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A hybrid method for numerical solution of Poisson’s equation in a domain with a dielectric corner

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Abstract

An electrostatic problem of determining a potential in a domain containing an incoming dielectric corner, which reduces to solving Poisson’s equation in this domain, is considered. A specific feature of the solution of this problem is that it is bounded in a neighborhood of the dielectric corner but its gradient increases without limit. An efficient hybrid algorithm for the numerical solution of the problem, based on the finite element method and taking into account the known asymptotic representation of the solution in the neighborhood of the dielectric corner, is proposed.

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Authors and Affiliations

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

    A. N. Bogolyubov, A. I. Erokhin, I. E. Mogilevskii & M. I. Svetkin

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  1. A. N. Bogolyubov
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  2. A. I. Erokhin
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  3. I. E. Mogilevskii
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  4. M. I. Svetkin
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Correspondence to A. N. Bogolyubov.

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Original Russian Text © A.N. Bogolyubov, A.I. Erokhin, I.E. Mogilevskii, M.I. Svetkin, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 8, pp. 1321–1330.

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Bogolyubov, A.N., Erokhin, A.I., Mogilevskii, I.E. et al. A hybrid method for numerical solution of Poisson’s equation in a domain with a dielectric corner. Comput. Math. and Math. Phys. 57, 1310–1319 (2017). https://doi.org/10.1134/S096554251708005X

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  • DOI: https://doi.org/10.1134/S096554251708005X

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