On Green's function in boundary elements method for some infinite triangular system of elliptic equations

We consider a Dirichlet boundary value problem for a system of elliptic equations of special type in domains with inclusions. The use of Green's function technique leads to boundary integral equations with unknown functions only on the surface of the inclusion. The direct and indirect approaches of the boundary integral equation method are discussed. A modified boundary elements method is obtained and a series of numerical experiments is conducted.