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  • 1.
    Beilina, Larissa
    et al.
    Chalmers University, Gothenburg University.
    Shestopalov, YuriKarlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Inverse problems and large-scale computations2013Conference proceedings (editor) (Refereed)
  • 2.
    Derevyanchuk, E.
    et al.
    Russia .
    Smirnov, Yurij
    Russia.
    Shestopalov, Yuri
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Permittivity determination of thin multi-sectional diaphragms in a rectangular waveguide2013In: Proceedings of the International Conference Days on Diffraction 2013, 2013, 32-35 p., 6712799Conference 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.

  • 3.
    Fuchs, Jürgen
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering.
    Stolin, AlexanderAbramov, ViktorPaal, EugenShestopalov, YouriSilvestrov, Sergei
    Algebra, Geometry, and Mathematical Physics 20102012Conference proceedings (editor) (Refereed)
  • 4. Il'inskij, A.
    et al.
    Chernokozhin, E.
    Shestopalov, Youri
    Development of Operator Methods for the Problem of Normal Waves in Coupled Microstrip Lines with Multilayered Substrate1984In: Mathematical Models of Applied Electrodynamics, pp. 116-136, Moscow: Moscow State Univ. Publ. House , 1984Chapter in book (Refereed)
  • 5.
    Karchevskiy, Evgueni
    et al.
    Russia.
    Shestopalov, Yuri
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Mathematical and numerical analysis of dielectric waveguides by the integral equation method2013In: Progress in Electromagnetics Research Symposium, ISSN 1559-9450, 388-393 p.Article in journal (Refereed)
    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.

  • 6. Kotik, N.
    et al.
    Shestopalov, Youri
    Approximate decomposition for the solution of boundary value problems for elliptic systems arising in mathematical models of layered structures2006In: Proc. Progress in Electromagnetics Research Symposium, Cambridge MA, USA, March 27-31,2006, pp. 514518Article in journal (Refereed)
  • 7. Kotik, Nikolai
    et al.
    Lestelius, Magnus
    Karlstad University, Faculty of Technology and Science, Department of Chemical Engineering. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Paper Surface Centre. Karlstad University, Faculty of Technology and Science, Materials Science.
    Shestopalov, Youri
    Modelling and Simulation of the Printing Plate-Contact System2006Conference paper (Refereed)
  • 8.
    Podlipenko, Yury
    et al.
    Russia.
    Shestopalov, Yuri
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Guaranteed Estimates of Functionals from Solutions and Data of Interior Maxwell Problems Under Uncertainties2013In: Springer Proceedings in Mathematics & statistics, ISSN 2194-1017, E-ISSN 2194-1009, Vol. 52, 135-167 p.Article in journal (Refereed)
    Abstract [en]

    We are looking for linear with respect to observations optimal estimates of solutions and right-hand sides of Maxwell equations called minimax or guaranteed estimates. We develop constructive methods for finding these estimates and estimation errors which are expressed in terms of solutions to special variational equations and prove that Galerkin approximations of the obtained variational equations converge to their exact solutions. © Springer International Publishing Switzerland 2013.

  • 9.
    Podlipenko, Yury
    et al.
    Kiev Natl Univ, Kiev, Ukraine..
    Shestopalov, Yuri V.
    Karlstad University.
    Guaranteed Estimates of Linear Continuous Functionals of Solutions and Right-hand Sides of the Helmholtz Equation in the Domains with Infinite Boundaries under Uncertainties2013In: PIERS 2013 STOCKHOLM: PROGRESS IN ELECTROMAGNETICS RESEARCH SYMPOSIUM, 2013, 65-69 p.Conference 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.

  • 10.
    Samokhin, Alexander
    et al.
    Moscow State Tech Univ Radio Engn & Automat, Moscow 117648, Russia..
    Shestopalov, Youri
    Karlstad University, Division for Engineering Sciences, Physics and Mathematics.
    Kobayashi, Kazuya
    Chuo Univ, Bunkyo Ku, Tokyo 1128551, Japan.
    Stationary iteration methods for solving 3D electromagnetic scattering problems2013In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 222, 107-122 p.Article in journal (Refereed)
    Abstract [en]

    Generalized Chebyshev iteration (GCI) applied for solving linear equations with nonselfadjoint operators is considered. Sufficient conditions providing the convergence of iterations imposed on the domain of localization of the spectrum on the complex plane are obtained. A minimax problem for the determination of optimal complex iteration parameters is formulated. An algorithm of finding an optimal iteration parameter in the case of arbitrary location of the operator spectrum on the complex plane is constructed for the generalized simple iteration method. The results are applied to numerical solution of volume singular integral equations (VSIEs) associated with the problems of the mathematical theory of wave diffraction by 3D dielectric bodies. In particular, the domain of the spectrum location is described explicitly for low-frequency scattering problems and in the general case. The obtained results are discussed and recommendations concerning their applications are given. (C) 2013 Elsevier Inc. All rights reserved.

  • 11. Schuermann, H.W.
    et al.
    Serov, V.S.
    Shestopalov, Youri
    Solutions to the Helmholtz equation for TE-guided waves in a three-layer structure with Kerr-type nonlinearity,2002In: J. Phys. A: Math. Gen., vol. 35, 50, pp. 10789-10801 (2002)Article in journal (Refereed)
  • 12. Shestopalov, Youri
    A Method of Calculating the Characteristic Numbers of a Meromorphic Operator-Function1985In: Zh. Vych. Matem. Matem. Fiz., 1985, Vol. 25, no 9, pp. 1413-1416Article in journal (Refereed)
  • 13. Shestopalov, Youri
    Advances in Mathematical Methods for Electromagnetics: Nonlinear Problems and Nonselfadjoint Operator Theory2006Conference paper (Refereed)
  • 14. Shestopalov, Youri
    Application of the Method of Generalized Potentials in Some Problems of Wave Propagation and Diffraction1990In: Zh. Vych. Matem. Matem. Fiz., 1990, Vol. 30, no 7, pp. 1081-1092Article in journal (Refereed)
  • 15. Shestopalov, Youri
    Approximate decomposition for the solution of impedance boundary value problems of electromagnetics2007Conference paper (Refereed)
  • 16. Shestopalov, Youri
    High-Q and Low-Q Resonators: Methods, Results, and Perspectives1998Conference paper (Refereed)
  • 17. Shestopalov, Youri
    Interaction of Oscillations in Slotted Resonators2001Conference paper (Refereed)
  • 18. Shestopalov, Youri
    Justification of a Method for Calculating the Normal Waves1979In: Vestnik Mosk. Gos. Univ., 1979, ser. 15, no 1, pp. 14-20Article in journal (Refereed)
  • 19. Shestopalov, Youri
    Justification of the Spectral Method for Calculating Normal Waves of Transmission Lines1980In: Diff. Uravn., 1980, Vol. 16, no 8, pp. 1504-1512Article in journal (Refereed)
  • 20. Shestopalov, Youri
    Nonlinear Eigenvalue Problems in Electrodynamics1993In: Electromagnetics, 1993, Vol. 13, no 2, pp. 5-18Article in journal (Refereed)
  • 21. Shestopalov, Youri
    Nonselfadjoint boundary eigenvalue problems of electromagnetics in open domains2007Conference paper (Refereed)
  • 22. Shestopalov, Youri
    Normal Modes of Bare and Shielded Slot Lines Formed by Domains of Arbitrary Cross Section1986In: Dokl. Akad. Nauk SSSR, 1986, Vol. 289, no 4, pp. 616-618Article in journal (Refereed)
  • 23. Shestopalov, Youri
    On a Spectrum of the Family of Nonselfadjoint Boundary Value Problems for the System of Helmholtz Equations1981In: Zh. Vych. Matem. Matem. Fiz., 1981, Vol. 21, no 6, pp. 1459--1470Article in journal (Refereed)
  • 24.
    Shestopalov, Youri
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    On Explicit Solutions to the Problem of Plane Wave Diffraction by Kerr-type Nonlinear Dielectric Layer2009In: Proceedings of the PIER Symposium, Cambridge, MA: EM Academy (MIT) , 2009, 774- p.Conference paper (Refereed)
  • 25. Shestopalov, Youri
    On the Theory of Cylindrical Resonators1991In: Math. Methods in the Applied Sciences, 1991, Vol. 14, pp. 355-375Article in journal (Refereed)
  • 26. Shestopalov, Youri
    Potential Theory for the Helmholtz Operator and Nonlinear Eigenvalue Problems1992In: Potential Theory, pp. 281-290 / [ed] M. Kishi, Berlin, New York: W. de Gruyter , 1992Chapter in book (Refereed)
  • 27. Shestopalov, Youri
    Properties of the Spectrum of a Class of Nonselfadjoint Boundary Value Problems for the Systems of Helmholtz Equations1980In: Dokl. Akad. Nauk SSSR, 1980, Vol. 252, no 5, pp. 1108--1111Article in journal (Refereed)
  • 28. Shestopalov, Youri
    Resonance Scattering by a Dielectric Cylinder2005In: J. Comm. Tech. Elec., 2005, Vol. 50, no 2, pp. 172-179Article in journal (Refereed)
  • 29. Shestopalov, Youri
    Scattering from a Thin Rectangular Dielectric Cylinder2003Conference paper (Refereed)
  • 30. Shestopalov, Youri
    Scattering Frequencies in Planar Domains with Noncompact Boundaries1997In: Modern Mathematical Methods in Diffraction Theory and its Applications in Engineering, pp. 227-233 / [ed] E. Meister, Frankfurt am Main: Peter Lang , 1997Chapter in book (Refereed)
  • 31. Shestopalov, Youri
    Scattering Frequencies of a Thin Rectangular Dielectric Cylinder2004Conference paper (Refereed)
  • 32. Shestopalov, Youri
    Seminars on Numerical Analysis1996Book (Refereed)
  • 33. Shestopalov, Youri
    Solitary waves in unbounded cubic-nonlinear media2005Conference paper (Refereed)
  • 34. Shestopalov, Youri
    Study of Spectral Problems of the Theory of Wave Propagation in the Complete Electrodynamical Statement1985In: Dokl. Akad. Nauk SSSR, 1985, Vol. 280, no 6, pp. 1235-1239Article in journal (Refereed)
  • 35. Shestopalov, Youri
    The Discrete Spectrum of Natural Waves of a Screened Open Slot Line1983In: USSR Comp. Maths. Math. Phys., 1983, Vol. 23, no 6, pp. 67-74Article in journal (Refereed)
  • 36. Shestopalov, Youri
    Theory of Nonselfadjoint Operator-Valued Functions and the Development of Mathematical Methods for Electromagnetics2006Conference paper (Refereed)
  • 37. Shestopalov, Youri
    et al.
    Chernokozhin, E.
    Boundary Integral Equations as Operator-valued Functions of Complex Frequency Parameter with Applications to the Wave Scattering1997Conference paper (Refereed)
  • 38. Shestopalov, Youri
    et al.
    Chernokozhin, E.
    Fredholm Property of an Integral Operator with the Kernel Having a Weak Singularity1982In: Vestnik Mosk. Gos. Univ., 1982, Ser. 15, no 1, pp.23-28Article in journal (Refereed)
  • 39. Shestopalov, Youri
    et al.
    Chernokozhin, E.
    Mathematical Methods for the Study of Wave Scattering by Open Cylindrical Structures1997In: J. Comm. Tech. Elec., 1997, Vol. 42, no 11, pp. 1211-1223Article in journal (Refereed)
  • 40. Shestopalov, Youri
    et al.
    Chernokozhin, E.
    Resonant and Nonresonant Diffraction by Open Image-type Slotted Structures2001In: IEEE Trans. Antennas Propag., 2001, Vol. 49, no 5, pp. 793-801Article in journal (Refereed)
  • 41. Shestopalov, Youri
    et al.
    Chernokozhin, E.
    Solvability of Boundary Value Problems for the Helmholtz Equation in an Unbounded Domain with Noncompact Boundary1998In: Diff. Equations, 1998, Vol. 34, no 4, pp. 546-553Article in journal (Refereed)
  • 42. Shestopalov, Youri
    et al.
    Il'inskij, A.
    Application of the Method of Integral Equations for Calculating the Propagation Constants in Microstrip Lines1978In: Numerical Methods of Electrodynamics, pp.3-21, Moscow: Moscow State Univ. Publ. House , 1978Chapter in book (Refereed)
  • 43. Shestopalov, Youri
    et al.
    Il'inskij, A.
    Diffraction by the Slot in the Perfectly Conducting Plane Screen on the Boundary Between Two Different Media1978In: Numerical Analysis and Computer Science, Vol. 28, pp. 70-89, Moscow: Moscow State Univ. Publ. House , 1978Chapter in book (Refereed)
  • 44. Shestopalov, Youri
    et al.
    Il'inskij, A.
    Mathematical Model for the Problem of Wave Propagation in Microstrip Devices1980In: Numerical Analysis and Computer Science, Vol. 32, pp. 85-103, Moscow: Moscow State Univ. Publ. House , 1980Chapter in book (Refereed)
  • 45. Shestopalov, Youri
    et al.
    Il'inskij, A.
    Chernokozhin, E.
    Development of Operator Methods for the Problem of Normal Waves in Coupled Microstrip Lines with Multilayered Substrate1984In: Mathematical Models of Applied Electrodynamics, pp. 116-136, Moscow: Moscow State Univ. Publ. House , 1984Chapter in book (Refereed)
  • 46.
    Shestopalov, Youri
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Kobayashi, K
    Smirnov, Y
    Investigation of Electromagnetic Diffraction by a Dielectric Body in a Waveguide using the Method of Volume Singular Integral Equation2009In: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 70, no 3, 969-983 p.Article in journal (Refereed)
    Abstract [en]

    The problem of diffraction of an electromagnetic field by a locally nonhomogeneous body in a perfectly conducting waveguide of rectangular cross section isconsidered. This problem is reduced to solving a volume singular integral equation (VSIE). The examination of this equation is based on the analysis of the corresponding boundary value problem(BVP) for the system of Maxwell's equations and the equivalence of this BVP and VSIE. The existence and uniqueness for VSIE in the space of square-integrable functions are proved. A numerical Galerkin method for the solution of VSIE is proposed, and its convergence is proved

  • 47. Shestopalov, Youri
    et al.
    Kotik, N.
    Development of the Method of Approximate Decomposition for the Solution of Boundary Value Problems for Elliptic Systems in Three-Dimensional Case2007Conference paper (Refereed)
  • 48. Shestopalov, Youri
    et al.
    Kotik, N.
    Solution to mixed boundary-contact problems by the method of integral equations2005Conference paper (Refereed)
  • 49. Shestopalov, Youri
    et al.
    Kotik, Nikolai
    Analysis of mixed boundary-value problems for a system of elliptic equations in the layer associated with boundary-contact problems of elasticity2005Conference paper (Refereed)
  • 50. Shestopalov, Youri
    et al.
    Kotik, Nikolai
    and Interaction of Waves in Gamma- and Cross-Shaped Slotted Waveguides2002Conference paper (Refereed)
12 1 - 50 of 98
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