  The aim of this paper is to describe a Matlab toolbox, called $\mu$-diff, for
modeling and numerically solving two-dimensional complex multiple scattering by
a large collection of circular cylinders. The approximation methods in
$\mu$-diff are based on the Fourier series expansions of the four basic
integral operators arising in scattering theory. Based on these expressions, an
efficient spectrally accurate finite-dimensional solution of multiple
scattering problems can be simply obtained for complex media even when many
scatterers are considered as well as large frequencies. The solution of the
global linear system to solve can use either direct solvers or preconditioned
iterative Krylov subspace solvers for block Toeplitz matrices. Based on this
approach, this paper explains how the code is built and organized. Some
complete numerical examples of applications (direct and inverse scattering) are
provided to show that $\mu$-diff is a flexible, efficient and robust toolbox
for solving some complex multiple scattering problems.
