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Theoretical Analysis and Numerical Implementation of a Stationary Diffusion–Drift Model of Polar Dielectric Charging

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Abstract

The global solvability and local uniqueness of the solution of a boundary value problem for the model of electron-induced charging of polar dielectrics are proved. The model is described by a semilinear diffusion–drift equation and Maxwell’s equations, which relate the charge density and the electric field. For the charge density function, the maximum and minimum principle is established, which is used to control the data of the computational experiment. The results of a finite element implementation of a mathematical model of polar dielectric charging under conditions of electron irradiation are presented and discussed.

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Funding

This work was carried out as part of research and development project no. АААА-А20-120120390006-0 of the Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, and was supported by the Ministry of Education and Science of the Russian Federation (agreement no. 075-02-2021-1395 and project no. 122082400001-8); project no. 1022052600018-5-1.2.1;1.1.2.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, 690041, Vladivostok, Russia

    R. V. Brizitskii

  2. Amur State University, 675000, Blagoveshchensk, Amur oblast, Russia

    N. N. Maksimova & A. G. Maslovskaya

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  1. R. V. Brizitskii
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  2. N. N. Maksimova
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  3. A. G. Maslovskaya
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Correspondence to R. V. Brizitskii, N. N. Maksimova or A. G. Maslovskaya.

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Translated by E. Chernokozhin

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Brizitskii, R.V., Maksimova, N.N. & Maslovskaya, A.G. Theoretical Analysis and Numerical Implementation of a Stationary Diffusion–Drift Model of Polar Dielectric Charging. Comput. Math. and Math. Phys. 62, 1680–1690 (2022). https://doi.org/10.1134/S0965542522100037

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  • DOI: https://doi.org/10.1134/S0965542522100037

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