  We modify the Green operator involved in Fourier-based computational schemes
in elasticity, in 2D and 3D. The new operator is derived by expressing
continuum mechanics in terms of centered differences on a rotated grid. Use of
the modified Green operator leads, in all systems investigated, to more
accurate strain and stress fields than using the discretizations proposed by
Moulinec and Suquet (1994) or Willot and Pellegrini (2008). Moreover, we
compared the convergence rates of the "direct" and "accelerated" FFT schemes
with the different discretizations. The discretization method proposed in this
work allows for much faster FFT schemes with respect to two criteria: stress
equilibrium and effective elastic moduli.
