  FFT-based solvers introduced in the 1990s for the numerical homogenization of
heterogeneous elastic materials have been extended to a wide range of physical
properties. In parallel, alternative algorithms and modified discrete Green
operators have been proposed to accelerate the method and/or improve the
description of the local fields. In this short note, filtering material
properties is proposed as a third complementary way to improve FFT-based
methods. It is evidenced from numerical experiments that, the grid refinement
and consequently the computation time and/or the spurious oscillations observed
on local fields can be significantly reduced. In addition, while the Voigt and
Reuss filters can improve or deteriorate the method depending on the
microstructure, a stiff inclusion within a compliant matrix or the reverse, the
proposed "2-layers" filter is efficient in both situations. The study is
proposed in the context of linear elasticity but similar results are expected
in a different physical context (thermal, electrical...).
