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International Workshop on Computer Algebra in Scientific Computing

CASC 2019: Computer Algebra in Scientific Computing pp 412–429Cite as

Symbolic-Numeric Implementation of the Four Potential Method for Calculating Normal Modes: An Example of Square Electromagnetic Waveguide with Rectangular Insert

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11661))

Abstract

In this paper, the Maple computer algebra system is used to construct a symbolic-numeric implementation of the method for calculating normal modes of square closed waveguides in a vector formulation. The method earlier proposed by Malykh et al. [M.D. Malykh, L.A. Sevastianov, A.A. Tiutiunnik, N.E. Nikolaev. On the representation of electromagnetic fields in closed waveguides using four scalar potentials // Journal of Electromagnetic Waves and Applications, 32 (7), 886–898 (2018)] will be referred to as the method of four potentials. The Maple system is used at all stages of treating the system of differential equations for four potentials: the generation of the Galerkin basis, the substitution of approximate solution into the system under study, the formulation of a computational problem, and its approximate solution.

Thanks to the symbolic-numeric implementation of the method, it is possible to carry out calculations for a large number of basis functions of the Galerkin decomposition with reasonable computation time and then to investigate the convergence of the method and verify it, which is done in the present paper, too.

The publication has been prepared with the support of the “RUDN University Program 5-100”  and funded by RFBR according to the research projects Nos. 18-07-00567 and 18-51-18005.

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Author information

Authors and Affiliations

  1. Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russia

    A. A. Tiutiunnik, D. V. Divakov, M. D. Malykh & L. A. Sevastianov

  2. Joint Institute for Nuclear Research (Dubna), Joliot-Curie, 6, Dubna, Moscow Region, 141980, Russia

    L. A. Sevastianov

Authors
  1. A. A. Tiutiunnik
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  2. D. V. Divakov
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  3. M. D. Malykh
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  4. L. A. Sevastianov
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Corresponding author

Correspondence to D. V. Divakov .

Editor information

Editors and Affiliations

  1. Coventry University, Coventry, UK

    Matthew England

  2. University of Kassel, Kassel, Germany

    Wolfram Koepf

  3. Plekhanov Russian University of Economics, Moscow, Russia

    Timur M. Sadykov

  4. University of Kassel, Kassel, Germany

    Werner M. Seiler

  5. Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Tiutiunnik, A.A., Divakov, D.V., Malykh, M.D., Sevastianov, L.A. (2019). Symbolic-Numeric Implementation of the Four Potential Method for Calculating Normal Modes: An Example of Square Electromagnetic Waveguide with Rectangular Insert. In: England, M., Koepf, W., Sadykov, T., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2019. Lecture Notes in Computer Science(), vol 11661. Springer, Cham. https://doi.org/10.1007/978-3-030-26831-2_27

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  • DOI: https://doi.org/10.1007/978-3-030-26831-2_27

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