivity, Diaphragms
National Category
Other Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-43956 (URN)2-s2.0-84877937493 (Scopus ID)978-1-934142-24-0 (ISBN)
Conference
Conference of Progress in Electromagnetics Research Symposium, PIERS 2013 Taipei ; Conference Date: 25 March 2013 Through 28 March 2013
Available from: 2016-06-30 Created: 2016-06-30 Last updated: 2019-12-02Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-2691-2820

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