A fast direct solver for scattering from periodic structures with multiple material interfaces in two dimensions

We present a new integral equation method for the calculation of two-dimensional scattering from periodic structures involving triple-points (multiple materials meeting at a single point). The combination of a robust and high-order accurate integral representation and a fast direct solver permits the efficient simulation of scattering from fixed structures at multiple angles of incidence. We demonstrate the performance of the scheme with several numerical examples.