Fourier-based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fieldsReport as inadecuate




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1 CMM - Centre de Morphologie Mathématique 2 DAM-DIF - DAM Île-de-France

Abstract : A modified Green operator is proposed as an improvement of Fourier-based numerical schemes commonly used for computing the electrical or thermal response of heterogeneous media. Contrary to other methods, the number of iterations necessary to achieve convergence tends to a finite value when the contrast of properties between the phases becomes infinite. Furthermore, it is shown that the method produces much more accurate local fields inside highly-conducting and quasi-insulating phases, as well as in the vicinity of the phases interfaces. These good properties stem from the discretization of Green-s function, which is consistent with the pixel grid while retaining the local nature of the operator that acts on the polarization field. Finally, a fast implementation of the -direct scheme- of Moulinec et al. 1994 that allows for parcimonious memory use is proposed.

Keywords : FFT methods Numerical homogenization Heterogeneous media Electrical conductivity





Author: François Willot - Bassam Abdallah - Yves-Patrick Pellegrini -

Source: https://hal.archives-ouvertes.fr/



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