Advertisement

Numerical Method for Solving a Diffraction Problem of Electromagnetic Wave on a System of Bodies and Screens

  • Mikhail Medvedik
  • Marina MoskalevaEmail author
  • Yury Smirnov
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 965)

Abstract

The three-dimensional vector problem of electromagnetic wave diffraction by systems of intersecting dielectric bodies and infinitely thin perfectly conducting screens of irregular shapes is considered. The original boundary value problem for Maxwell‘s equations is reduced to a system of integro-differential equations. Methods of surface and volume integral equations are used. The system of linear algebraic equations is obtained using the Galerkin method with compactly supported basis functions. The subhierarchical method is applied to solve the diffraction problem by scatterers of irregular shapes. Several results are presented. Also we used a parallel algorithm.

Keywords

Boundary value problem Inverse problem of diffraction Permittivity tensor Tensor Green’s function Integro-differential equation 

Notes

Acknowledgments

This study is supported by the Ministry of Education and Science of the Russian Federation [project 1.894.2017/4.6] and by the Russian Foundation for Basic Research [project 18-31-00108]. The research is carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University.

References

  1. 1.
    Samokhin, A.B.: Integral Equations and Iteration Methods in Electromagnetic Scattering. VSP, Utrecht (2001)CrossRefGoogle Scholar
  2. 2.
    Costabel, M.: Boundary integral operators on curved polygons. Ann. Mat. Pura Appl. 133, 305–326 (1983)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Costabel, M., Darrigrand, E., Kon’e, E.: Volume and surface integral equations for electromagnetic scattering by a dielectric body. J. Comput. Appl. Math. 234, 1817–1825 (2010)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Colton, D., Kress, R.: Integral Equation Methods in Scattering Theory. Wiley, New York (1983)zbMATHGoogle Scholar
  5. 5.
    Ilyinsky, A.S., Smirnov, Y.G.: Electromagnetic Wave Diffraction by Conducting Screens. VSP, Utrecht (1998)Google Scholar
  6. 6.
    Medvedik, M.Y., Moskaleva, M.A.: Analysis of the problem of electromagnetic wave diffraction on non-planar screens of various shapes by the subhierarchic method. J. Commun. Technol. Electron. 60(6), 543–551 (2015)CrossRefGoogle Scholar
  7. 7.
    Medvedik, M.Y.: Solution of integral equations by the subhierarchic method for generalized computational grids. Math. Models Comput. Simul. 7(6), 570–580 (2015)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Medvedik, M.Y.: Numerical solution of the problem of diffraction of electromagnetic waves by nonplanar screens of complex geometric shapes by means of a subhierarchic method. J. Commun. Technol. Electron. 58(10), 1019–1023 (2013)CrossRefGoogle Scholar
  9. 9.
    Smirnov, Y.G., Tsupak, A.A.: Integrodifferential equations of the vector problem of electromagnetic wave diffraction by a system of nonintersecting screens and inhomogeneous bodies. Adv. Math. Phys. 2015 (2015).  https://doi.org/10.1155/2015/945965
  10. 10.
    Valovik, D.V., Smirnov, Y.G., Tsupak, A.A.: On the volume singular integro-differential equation approach for the electromagnetic diffraction problem. Appl. Anal. 2015, 173–189 (2015).  https://doi.org/10.1080/00036811.2015.1115839MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Smirnov, Y.G., Tsupak, A.A.: Diffraction of acoustic and electromagnetic waves by screens and inhomogeneous solids: mathematical theory. M. RU-SCIENCE (2016)Google Scholar
  12. 12.
    Kress, R.: Linear Integral Equations. Applied Mathematical sciences, vol. 82, 2nd edn. Springer, Hedielberg (1989).  https://doi.org/10.1007/978-3-642-97146-4CrossRefzbMATHGoogle Scholar
  13. 13.
    Kobayashi, K., Shestopalov, Y., Smirnov, Y.: Investigation of electromagnetic diffraction by a dielectric body in a waveguide using the method of volume singular integral equation. SIAM J. Appl. Math. 70(3), 969–983 (2009)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Medvedik, M.Y., Smirnov, Y.G., Sobolev, S.I.: A parallel algorithm for computing surface currents in a screen electromagnetic diffraction problem. Numer. Methods Program. 6, 99–108 (2005)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Penza State UniversityPenzaRussia

Personalised recommendations