Abstract:
This paper presents a new explicit scheme for the numerical integration of Maxwell's equations in isotropic and anisotropic dielectrics and conductors, as well as in the plasma in the case of the Vlasov–Maxwell system. In this scheme, the electric and magnetic fields are calculated in the same time points in the same spatial grid nodes, and a splitting in spatial directions and physical processes has been used. Scheme is monotonic and has 2nd order accuracy in time and 3rd order accuracy in the spatial variables. The presented scheme allows us to use a much larger step of time integration in modeling the propagation of low-frequency signals in the ionosphere than the widely used method of finite differences in the time domain for the same accuracy.
Citation:
I. V. Mingalev, O. V. Mingalev, O. I. Ahmetov, Z. V. Suvorova, “The explicit splitting scheme for Maxwell's equations”, Mat. Model., 30:12 (2018), 17–38; Math. Models Comput. Simul., 11:4 (2019), 551–563
This publication is cited in the following 7 articles:
Z. V. Suvorova, I. V. Mingalev, O. V. Mingalev, O. I. Akhmetov, L. B. Volkomirskaya, O. A. Gulevich, A. E. Reznikov, “Simulation of propagation of video pulse signals of GPR in the Earth's lithosphere”, Math. Models Comput. Simul., 16:2 (2024), 254–266
O. I. Akhmetov, V. B. Belakhovsky, I. V. Mingalev, O. V. Mingalev, A. V. Larchenko, Z. V. Suvorova, “About the Propagation of RSDN‐20 “Alpha” Signals in the Earth‐Ionosphere Waveguide During Geomagnetic Disturbances”, Radio Science, 58:1 (2023)
Oxana Gulevich, Liudmila Volkomirskaya, Igor Mingalev, Vladimir Varenkov, Zoya Suvorova, Oleg Akhmetov, Oleg Mingalev, Aleksander Reznikov, “Results of numerical modelling of the problem of video pulse ground penetrating radar research in freshwater bodies”, Russian Journal of Earth Sciences, 2022, 1
O. I. Akhmetov, I. V. Mingalev, O. V. Mingalev, V. B. Belakhovsky, Z. V. Suvorova, “Propagation of electromagnetic waves in the region of high latitudes at various states of the ionosphere at the frequencies of the RSDN-20 (alpha) radionavigation system”, Geomagn. Aeron., 61:3 (2021), 376–388
Akhmetov I O., Mingalev V I., Mingalev V O., Belakhovsky V.B., Suvorova V Z., 2020 Xxxiiird General Assembly and Scientific Symposium of the International Union of Radio Science, IEEE, 2020
O. I. Akhmetov, I. V. Mingalev, O. V. Mingalev, Z. V. Suvorova, V. B. Belakhovsky, S. M. Chernyakov, “Determination of ulf-wave characteristics most strongly reacting to minor changes of ionospheric electron density in a high-latitude region”, Sol.-Terr. Phys., 5:4 (2019), 81–90
O. Akhmetov, O. Mingalev, I. Mingalev, Z. Suvorova, V. Belakhovsky, S. Cherniakov, “About horizontal inhomogeneities of electron concentration influence on the propagation of ulf signals in the earth-ionosphere waveguide”, 2019 Russian Open Conference on Radio Wave Propagation (Rwp), Vol 1, IEEE, 2019, 224–227
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