On the convergence the barycentric method in solving diffraction problems on conductive thin screens

In this article, the use of the barycentric method is proposed for the numerical solution of problems of diffraction of electromagnetic waves on infinitely thin perfectly conducting screens of arbitrary shape. The numerical solution is formed in the projection formulation of the Galerkin method. The essence of the barycentric method is to form a global system of basic functions for opening the screen when determining the approximation of the desired function of the current plane on its surface. Basis functions are defined by Bernstein-type polynomials in terms of barycentric coordinates that are entered for opening the screen when it is represented as a closed simply connected polygonal region. The features of the algorithmic implementation of the barycentric method in solving diffraction problems on conducting thin screens are considered. The rate of convergence is estimated. Comparative results of calculations performed under equivalent conditions using the barycentric method and the RWG method are presented.