A numerical scheme is presented to compute the response of a composite mate
rial to an applied field. The scheme is based on an iteration that uses a F
ourier transform based projection method to compute the response of a refer
ence material to the applied field, and a contraction mapping to relate the
response of the reference material to the response of the composite materi
al. The scheme also utilizes nested uniform grids to improve performance, a
nd to evaluate the refinement of the grid.