Method of integral equations in the scalar problem of diffraction on a system consisting of a ``soft'' and a ``hard'' screen and an inhomogeneous body
The authors study the scalar problem on the diffraction of a plane wave on a system that consists of a ``soft'' and a ``hard'' screen and a solid inhomogeneous body. The boundary value problem consists of the Helmholtz equation with Dirichlet, respectively Neumann conditions on the surfaces of the screens and transmission conditions on the boundary of the body. The differential statement of the problem is reduced to an equivalent system of singular integral equations over the body domain and the screen surfaces. The solvability of the system of integral equations in Sobolev spaces and the smoothness of the solutions are demonstrated. Approximate solutions of the system of integral equations are found by the Bubnov-Galerkin method. Piecewise constant basis functions in the body domain and on the ``soft'' screen surface and piecewise linear basis functions on the ``hard'' screen are used. The consistency property and the convergence theorem for the numerical method are proved.
scientific article; zbMATH DE number 6386867
scientific article