Numerical solution to boundary problems for Poisson equation by point-source method

The aim of this paper is the efficiency improvement of one of the most advanced techniques of solving the elliptic boundary value problems - the field point-source method designated as the fundamental solution technique in the foreign literature. Now it is used primarily for solving Laplace equation. Several alternate numerical solutions to the boundary value problems for Poisson equation using the field point-source method are proposed. This method application to the nonhomogeneous equation solution, such as Poisson equation, in most cases leads to the dramatic increase of the numerical error due to mistakes in Poisson equation specific solution. The right member of Poisson equation is approximated by a two-dimensional trigonometric polynomial (in the solution of two-dimensional boundary value problems), then it becomes possible to obtain the specific solution necessary for solving an initial boundary value problem by the field point-source method. The testing results of the proposed technique imply its efficiency, as they allow obtaining the solution with a relative error of 10 −6 at minimum machine time spending. The developed technique of the numerical solution to the boundary value problems for Poisson equation can be used for modeling physical fields in the engineering devices of various applications.