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

Аннотация

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.