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Shestopalov, Yury

Open this publication in new window or tab >>Diffraction of a TE-Polarized Wave by a Nonlinear Goubau Line### Smirnov, Yuri

### Smolkin, Eugene

### Shestopalov, Yury

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 54, no 1, p. 151-157Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Blackwell Publishing Ltd, 2019
##### Keywords

nonlinear waveguide, numerical method, TE polarization, the diffraction problem, Dielectric waveguides, Numerical methods, Analytical and numerical solutions, Diffraction problem, Kerr nonlinearity, Nonlinear metals, Nonlinear waveguides, Numerical results, TE polarizations, Transmitted field, Diffraction
##### National Category

Mathematics Other Engineering and Technologies
##### Identifiers

urn:nbn:se:hig:diva-30478 (URN)10.1029/2018RS006629 (DOI)000458731300012 ()2-s2.0-85060646358 (Scopus ID)
#####

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##### Projects

Largescale
##### Funder

Swedish Institute
##### Note

Department of Mathematics and Supercomputing, Penza State University, Russian Federation.

Department of Mathematics and Supercomputing, Penza State University, Russian Federation.

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.

The diffraction of a cylindrical wave by a nonlinear metal-dielectric waveguide filled with nonlinear medium is considered. Two widely used types of nonlinearities (Kerr nonlinearity and nonlinearity with saturation) are considered. The problem is to find amplitudes of the reflected and the transmitted fields when the amplitude of the incident field is known. The analytical and numerical solution techniques are developed. Numerical results are presented. ©2019. American Geophysical Union. All Rights Reserved.

Funding agencies:

- Ministry of Education and Science of the Russian Federation Grant no. 1.894.2017/4.6

- University of Gavle, Sweden

Available from: 2019-08-09 Created: 2019-08-09 Last updated: 2019-08-09Bibliographically approvedOpen this publication in new window or tab >>Inverse Scattering and Imaging Using Second Order Optical Nonlinearities### Khulbe, Manisha

### Tripathy, Malay Ranjan

### Parthasarathy, Harish

### Shestopalov, Yury

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); ### Lagovsky, Boris

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_1_j_idt188_j_idt202",{id:"formSmash:j_idt184:1:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2019 (English)In: 2019 6th International Conference on Signal Processing and Integrated Networks, SPIN 2019, IEEE, 2019, p. 1086-1089Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

IEEE, 2019
##### Keywords

Inverse scattering, least square estimation techniques, Optical nonlinearity, parameter extraction, permeability, permittivity, RF imaging, Electromagnetic fields, Electromagnetic wave diffraction, Mechanical permeability, Parameter estimation, Perturbation techniques, Signal processing, Least square estimation, Perturbation theory, Scattered electromagnetic fields, Second order optical nonlinearity, Third-order optical nonlinearities, Nonlinear optics
##### National Category

Signal Processing
##### Identifiers

urn:nbn:se:hig:diva-30501 (URN)10.1109/SPIN.2019.8711652 (DOI)2-s2.0-85066895033 (Scopus ID)9781728113791 (ISBN)
##### Conference

6th International Conference on Signal Processing and Integrated Networks, SPIN 2019, 7-8 March 2019, Noida, India
#####

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Available from: 2019-08-15 Created: 2019-08-15 Last updated: 2019-08-15Bibliographically approved

Ambedkar Institute of Advanced Communication Technologies and Research (AIACTR), Delhi, India.

Amity School of Engineerng and Technology, Amity University, Noida, India.

Netaji Subhash Institute of Technology (NSIT), N. Delhi, India.

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.

Russian Technological University, MIREA, Moscow, Russia.

In this paper a mathematical technique is developed to find the parameters of a medium in terms of its scattered electromagnetic fields. Optical nonlinearity plays an important role in finding the scattering parameters of a medium. Using perturbation theory and nonlinear inverse scattering techniques with first order, second order and third order optical nonlinearity we find scattered electromagnetic fields. Using error minimization techniques parameters are estimated in term of permittivity and permeability up to second order. © 2019 IEEE.

Open this publication in new window or tab >>Trigonometric and cylindrical polynomials and their applications in electromagnetics### Shestopalov, Yury

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504XArticle in journal (Refereed) Epub ahead of print
##### Abstract [en]

##### Place, publisher, year, edition, pages

Taylor & Francis, 2019
##### Keywords

cylindrical polynomials; dispersion equation; zeros; electromagnetic waves
##### National Category

Mathematics Electrical Engineering, Electronic Engineering, Information Engineering
##### Identifiers

urn:nbn:se:hig:diva-30485 (URN)10.1080/00036811.2019.1584290 (DOI)2-s2.0-85062349423 (Scopus ID)
#####

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Available from: 2019-08-12 Created: 2019-08-12 Last updated: 2019-08-12Bibliographically approved

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.

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.

Open this publication in new window or tab >>A nonlinear multiparameter EV problem### Angermann, L.

### Shestopalov, Yury V.

### Smirnov, Y. G.

### Yatsyk, V. V.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Progress In Electromagnetics Research Symposium: PIERS 2017, PIERS 2017: Nonlinear and Inverse Problems in Electromagnetics / [ed] Beilina L., Smirnov Y., Springer New York LLC , 2018, p. 55-70Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer New York LLC, 2018
##### Series

Springer Proceedings in Mathematics & Statistics (PROMS) ; 243
##### Keywords

Dispersion equations, Multi-parameter eigenvalue problems, Nonlinear spectral theory, Dispersion (waves), Integral equations, Inverse problems, Mathematical operators, Nonlinear equations, Wave propagation, Eigenvalue problem, Eigenvalues, Integral equation approaches, Multiparameters, Non-linear media, Nonlinear operator, Spectral theory, Eigenvalues and eigenfunctions
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:hig:diva-27866 (URN)10.1007/978-3-319-94060-1_5 (DOI)2-s2.0-85051146418 (Scopus ID)9783319940595 (ISBN)978-3-319-94060-1 (ISBN)
##### Conference

PIERS 2017
#####

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Available from: 2018-09-06 Created: 2018-09-06 Last updated: 2018-09-06Bibliographically approved

Institut für MathematikTechnische Universität Clausthal, Clausthal-Zellerfeld, Germany.

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.

Department of Mathematics and Supercomputing, Penza State University, Penza, Russia.

O.Ya. Usikov Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, Kharkiv, Ukraine.

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

Open this publication in new window or tab >>Complex waves in a dielectric waveguide### Shestopalov, Yury

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 82, p. 16-19Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2018
##### Keywords

Complex wave, Dielectric waveguide, Dispersion equation, Surface wave, Eigenvalues and eigenfunctions, Surface waves, Circular cross-sections, Complex waves, Dispersion equations, Eigenvalues, Half-line, Liouville problem, Symmetric complexes, Dielectric waveguides, complexity, dielectric property, eigenvalue, symmetry, wave dispersion
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:hig:diva-27648 (URN)10.1016/j.wavemoti.2018.07.005 (DOI)000444790500002 ()2-s2.0-85050078848 (Scopus ID)
#####

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Available from: 2018-08-15 Created: 2018-08-15 Last updated: 2018-10-15Bibliographically approved

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.

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

Open this publication in new window or tab >>Complex Waves in Multi-Layered Metal-Dielectric Waveguides### Kuzmina, E. A.

### Shestopalov, Yury

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Proceedings of the 2018 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2018, p. 122-125, article id 8520457Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Keywords

Dielectrics, Surface waves, Permittivity, Propagation constant, Media, Task analysis, Metals
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:hig:diva-28683 (URN)10.1109/ICEAA.2018.8520457 (DOI)2-s2.0-85057429240 (Scopus ID)978-1-5386-6763-7 (ISBN)978-1-5386-6762-0 (ISBN)978-1-5386-6761-3 (ISBN)
##### Conference

2018 International Conference on Electromagnetics in Advanced Applications (ICEAA), 10-14 September 2018, Cartagena des Indias, Colombia
#####

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Available from: 2018-11-27 Created: 2018-11-27 Last updated: 2018-12-10Bibliographically approved

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.

We consider normal waves in multi-layered dielectric rod and Goubau line that are basic types of open metal-dielectric waveguides. The dispersion equations are analyzed using the notion of generalized cylindrical polynomials and methods of calculating determinants of block-diagonal matrices. Suﬃcient conditions of the existence of symmetric waves are established.

Open this publication in new window or tab >>Creating Two-Dimensional Images of Objects with High Angular Resolution### Lagovsky, B. A.

### Samokhin, A. B.

### Shestopalov, Yury

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Proceedings of 2018 IEEE Asia-Pacific Conference on Antennas and Propagation (APCAP), 2018, p. 114-115Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Keywords

Signal resolution, Image resolution, Image reconstruction, Conferences, Integral equations, Antenna arrays, Solids, angular resolution, Rayleigh criterion, superresolution, two-dimensional linear integral equation
##### National Category

Other Mathematics Electrical Engineering, Electronic Engineering, Information Engineering
##### Identifiers

urn:nbn:se:hig:diva-28697 (URN)10.1109/APCAP.2018.8538220 (DOI)2-s2.0-85059420755 (Scopus ID)978-1-5386-5649-5 (ISBN)978-1-5386-5648-8 (ISBN)978-1-5386-5647-1 (ISBN)
##### Conference

2018 IEEE Asia-Pacific Conference on Antennas and Propagation (APCAP), 5-8 August 2018, Auckland, New Zealand
#####

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Available from: 2018-11-28 Created: 2018-11-28 Last updated: 2019-02-25Bibliographically approved

Deptartment of Applied Mathematics, Moscow Technological University, Moscow, Russian Federation.

Deptartment of Applied Mathematics, Moscow Technological University, Moscow, Russian Federation.

A new method of digital radar signal processing for remote sensing is proposed. The technique allows one to obtain two-dimensional images of objects with super resolution. The method is based on solving a convolution-type two- dimensional linear integral equation of the first kind by algebraic methods.

Open this publication in new window or tab >>Development of Numerical Techniques for Forward and Inverse Waveguide Scattering Problems### Shestopalov, Yury

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.### Sheina, Elena

### Smirnov, Alexander

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: 2018 2ND URSI Atlantic Radio Science Meeting (AT-RASC), IEEE, 2018Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

IEEE, 2018
##### National Category

Mathematics Other Engineering and Technologies
##### Identifiers

urn:nbn:se:hig:diva-28319 (URN)10.23919/URSI-AT-RASC.2018.8471577 (DOI)000462069500279 ()978-90-82598-73-5 (ISBN)
##### Conference

AT-RASC 2018, 2nd URSI Atlantic Radio Science Meeting, 28 May-1 June 2018, Meloneras, Gran Canaria, Spain
#####

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Available from: 2018-10-15 Created: 2018-10-15 Last updated: 2019-08-15Bibliographically approved

M. V. Lomonosov Moscow State University, Moscow, Russia.

M. V. Lomonosov Moscow State University, Moscow, Russia.

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.

Open this publication in new window or tab >>Diffraction of TM Polarized EM Waves by a Nonlinear Inhomogeneous Dielectric Cylinder### Smolkin, Eugene

### Snegur, Maxim

### Shestopalov, Yury

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 2018, p. 66-70Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Keywords

Electromagnetics, Optical waveguides, Nonhomogeneous media, Dielectrics, Electromagnetic scattering, Permittivity
##### National Category

Electrical Engineering, Electronic Engineering, Information Engineering Mathematics
##### Identifiers

urn:nbn:se:hig:diva-29194 (URN)10.23919/PIERS.2018.8598028 (DOI)000458673700007 ()2-s2.0-85060956964 (Scopus ID)978-4-88552-315-1 (ISBN)
##### Conference

2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 1-4 August 2018, Toyama, Japan
#####

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##### Funder

Swedish Institute
##### Note

Penza State University, Penza, Russia.

Penza State University, Penza, Russia.

In this work, we consider the diffraction of TM waves by a nonlinear inhomogeneous dielectric cylinder. Numerical experiments are carried out for the nonlinearity with saturation. The physical problem is reduced to solving a nonlinear boundary value problem for a system of ordinary differential equations. Numerical results are obtained using a modification of the shooting method which makes it possible to determine and plot the amplitude of the reflected field with respect to the amplitude of the incident field. Comparison between the nonlinear problem and the corresponding linear setting is performed.

Funding:

- RFBR 18-31-00109- University of Gävle

Available from: 2019-02-25 Created: 2019-02-25 Last updated: 2019-08-12Bibliographically approvedOpen this publication in new window or tab >>Discretization Methods for Three-Dimensional Singular Integral Equations of Electromagnetism### Samokhin, Alexander

### Samokhina, Anna

### Shestopalov, Yury

University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Differential equations, ISSN 0012-2661, E-ISSN 1608-3083, Vol. 54, no 9, p. 1225-1235Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer Berlin/Heidelberg, 2018
##### Keywords

Linear operator equations, volume singular integral equations, iterations, dielectric bodies
##### National Category

Computational Mathematics
##### Identifiers

urn:nbn:se:hig:diva-27910 (URN)10.1134/S0012266118090100 (DOI)000448479100010 ()2-s2.0-85054637275 (Scopus ID)
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##### Note

Moscow Technical University MIREA, Moscow, Russia.

Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia.

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

Funding:

Ministry of Education and Science of the Russian Federation grant no: 2.1361.2017/4.6

Available from: 2018-09-17 Created: 2018-09-17 Last updated: 2018-11-27Bibliographically approved