Solution of a screened Poisson equation with Dirichlet boundary condition with the method of iterative extensions

In this paper, numerical solution of the screened Poisson equation with the Dirichlet boundary condition in two-dimensional and three-dimensional domains is proposed. The continuation of the boundary value problems is carried out, and then they are approximated by the finite element method. In the developed method of iterative extensions, solutions to extended problems after approximation are iteratively approximated by solutions of the proposed extended problems. This method has optimal asymptotics in terms of the number of operations.