Method of iterative extensions for analysis of a screened harmonic systems

In this paper, mixed boundary value problem for screened Poisson equation is considered in a geometrically complex domain. The asymptotically optimal method of iterative extensions is described. An analysis of screened harmonic system is carried out with the method of iterative extensions. An algorithm is written that implements the method of iterative extensions in matrix form. An example of calculating the bending of a membrane on an elastic base is given.