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Communication Dans Un Congrès Année : 2015

A posteriori error estimators for FFT-based numerical techniques

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Sébastien Brisard
Ludovic Chamoin

Résumé

Initially proposed by Moulinec and Suquet (1994, 1998), FFT-based homogenization methods have gained in popularity within the last decade. Recent developments include (the list is not exhaustive) alternative iterative schemes (Monchiet and Bonnet, 2012), improved discrete Green operators (Brisard and Dormieux, 2012; Willot, 2015), geometric non-linearities (Kabel et al., 2014), convergence with respect to the grid-size (Brisard and Dormieux, 2012; Schneider 2014). Very little attention has been paid so far to the quantitative estimation of the quality of the numerical solution. In this talk, we will present a strategy for an a-posteriori evaluation of the numerical error. The approach is based on the so-called error in constitutive law (Ladevèze, 1983). Initially devised for the finite element method, it is extended here to FFT-based methods on cartesian grds. This requires the reconstruction of the displacement (which is usually not carried out in a standard FFT analysis), and an efficient procedure will be presented. The technique will be illustrated on a few simple examples. It should be noted that the aposteriori error estimator thus introduced applies to any FFT-based scheme. Therefore, the present framework allows a quantitative comparison of the various discrete Green operators.
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Dates et versions

hal-01199166 , version 1 (15-09-2015)

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Paternité - CC BY 4.0

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  • HAL Id : hal-01199166 , version 1

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Sébastien Brisard, Ludovic Chamoin. A posteriori error estimators for FFT-based numerical techniques. MAI workshop and training session: Micromechanics of cementitious materials, Materials Ageing Institute (MAI), Sep 2015, Ecuelles, France. ⟨hal-01199166⟩
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