Scalar problem of diffraction of a plane wave from a system of two- and three-dimensional scatterers

The scalar problem of diffraction from a system of screens and bodies in quasi-classical statement is considered. The boundary value problem leads to a system of integral equations on two- and three-dimensional manifolds with boundary. The equivalence of the integral and differential formulations of the problem is established; the Fredholm property and invertibility of the matrix operator are proved. Galerkin method for numerical solving of the integral equations is proposed. The approximation property for piecewise constant basis functions as well as the convergence of Galerkin method is proved. Numerical results are provided.