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Bicompact Finite-Difference Scheme for Maxwell’s Equations in Layered Media

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Abstract

In layered media, the solution of Maxwell’s equations suffers a strong or weak discontinuity at the layer boundaries. Finite-difference schemes providing convergence on strong discontinuities have been proposed for the first time. These are conservative bicompact two-point schemes with mesh nodes lying on the layer boundaries. A fundamentally new technique for taking into account the medium dispersion is proposed. All these features ensure the second order of accuracy of the schemes on discontinuous solutions. Numerical examples illustrating these results are given.

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ACKNOWLEDGMENTS

We are sincerely grateful to the Corresponding Member of the RAS N.N. Kalitkin for valuable comments and discussions and to A.N. Bogolyubov for his interest in this work.

Funding

This work was supported by MK-1780.2019.1 grants (development of the bicompact scheme), by the Russian Foundation for Basic Research (project no. 19-01-00593) (test computations), and by the RUDN 5-100 program (construction of the exact solutions to the test problems).

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Authors and Affiliations

  1. Faculty of Physics, Lomonosov Moscow State University, 119991, Moscow, Russia

    A. A. Belov & Zh. O. Dombrovskaya

  2. RUDN University, 117198, Moscow, Russia

    A. A. Belov

Authors
  1. A. A. Belov
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  2. Zh. O. Dombrovskaya
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Corresponding authors

Correspondence to A. A. Belov or Zh. O. Dombrovskaya.

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Translated by I. Ruzanova

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Belov, A.A., Dombrovskaya, Z.O. Bicompact Finite-Difference Scheme for Maxwell’s Equations in Layered Media. Dokl. Math. 101, 185–188 (2020). https://doi.org/10.1134/S1064562420020039

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  • DOI: https://doi.org/10.1134/S1064562420020039

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