Galerkin method for solving scalar problems of diffraction by a partially shielded inhomogeneous body

The scalar problem of diffraction by an inhomogeneous partially shielded body 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 compactly supported basis functions as well as the convergence of Galerkin method in proper Sobolev spaces is proved. Numerical results are provided.