Vector Barycentric Method in Computational Electrodynamics

Abstract

The article presents a vector barycentric method for solving the internal problem of electrodynamics, i.e. solving Maxwell's equations or their respective wave equations in a bounded computational domain with prescribed boundary conditions. The developed method refers to the method of direct solution of the boundary value problems of mathematical physics, the basis for the formation of which are the results obtained by V. Ritz, I.G. Bubnov and B.G. Galerkin. The basic idea of the method lies in the synthesis of a procedure of the vector potential approximation, done by the polynomials of the Lagrange type. The approximating polynomial is formed in the barycentric coordinate system for the entire region of analysis as a whole without partitioning into elementary sub-areas. It is assumed that the scope of analysis is a region with a piecewise linear boundary, and the dimension of the barycentric coordinate system is determined by the number of vertices of the analyzed region. The vector barycentric method is implemented both in the frequency and time domains. The solution to the problem of controlling the electromagnetic field in the approximation of the vector barycentric method is considered.