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Differential Equations

, Volume 54, Issue 9, pp 1225–1235 | Cite as

Discretization Methods for Three-Dimensional Singular Integral Equations of Electromagnetism

  • A. B. Samokhin
  • A. S. Samokhina
  • Yu. V. Shestopalov
Integral Equations

Abstract

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.

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References

  1. 1.
    Samokhin, A.B., Integral’nye uravneniya i iteratsionnye metody v elektromagnitnom rasseyanii (Integral Equations and Iteration Methods in Electromagnetic Scattering), Moscow: Radio i Svyaz’, 1998.Google Scholar
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    Samokhin, A.B., Integral Equations and Iteration Methods in Electromagnetic Scattering, Utrecht: VSP, 2001.CrossRefzbMATHGoogle Scholar
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    Samokhin, A.B., Volume singular integral equations for problems of scattering on three-dimensional dielectric structures, Differ. Equations, 2014, vol. 50, no. 9, pp. 1201–1216.MathSciNetCrossRefzbMATHGoogle Scholar
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    Yaghijian, A.D., Electric Green’s functions in the source region, Proc. IEEE, 1980, vol. 68, pp. 248–263.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • A. B. Samokhin
    • 1
  • A. S. Samokhina
    • 2
  • Yu. V. Shestopalov
    • 3
  1. 1.Moscow Technological University (MIREA)MoscowRussia
  2. 2.Trapeznikov Institute of Control Sciences of the Russian Academy of SciencesMoscowRussia
  3. 3.Faculty of Engineering and Sustainable DevelopmentUniversity of GävleGävleSweden

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