Modified algorithm of the R-functions method for solving electromagnetics boundary value problems

The Dirichlet problem for 2D second order partial differential equation in an arbitrary domain is considered. To solve this problem, the variational R-functions method (RFM) with the Kantorovich (1962) general structure of solution (GSS) is used. Instead of the traditional RFM scheme, the complicated implicit function of the boundary is substituted here with its approximation by a set of functions with compact supports. It is important that this set is also used in the GSS. This approach allows one to decrease significantly the quantity of numerically calculated integrals expressing the elements of the matrices of systems of linear equations.