Filtering material properties to improve FFT-based methods for numerical homogenization

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, if the two filters based on Voigt or Reuss homogenization rules can improve or deteriorate the method depending on the microstructure, a stiff inclusion within a compliant matrix or the reverse, the proposed ‘2-layer’ 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…).