paper

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

arXiv:1412.3228 · doi:10.1016/j.jcp.2015.03.048

Abstract

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...).

submitted to Journal of Computational Physics, November 2014

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