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Hierarchy of Models of Quasi-stationary Electromagnetic Fields

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Mathematical Modeling and Supercomputer Technologies (MMST 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1413))

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Abstract

The hierarchy of quasi-stationary models for the system of Maxwell’s equations in homogeneous and inhomogeneous media is studied. The non-relativistic magnetic approximation, the non-relativistic electric approximations and the generalizing quasi-stationary approximation, in which the displacement current contains only a component corresponding to the potential part of the electric field, are considered. The relationship between solutions of initial-boundary value problems for the system of Maxwell’s equations in various approximations is established and estimates of the proximity of these solutions are given. The obtained results show that the generalizing quasi-stationary approximation considered in this work has the same accuracy as the non-relativistic magnetic approximation in determining the magnetic field and the transverse component of the electric field and allows more accurate determination of the potential component of the electric field and the volume density of charges. The resulting generalized quasi-stationary approximation thus covers both classical non-relativistic approximations and can be used in modeling electromagnetic processes in substantially inhomogeneous media, in particular, in solving problems of atmospheric electricity.

Supported by the Scientific and Education Mathematical Center “Mathematics for Future Technologies” (Project No. 075-02-2020-1483/1).

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Authors and Affiliations

  1. N.I. Lobachevsky State University, 23 Gagarin Avenue, 603950, Nizhny Novgorod, Russia

    Aleksey Kalinin & Alla Tyukhtina

  2. Institute of Applied Physics, Russian Academy of Sciences, 46 Ulyanova Street, 603950, Nizhny Novgorod, Russia

    Aleksey Kalinin

Authors
  1. Aleksey Kalinin
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  2. Alla Tyukhtina
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Editor information

Editors and Affiliations

  1. Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, Russia

    Dmitry Balandin

  2. Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, Russia

    Konstantin Barkalov

  3. Lobachevsky State University of Nizhni Novgorod, Nizhniy Novgorod, Russia

    Victor Gergel

  4. Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, Russia

    Iosif Meyerov

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Kalinin, A., Tyukhtina, A. (2021). Hierarchy of Models of Quasi-stationary Electromagnetic Fields. In: Balandin, D., Barkalov, K., Gergel, V., Meyerov, I. (eds) Mathematical Modeling and Supercomputer Technologies. MMST 2020. Communications in Computer and Information Science, vol 1413. Springer, Cham. https://doi.org/10.1007/978-3-030-78759-2_6

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  • DOI: https://doi.org/10.1007/978-3-030-78759-2_6

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  • Online ISBN: 978-3-030-78759-2

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