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In this short note, we present a new technique to accelerate the convergenceof a FFT-based solver for numerical homogenization of complex periodic mediaproposed by Moulinec and Suquet in 1994. The approach proceeds fromdiscretization of the governing integral equation by the trigonometriccollocation method due to Vainikko (2000), to give a linear system which can beefficiently solved by conjugate gradient methods. Computational experimentsconfirm robustness of the algorithm with respect to its internal parameters anddemonstrate significant increase of the convergence rate for problems withhigh-contrast coefficients at a low overhead per iteration.

Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients