The last decade has witnessed a growing interest for the so-called " FFT-based methods " for computing the overall and local properties of heterogeneous materials submitted to mechanical solicitations. Since the original method was introduced by Moulinec and Suquet [1], several authors have proposed different algorithms to better deal with non-linear materials or with materials whith highly contrasted mechanical properties between their constituents. The present paper aims to compare three methods of this family of algorithms which were designed to accelerate the convergence of the scheme. The study concerns a linear elastic material-although the methods involved can be extended into the case of non-linear behavior-submitted to a prescribed overall strain E. The stiffness tensor c(x) of the material varies with the position x. The numerical method proposed by Moulinec & Suquet lies on the iterative resolution of the Lippmann-Schwinger equation and can be summarized by the following relation between two successive iterates ε i and ε i+1 of the strain field: ε i+1 (x) = −Γ 0 * (c(x) − c 0) : ε i (x) + E (1)