Comparison of three accelerated FFT-based schemes for computing the mechanical response of composite materials

Since the early 1990s when an iterative method based on Fourier transforms was introduced to compute the mechanical properties of heterogeneous materials, several algorithms have been proposed to increase the convergence rate of the initial scheme. This paper is devoted to the comparison of three of these accelerated schemes. It shows that two of them are special cases of the third, corresponding to particular choices of parameters of the method. An upper bound of the spectral radius of the schemes is determined, from which sufficient conditions of convergence of the schemes are derived. Conditions are found for minimizing this upper bound. In particular, the accelerated scheme, which minimizes this upper bound, is exhibited. The paper discusses the choice of the convergence test used in the schemes. Copyright (c) 2013 John Wiley & Sons, Ltd.