Skip to main content
SpringerLink
Log in

Features of Constructing an Orthonormal Basis Based on Atomic Functions as Applied to Solving Boundary Value Electrodynamics Problems for Regions of Complex Shape

  • ELECTRODYNAMICS AND WAVE PROPAGATION
  • Published:
Journal of Communications Technology and Electronics Aims and scope Submit manuscript

Abstract—

A method for orthonormalizing atomic functions is proposed and substantiated. The efficiency of using a basic system to solve a number of boundary value electrodynamics problems is shown. Numerical experiment and analysis of the physical results showed that the R-functions method combined with basis functions is universal for waveguides and resonators of arbitrary shape.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.

Similar content being viewed by others

REFERENCES

  1. V. F. Kravchenko and O. V. Kravchenko, Constructive Methods of the Algebra of Logic, Atomic Functions, Wavelets, Fractals in Problems of Physics and Technology (Tekhnosfera, Moscow, 2018) [in Russian].

    Google Scholar 

  2. V. F. Kravchenko and V. L. Rvachev, Boolean Algebra, Atomic Functions and Wavelets in Physical Applications (Fizmatlit, Moscow, 2006) [in Russian].

    MATH  Google Scholar 

  3. V. F. Kravchenko, Lecture on Theory of Atomic Functions and Some Their Applications (Radiotekhnika, Moscow, 2003) [in Russian].

    Google Scholar 

  4. S. G. Mikhlin, NumericalPerformance of Variational Methods (Nauka, Moscow, 1966; Wolters-Noordhoff Publ., Groningen, 1971).

  5. V. F. Kravchenko and A. V. Yurin, in Proc. 3rd Conf. on Mathematical Modeling of Wave Phenomena, 20th Nordic Conf. on Radio Science and Communication, Vaxio, Sweden, June 13–19, 2008, p. 18; AIP Conf. Proc. 1106 (2009).

  6. V. F. Kravchenko, O. V. Kravchenko, V. I. Pustovoit, D. V. Churikov, and A. V. Yurin, J. Commun. Technol. Electron. 60, 1153 (2015).

    Article  Google Scholar 

  7. I. Ya. Novikov, V. Yu. Protasov, and M. A. Skopina, Surge Theory (Fizmatlit, Moscow, 2006).

    Google Scholar 

  8. G. A. Battle, Comm. Math. Phys. 110, 601 (1987).

    Article  MathSciNet  Google Scholar 

  9. N. N. Voitovich, B. Z. Katsenelenbaum, and A. N. Sivov, A Generalized Method of Eigenoscillations in the Diffraction Theory, with Supplement by M. S. Agranovich (Nauka, Moscow, 1977) [in Russian].

Download references

Author information

Authors and Affiliations

  1. Institute of Radio Engineering and Electronics, Russian Academy of Sciences, 125009, Moscow, Russia

    V. F. Kravchenko

  2. Scientific and Technological Center of Unique Instrumentation, Russian Academy of Sciences, 117342, Moscow, Russia

    V. F. Kravchenko & V. I. Pustovoit

  3. Moscow Bauman State Technical University, 105005, Moscow, Russia

    V. F. Kravchenko & A. V. Yurin

Authors
  1. V. F. Kravchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. I. Pustovoit
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. V. Yurin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to V. F. Kravchenko or A. V. Yurin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kravchenko, V.F., Pustovoit, V.I. & Yurin, A.V. Features of Constructing an Orthonormal Basis Based on Atomic Functions as Applied to Solving Boundary Value Electrodynamics Problems for Regions of Complex Shape. J. Commun. Technol. Electron. 64, 1218–1223 (2019). https://doi.org/10.1134/S1064226919110147

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064226919110147

Search

Navigation