  In this short note, we present a new technique to accelerate the convergence
of a FFT-based solver for numerical homogenization of complex periodic media
proposed by Moulinec and Suquet in 1994. The approach proceeds from
discretization of the governing integral equation by the trigonometric
collocation method due to Vainikko (2000), to give a linear system which can be
efficiently solved by conjugate gradient methods. Computational experiments
confirm robustness of the algorithm with respect to its internal parameters and
demonstrate significant increase of the convergence rate for problems with
high-contrast coefficients at a low overhead per iteration.
