Scattering by a class of composite bodies using generalized separation of variables

A generalized method of separation of variables is used to solve the problem of scattering by a class of two-dimensional bodies that are bounded by circular arcs and radial segments in a cylindrical coordinate system. These bodies are sectored cylinders and hollow sectored cylinders, which are not amenable to closed-form solution by simple separation of variables. They can serve as simple models for composite bodies with cavities, and as test or benchmark problems against which to validate other solutions of scattering by more general shapes. Generalized separation of variables leads to an infinite system of linear equations for the model coefficients, which can be computed by truncation of that system. The scattering width (SW) is expressed in terms of those coefficients.