Local solutions to high-frequency 2D scattering problems

We consider the solution of high-frequency scattering problems in two dimensions, modelled by an integral equation on the boundary of the scattering object. We devise a numerical method to obtain solutions on only parts of the boundary with little computational effort. The method incorporates asymptotic properties of the solution and can therefore attain particularly good results for high frequencies. Potential uses of such partial solutions for non-convex objects and multiple scattering configurations are presented and a brief error analysis is included. We show that in the simplest implementation of the method the integral equation reduces to an ordinary differential equation.