differential equations,
boundary value problems in electromagnetics,
eigenvalue problens,
supercomputing.
UDC:
517.958, 519.634
Subject:
Partial differential equations, eigenvalue problens, pseudodifferential and integral equations, boundary value problems in electromagnetics, inverse problems, numerical methods, supercomputing
Main publications:
K. Kobayashi, Yu.V. Shestopalov, Yu.G. Smirnov, “Investigation of Electromagnetic Diffraction by a Dielectric Body in a Waveguide Using the Method of Volume Singular Integral Equation”, SIAM Journal of Applied Mathematics, 70:3 (2009), 969–983
Yu.V. Shestopalov, Yu.G. Smirnov, “Existence and Uniqueness of a Solution to the Inverse Problem of the Complex Permittivity Reconstruction of a Dielectric Body in a Waveguide”, Inverse Problems, 26 (2010), 105002
Yu.G. Smirnov, D.V. Valovik, “Coupled electromagnetic transverse-electric.transverse magnetic wave propagation in a cylindrical waveguide with Kerr nonlinearity”, Journal of Mathematical Physics, 54:4 (2013), 043506-1–22
A.S. Ilyinsky, Yu.G. Smirnov, Electromagnetic Wave Diffraction by Conducting Screens, VSP Int. Science Publishers, Utrecht, the Netherlands, 1998
Yu.G. Shestopalov, Yu.G. Smirnov, “Eigenwaves in waveguides with dielectric inclusions: completeness”, Applicable Analysis: An International Journal, 93:9 (2014), 1824–1845
Yu. G. Smirnov, “On the fredholm property of integral equations system in the problem of electromagnetic waves propagation in a graphene-coated rod”, University proceedings. Volga region. Physical and mathematical sciences, 2023, no. 3, 74–86
2.
Yu. G. Smirnov, D. A. Labutkina, “On the solution of the nonlinear Lippmann - Schwinger integral equation by the method of contracting maps”, University proceedings. Volga region. Physical and mathematical sciences, 2023, no. 3, 3–10
Yu. G. Smirnov, S. V. Tikhov, “The propagation of the TM-wave in a flat semi-open dielectric layer with nonlocal nonlinearity”, University proceedings. Volga region. Physical and mathematical sciences, 2023, no. 1, 40–53
4.
Yu. G. Smirnov, “A modified method for separating variables in the diffraction problem of TM-polarized wave on diffraction grating”, University proceedings. Volga region. Physical and mathematical sciences, 2023, no. 1, 3–14
2022
5.
Yu. G. Smirnov, Yu. A. Petrova, “Numerical study of the problem of electromagnetic oscillations of a three-layer spherical resonator filled with a metamaterial”, University proceedings. Volga region. Physical and mathematical sciences, 2022, no. 4, 69–75
6.
V. Yu. Martynova, Yu. G. Smirnov, A. V. Tikhonravov, “Optimization of parameters of multilayer diffraction gratings using needle variations”, University proceedings. Volga region. Physical and mathematical sciences, 2022, no. 4, 56–68
Yu. G. Smirnov, S. V. Tikhov, E. V. Gusarova, “On the propagation of electromagnetic waves in a dielectric layer coated with graphene”, University proceedings. Volga region. Physical and mathematical sciences, 2022, no. 3, 11–18
Yu. G. Smirnov, E. Yu. Smol'kin, “On the existence of nonlinear coupled surface TE- and leaky TM-electromagnetic waves in a circular cylindrical waveguide”, University proceedings. Volga region. Physical and mathematical sciences, 2022, no. 1, 13–27
9.
Yu. G. Smirnov, “Method of $Y$-mappings for study of multiparameter nonlinear eigenvalue problems”, Zh. Vychisl. Mat. Mat. Fiz., 62:1 (2022), 159–165; Comput. Math. Math. Phys., 62:1 (2022), 150–156
2021
10.
A. B. Samokhin, Yu. G. Smirnov, “Uniqueness and existence theorems for solving problems of scattering electromagnetic waves by anisotropic bodies”, Dokl. RAN. Math. Inf. Proc. Upr., 496 (2021), 59–63; Dokl. Math., 103:1 (2021), 50–53
Yu. G. Smirnov, V. Yu. Martynova, M. A. Moskaleva, A. A. Tsupak, “Study of diffraction efficiency of diffraction gratings by the modified method of variables separation”, University proceedings. Volga region. Physical and mathematical sciences, 2021, no. 4, 57–70
Yu. G. Smirnov, E. Yu. Smol'kin, “Problem research of an open circular waveguide normal waves with an inhomogeneous chiral layer”, University proceedings. Volga region. Physical and mathematical sciences, 2021, no. 1, 85–101
13.
Yu. G. Smirnov, E. Yu. Smol'kin, M. O. Snegur, “Numerical study of propagation of nonlinear coupled surface and leaky electromagnetic waves in a circular cylindrical metal–dielectric waveguide”, Zh. Vychisl. Mat. Mat. Fiz., 61:8 (2021), 1378–1389; Comput. Math. Math. Phys., 61:8 (2021), 1353–1363
A. B. Samokhin, Yu. G. Smirnov, “Uniqueness and existence theorems for the problems of electromagnetic-wave scattering by three-dimensional anisotropic bodies in differential and integral formulations”, Zh. Vychisl. Mat. Mat. Fiz., 61:1 (2021), 85–94; Comput. Math. Math. Phys., 61:1 (2021), 80–89
Yu. G. Smirnov, E. Yu. Smol'kin, “On the existence of an infinite number of leaky complex waves in a dielectric layer”, Dokl. RAN. Math. Inf. Proc. Upr., 490 (2020), 63–66; Dokl. Math., 101:1 (2020), 53–56
M. A. Moskaleva, Yu. G. Smirnov, “On the discreteness of the spectrum of integrodifferential operator-functions in the problem of oscillations in open volume resonators”, University proceedings. Volga region. Physical and mathematical sciences, 2020, no. 4, 22–31
17.
M. Yu. Medvedik, Yu. G. Smirnov, A. A. Tsupak, “The solution of a vector 3D inverse diffraction ploblem on a 3D heterogeneous body by a two-sweep method”, University proceedings. Volga region. Physical and mathematical sciences, 2020, no. 4, 3–21
18.
E. V. Gusarova, Yu. G. Smirnov, A. A. Tsupak, “On a method for solving the problem of electromagnetic wave diffraction on a diffraction grating”, University proceedings. Volga region. Physical and mathematical sciences, 2020, no. 3, 31–38
Yu. G. Smirnov, V. E. Oleynikov, S. N. Kupriyanova, V. A. Galimskaya, E. A. Gundarev, A. V. Golubeva, “Numerical method for calculating the segments' work of the left ventricle”, University proceedings. Volga region. Physical and mathematical sciences, 2020, no. 1, 22–35
R. O. Evstigneev, M. Yu. Medvedik, Yu. G. Smirnov, A. A. Tsupak, “Two-step method for solving the scalar reverse three-dimensional diffraction problem on a volume heterogeneous body”, University proceedings. Volga region. Physical and mathematical sciences, 2019, no. 4, 12–28
Yu. G. Smirnov, M. A. Moskaleva, “Substantiation of the numerical method for solving the diffraction problem on a system of intersecting bodies and screens”, University proceedings. Volga region. Physical and mathematical sciences, 2019, no. 4, 4–11
22.
V. Yu. Kurseeva, Yu. G. Smirnov, E. Yu. Smol'kin, “On the solvability of the problem of electromagnetic wave diffraction by a layer filled with a nonlinear medium”, Zh. Vychisl. Mat. Mat. Fiz., 59:4 (2019), 684–698; Comput. Math. Math. Phys., 59:4 (2019), 644–658
2018
23.
Yu. G. Smirnov, A. A. Tsupak, “The two-dimensional inverse scalar problem of diffraction by an inhomogeneous obstacle with a piecewise continuous refractive index”, University proceedings. Volga region. Physical and mathematical sciences, 2018, no. 3, 3–16
Yu. G. Smirnov, E. Yu. Smolkin, M. O. Snegur, “Analysis of the spectrum of azimuthally symmetric waves of an open inhomogeneous anisotropic waveguide with longitudinal magnetization”, Zh. Vychisl. Mat. Mat. Fiz., 58:11 (2018), 1955–1970; Comput. Math. Math. Phys., 58:11 (2018), 1887–1901
Yu. G. Smirnov, M. A. Moskaleva, “The two-sweep method for heterogeneous body's permittivity determination in a waveguide”, University proceedings. Volga region. Physical and mathematical sciences, 2017, no. 4, 106–118
26.
R. O. Evstigneev, M. Yu. Medvedik, Yu. G. Smirnov, A. A. Tsupak, “The inverse problem of body's heterogeneity recovery for early diagnostics of diseases using microwave tomography”, University proceedings. Volga region. Physical and mathematical sciences, 2017, no. 4, 3–17
Yu. G. Smirnov, E. Yu. Smol'kin, M. O. Snegur, “On spectrum's discrete nature in the problem of azimuthal symmetrical waves of an open nonhomogeneous anisotropic waveguide with longitudinal magnetization”, University proceedings. Volga region. Physical and mathematical sciences, 2017, no. 3, 50–64
Yu. G. Smirnov, M. Yu. Medvedik, A. A. Tsupak, M. A. Moskaleva, “The problem of diffraction of acoustic waves on a system of bodyes, screens and antennas”, Matem. Mod., 29:1 (2017), 109–118
29.
Yu. G. Smirnov, A. A. Tsupak, “On the unique existence of the classical solution to the problem of electromagnetic wave diffraction by an inhomogeneous lossless dielectric body”, Zh. Vychisl. Mat. Mat. Fiz., 57:4 (2017), 702–709; Comput. Math. Math. Phys., 57:4 (2017), 698–705
Yu. G. Smirnov, M. A. Moskaleva, “Convergence of the Galerkin method in the electromagnetic waves diffraction problem on a system of arbitrary located bodies and screens”, University proceedings. Volga region. Physical and mathematical sciences, 2016, no. 2, 78–86
Yu. G. Smirnov, “On the equivalence of the electromagnetic problem of diffraction by an inhomogeneous bounded dielectric body to a volume singular integro-differential equation”, Zh. Vychisl. Mat. Mat. Fiz., 56:9 (2016), 1657–1666; Comput. Math. Math. Phys., 56:9 (2016), 1631–1640
R. O. Evstigneev, M. Yu. Medvedik, Yu. G. Smirnov, “Inverse problem of determining parameters of inhomogeneity of a body from acoustic field measurements”, Zh. Vychisl. Mat. Mat. Fiz., 56:3 (2016), 490–497; Comput. Math. Math. Phys., 56:3 (2016), 483–490
Yu. G. Smirnov, “On the smoothness of solutions of electric field volume singular integro-differential equation”, University proceedings. Volga region. Physical and mathematical sciences, 2015, no. 2, 46–56
34.
D. V. Valovik, M. Yu. Medvedik, Yu. G. Smirnov, A. A. Tsupak, “Existence and unicity of the solution of the diffraction problem for an electromagnetic wave on a system of non-intersecting bodies and screens”, University proceedings. Volga region. Physical and mathematical sciences, 2015, no. 1, 89–97
M. A. Maximova, M. Yu. Medvedik, Yu. G. Smirnov, A. A. Tsupak, “Numerical solution of the electromagnetic wave difraction problem on the sytem of bodies and screens”, University proceedings. Volga region. Physical and mathematical sciences, 2014, no. 3, 114–133
M. Yu. Medvedik, Yu. G. Smirnov, A. A. Tsupak, “Scalar problem of plane wave diffraction by a system of nonintersecting screens and inhomogeneous bodies”, Zh. Vychisl. Mat. Mat. Fiz., 54:8 (2014), 1319–1331; Comput. Math. Math. Phys., 54:8 (2014), 1280–1292
D. V. Valovik, Yu. G. Smirnov, “On the problem of propagation of nonlinear coupled TE–TM waves in a layer”, Zh. Vychisl. Mat. Mat. Fiz., 54:3 (2014), 504–518; Comput. Math. Math. Phys., 54:3 (2014), 522–536
M. Yu. Medvedik, Yu. G. Smirnov, “Ellipticity of the electric field integral equation for absorbing media and the convergence of the Rao–Wilton–Glisson method”, Zh. Vychisl. Mat. Mat. Fiz., 54:1 (2014), 105–113; Comput. Math. Math. Phys., 54:1 (2014), 114–122
D. V. Valovik, E. A. Marennikova, Yu. G. Smirnov, “A nonlinear transmission eigenvalue problem that describes electromagnetic ТЕ wave propagation in a plane inhomogeneous nonlinear dielectric waveguide”, University proceedings. Volga region. Physical and mathematical sciences, 2013, no. 2, 50–63
41.
M. Yu. Medvedik, Yu. G. Smirnov, “Restoration of dielectric permittivity of a heterogeneous body placed into a rectangular waveguide according to transmission and reflection coefficients”, University proceedings. Volga region. Physical and mathematical sciences, 2013, no. 1, 5–18
Yu. G. Smirnov, M. Yu. Medvedik, M. A. Maximova, “Solving the problem of electromagnetic wave diffraction on screens of complex shape”, University proceedings. Volga region. Physical and mathematical sciences, 2012, no. 4, 59–72
D. V. Valovik, Yu. G. Smirnov, “Propagation of coupled electromagnetic TE and TM waves in a plane layer with Kerr nonlinearity”, University proceedings. Volga region. Physical and mathematical sciences, 2012, no. 4, 21–48
45.
Yu. G. Smirnov, S. N. Kupriyanova, D. V. Valovik, “On the propagation of electromagnetic waves in cylindrical inhomogeneous dielectric waveguides filled with a nonlinear medium”, University proceedings. Volga region. Physical and mathematical sciences, 2012, no. 3, 3–16
46.
Yu. G. Smirnov, A. A. Shcherbakov, A. V. Cvetkov, “The method of integral equations for solving the Dirichlet problem in a perturbed three-dimensional layer”, University proceedings. Volga region. Physical and mathematical sciences, 2012, no. 1, 92–102
47.
D. V. Valovik, Yu. G. Smirnov, E. A. Shirokova, “Numerical method in the problem of propagation of electromagnetic TE waves in a two-layer nonlinear waveguide structure”, University proceedings. Volga region. Physical and mathematical sciences, 2012, no. 1, 66–74
M. Yu. Medvedik, Yu. G. Smirnov, “Итерационный метод определения диэлектрической проницаемости образца неоднородного материала, расположенного в прямоугольном волноводе”, Zh. Vychisl. Mat. Mat. Fiz., 52:12 (2012), 2228–2237
V. D. Krevchik, M. B. Semenov, Yu. G. Smirnov, R. V. Zaitsev, V. A. Rudin, P. V. Krevchik, M. A. Manukhina, S. E. Kozenko, “Influence of a metamaterial matrix on the stability of 2D tunnel bifurcations in quantum molecules”, University proceedings. Volga region. Physical and mathematical sciences, 2011, no. 4, 127–141
50.
Yu. G. Smirnov, M. Yu. Medvedik, E. E. Grishina, “Iterative method for determining the effective dielectric constant of a non-uniform material sample”, University proceedings. Volga region. Physical and mathematical sciences, 2011, no. 3, 3–13
V. D. Krevchik, M. B. Semenov, Yu. G. Smirnov, R. V. Zaitsev, V. A. Rudin, P. V. Krevchik, Z. A. Gavrina, “Influence of the dielectric matrix on 2D tunnel bifurcations under external electric field conditions”, University proceedings. Volga region. Physical and mathematical sciences, 2011, no. 1, 140–153
52.
Yu. G. Smirnov, D. I. Vasyunin, “Iterative method for determining the dielectric constant of a non-uniform material sample”, University proceedings. Volga region. Physical and mathematical sciences, 2011, no. 1, 20–30
2010
53.
D. V. Valovik, Yu. G. Smirnov, “Collocation method for solving the electric field equation”, University proceedings. Volga region. Physical and mathematical sciences, 2010, no. 4, 89–100
54.
E. E. Grishina, E. D. Derevyanchyk, M. Yu. Medvedik, Yu. G. Smirnov, “Numerical and analytical solution of the problem of electromagnetic field diffraction on two sections with different permittivity located in a rectangular waveguide”, University proceedings. Volga region. Physical and mathematical sciences, 2010, no. 4, 73–81
D. V. Valovik, Yu. G. Smirnov, “Propagation of TM-polarized electromagnetic waves in a dielectric layer of a nonlinear metamaterial”, University proceedings. Volga region. Physical and mathematical sciences, 2010, no. 3, 71–87
56.
E. A. Khorosheva, Yu. G. Smirnov, “On the solvability of a nonlinear eigenvalue boundary value problem for propagating TM waves in a circular nonlinear waveguide”, University proceedings. Volga region. Physical and mathematical sciences, 2010, no. 3, 55–70
E. E. Gurina, M. Yu. Medvedik, Yu. G. Smirnov, “Numerical and analytical solution of the problem of electromagnetic field diffraction on a dielectric parallelepiped located in a rectangular waveguide”, University proceedings. Volga region. Physical and mathematical sciences, 2010, no. 2, 44–53
M. Yu. Medvedik, D. A. Mironov, Yu. G. Smirnov, “A sub-hierarchical approach for solving the volumetric singular integral equation of the diffraction problem on a dielectric body in a waveguide by collocation”, University proceedings. Volga region. Physical and mathematical sciences, 2010, no. 2, 32–43
D. V. Valovik, Yu. G. Smirnov, “Dispersion equations in the problem of electromagnetic wave propagation in a linear layer and metamaterials”, University proceedings. Volga region. Physical and mathematical sciences, 2010, no. 1, 28–42
M. Yu. Medvedik, Yu. G. Smirnov, E. A. Khorosheva, “Numerical solution of the problem of propagation of electromagnetic TM waves in circular dielectric waveguides filled with a nonlinear medium”, University proceedings. Volga region. Physical and mathematical sciences, 2010, no. 1, 2–13
D. A. Mironov, Yu. G. Smirnov, “On the existence and uniqueness of solutions of the inverse boundary value problem for determining the dielectric permittivity of materials”, Zh. Vychisl. Mat. Mat. Fiz., 50:9 (2010), 1587–1597; Comput. Math. Math. Phys., 50:9 (2010), 1511–1521
D. V. Valovik, Yu. G. Smirnov, “A nonlinear boundary eigenvalues problem for TM-polarized electromagnetic waves in a nonlinear layer”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 10, 70–74; Russian Math. (Iz. VUZ), 52:10 (2008), 60–63
D. V. Valovik, Yu. G. Smirnov, “Propagation of TM waves in a Kerr nonlinear layer”, Zh. Vychisl. Mat. Mat. Fiz., 48:12 (2008), 2186–2194; Comput. Math. Math. Phys., 48:12 (2008), 2217–2225
Yu. G. Smirnov, “Convergence of the Galerkin methods for equations with elliptic operators on subspaces and solving the electric field equation”, Zh. Vychisl. Mat. Mat. Fiz., 47:1 (2007), 129–139; Comput. Math. Math. Phys., 47:1 (2007), 126–135
Yu. G. Smirnov, A. A. Tsupak, “Existence and Uniqueness of a Solution of a Singular Volume Integral Equation in a Diffraction Problem”, Differ. Uravn., 41:9 (2005), 1190–1197; Differ. Equ., 41:9 (2005), 1253–1261
M. Yu. Medvedik, Yu. G. Smirnov, S. I. Sobolev, “A parallel algorithm for computing surface currents in a screen electromagnetic diffraction problem”, Num. Meth. Prog., 6:1 (2005), 99–108
Yu. G. Smirnov, A. A. Tsupak, “Investigation of an electromagnetic problem of diffraction by a dielectric body using the method of a volume singular integral equation”, Zh. Vychisl. Mat. Mat. Fiz., 44:12 (2004), 2252–2267; Comput. Math. Math. Phys., 44:12 (2004), 2143–2158
S. N. Kupriyanova, Yu. G. Smirnov, “The propagation of electromagnetic waves in cylindrical dielectric waveguides filled with a nonlinear medium”, Zh. Vychisl. Mat. Mat. Fiz., 44:10 (2004), 1850–1860; Comput. Math. Math. Phys., 44:10 (2004), 1762–1773
I. V. Slavin, Yu. G. Smirnov, “Strong ellipticity of the hybrid formulation of the electromagnetic diffraction problem”, Zh. Vychisl. Mat. Mat. Fiz., 40:2 (2000), 286–299; Comput. Math. Math. Phys., 40:2 (2000), 273–286
Yu. G. Smirnov, “The solvability of vector integro-differential equations for the problem of the diffraction of an electromagnetic field by screens of arbitrary shape”, Zh. Vychisl. Mat. Mat. Fiz., 34:10 (1994), 1461–1475; Comput. Math. Math. Phys., 34:10 (1994), 1265–1276
Yu. G. Smirnov, “On the solvability of vector problems of diffraction in domains connected through an opening in a screen”, Zh. Vychisl. Mat. Mat. Fiz., 33:9 (1993), 1427–1440; Comput. Math. Math. Phys., 33:9 (1993), 1263–1273
1992
72.
Yu. G. Smirnov, “On the Fredholm property of a system of pseudodifferential equations in the problem of diffraction by a bounded screen”, Differ. Uravn., 28:1 (1992), 136–143; Differ. Equ., 28:1 (1992), 130–136
Yu. G. Smirnov, “The Fredholm property of the problem of diffraction by a flat
bounded ideally conducting screen”, Dokl. Akad. Nauk SSSR, 319:1 (1991), 147–149; Dokl. Math., 36:7 (1991), 512–513
Yu. G. Smirnov, “The method of operator pencils in boundary value problems of conjugation for a system of elliptic equations”, Differ. Uravn., 27:1 (1991), 140–147; Differ. Equ., 27:1 (1991), 112–118
Yu. G. Smirnov, “The application of the operator pencil method in a problem
concerning the natural waves of a partially filled wave guide”, Dokl. Akad. Nauk SSSR, 312:3 (1990), 597–599; Dokl. Math., 35:5 (1990), 430–431
Yu. G. Smirnov, “Completeness of the system of eigen- and associated waves of a
partially filled waveguide with an irregular boundary”, Dokl. Akad. Nauk SSSR, 297:4 (1987), 829–832; Dokl. Math., 32:12 (1987), 963–964
A. S. Il'inskii, Yu. G. Smirnov, “Mathematical modeling of the process of propagation of electromagnetic oscillations in a slot transmission line”, Zh. Vychisl. Mat. Mat. Fiz., 27:2 (1987), 252–261; U.S.S.R. Comput. Math. Math. Phys., 27:1 (1987), 163–170
D. V. Valovik, Yu. G. Smirnov, “The method of pseudodifferential operators for the study of a volumetric singular integral equation of an electric field”, University proceedings. Volga region. Physical and mathematical sciences, 2009, no. 4, 70–84
M. Yu. Medvedik, Yu. G. Smirnov, “Numerical solution of a volumetric singular integral equation by the collocation method”, University proceedings. Volga region. Physical and mathematical sciences, 2009, no. 4, 54–69
Yu. G. Smirnov, M. Yu. Medvedik, D. I. Vasyunin, “A collocation method for solving a volumetric singular integral equation in the problem of determining the dielectric constant of a material”, University proceedings. Volga region. Physical and mathematical sciences, 2009, no. 3, 71–87
V. Ch. Zhukovskii, O. N. Gorshkov, V. D. Krevchik, M. B. Semenov, Yu. G. Smirnov, E. V. Chuprunov, V. A. Rudin, N. Yu. Skibitskaya, P. V. Krevchik, D. O. Filatov, D. A. Antonov, M. A. Lapshina, M. E. Shenina, Ya. Kendji, “Features of two-dimensional tunnel bifurcations under conditions of an external electric field”, University proceedings. Volga region. Physical and mathematical sciences, 2009, no. 2, 123–135
82.
Yu. G. Smirnov, D. V. Valovik, “Analytical continuation of the Green's function for the equation Helmholtz in the layer”, University proceedings. Volga region. Physical and mathematical sciences, 2009, no. 2, 83–90
83.
V. D. Krevchik, M. B. Semenov, Yu. G. Smirnov, E. V. Groznaya, P. V. Krevchik, “Transformation of two-photon impurity absorption spectra under conditions of dissipative tunneling in a quantum molecule”, University proceedings. Volga region. Physical and mathematical sciences, 2009, no. 1, 145–155
84.
M. Yu. Medvedik, I. A. Rodionova, Yu. G. Smirnov, “A numerical method for solving a pseudodifferential equation in the diffraction problem in layers connected through a hole”, University proceedings. Volga region. Physical and mathematical sciences, 2009, no. 1, 87–99
Yu. G. Smirnov, “On the existence and uniqueness of solutions to the inverse boundary value problem for determining the effective permittivity of nanomaterials”, University proceedings. Volga region. Physical and mathematical sciences, 2009, no. 1, 11–24
S. N. Kupriyanova, Yu. G. Smirnov, “The method of integral equations for an inhomogeneous waveguide with nonlinear filling according to Kerr's law”, University proceedings. Volga region. Physical and mathematical sciences, 2008, no. 4, 26–31
87.
Yu. G. Smirnov, “Application of GRID technologies for solving a nonlinear volumetric singular integral equation to determine the effective permittivity of nanomaterials”, University proceedings. Volga region. Physical and mathematical sciences, 2008, no. 3, 39–54
M. Yu. Medvedik, Yu. G. Smirnov, “Application of GRID technologies for solving a volumetric singular integral equation for the problem of diffraction on a dielectric body by the subierarchical method”, University proceedings. Volga region. Physical and mathematical sciences, 2008, no. 2, 2–14
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