A hybrid method for the solution of the Poisson equation in the domain of metal-dielectric corners

A. N. Bogolyubov; A. I. Erokhin; I. E. Mogilevsky; M. I. Svetkin

doi:10.3103/S0027134916050064

A hybrid method for the solution of the Poisson equation in the domain of metal-dielectric corners

Authors: Bogolyubov A.N.¹, Erokhin A.I.¹, Mogilevsky I.E.¹, Svetkin M.I.¹
Affiliations:
1. Faculty of Physics
Issue: Vol 72, No 1 (2017)
Pages: 16-22
Section: Theoretical and Mathematical Physics
URL: https://journals.rcsi.science/0027-1349/article/view/164660
DOI: https://doi.org/10.3103/S0027134916050064
ID: 164660

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Abstract

The Poisson’s equation in a two-dimensional domain that contains star metal-dielectric corners is considered. The corners can be only metal or only dielectric. In their neighborhood, the solution is bounded, but the gradient has power-law singularities. A numerical algorithm for solving this problem is proposed. The algorithm is based on the finite-element method and takes the asymptotic behavior of the solution in the neighborhood of metal-dielectric corners into account.