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

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...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2017-08, Vol.57 (8), p.1310-1319
Main Authors: Bogolyubov, A. N., Erokhin, A. I., Mogilevskii, I. E., Svetkin, M. I.
Format: Article
Language:English
Subjects:
Algorithms
Asymptotic methods
Computational Mathematics and Numerical Analysis
Dielectrics
Finite element method
Mathematics
Mathematics and Statistics
Nonlinear programming
Poisson equation
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S096554251708005X