Poisson equation numerical solution method based on bidirectional multiple passage of grid cells and parallel computations

This article is devoted to the numerical solution of Poisson equation. The main method of the work based on the assumption of the monotony of unknown function. A an algorithm for numerical solution of the Dirichlet problem for the Poisson equation for a complex domain is shown, the idea of the method is that, the values in the internal grid nodes are searched as arithmetic averages over three neighboring nodes, taking into account the known function. It is shown that the proposed method can be implemented in parallel computing. As a result, a comparison is made with the finite element method.