  In this paper, we consider acoustic or electromagnetic scattering in two
dimensions from an infinite three-layer medium with thousands of
wavelength-size dielectric particles embedded in the middle layer. Such
geometries are typical of microstructured composite materials, and the
evaluation of the scattered field requires a suitable fast solver for either a
single configuration or for a sequence of configurations as part of a design or
optimization process. We have developed an algorithm for problems of this type
by combining the Sommerfeld integral representation, high order integral
equation discretization, the fast multipole method and classical multiple
scattering theory. The efficiency of the solver is illustrated with several
numerical experiments.
