Scalar problem of plane wave diffraction by a system of nonintersecting screens and inhomogeneous bodies

The scalar problem of plane wave diffraction by a system of bodies and infinitely thin screens is considered in a quasi-classical formulation. The solution is sought in the classical sense but is defined not in the entire space $\mathbb{R}^3$ but rather everywhere except for the screen edges. The original boundary value problem for the Helmholtz equation is reduced to a system of weakly singular integral equations in the regions occupied by the bodies and on the screen surfaces. The equivalence of the integral and differential formulations is proven, and the solvability of the system in the Sobolev spaces is established. The integral equations are approximately solved by the Bubnov–Galerkin method. The convergence of the method is proved, its software implementation is described, and numerical results are presented.