[Accélération du schéma Eyre–Milton adaptatif pour l’homogénéisation par FFT des milieux à double contraste infini]
Sab et al. (2024) ont récemment proposé un algorithme itératif basé sur la FFT, appelé Adaptive Eyre–Milton (AEM), pour résoudre l’équation de Lippmann–Schwinger dans le contexte de l’homogénéisation périodique de composites élastiques linéaires à double contraste infini (matériaux hétérogènes avec des lois constitutives linéaires contenant à la fois des pores et des inclusions rigides). Ils ont démontré la convergence linéaire inconditionnelle de ce schéma, quel que soit l’initialisation et le matériau de référence choisis. Cependant, les simulations numériques ont montré que la vitesse de convergence du schéma AEM dépend fortement du choix du matériau de référence. Dans cet article, nous introduisons une nouvelle version du schéma AEM, où le matériau de référence est mis à jour de manière itérative, aboutissant à un schéma rapide et polyvalent, appelé Accelerated Adaptive Eyre–Milton (A2EM). Des simulations numériques avec le schéma A2EM sur des composites élastiques linéaires avec des pores et des inclusions infiniment rigides montrent que, quel que soit le matériau de référence initial choisi, cet algorithme a la même vitesse de convergence que le schéma AEM avec le meilleur choix du matériau de référence.
Sab et al. (2024) have recently proposed an FFT-based iterative algorithm, termed Adaptive Eyre–Milton (AEM), for solving the Lippmann–Schwinger equation in the context of periodic homogenization of infinitely double contrasted linear elastic composites (heterogeneous materials with linear constitutive laws that contain both pores and rigid inclusions). They have demonstrated the unconditional linear convergence of this scheme, regardless of initialization and the chosen reference material. However, numerical simulations have shown that the rate of convergence of AEM strongly depends on the chosen reference material. In this paper, we introduce a new version of the AEM scheme where the reference material is updated iteratively, resulting in a fast and versatile scheme, termed Accelerated Adaptive Eyre–Milton (A2EM). Numerical simulations with A2EM on linear elastic composites with both pores and infinitely rigid inclusions show that, regardless of the initial chosen reference material, this algorithm has the same rate of convergence as AEM with the best choice of reference material.
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Mot clés : homogénéisation computationnelle, méthode basée sur la FFT, schéma itératif, élasticité linéaire, matériaux composites
Martin Dolbeau 1 ; Jérémy Bleyer 2 ; Karam Sab 2
CC-BY 4.0
@article{CRMECA_2024__352_G1_251_0,
author = {Martin Dolbeau and J\'er\'emy Bleyer and Karam Sab},
title = {Accelerating the {Adaptive} {Eyre{\textendash}Milton} {FFT-based} method for infinitely double contrasted media},
journal = {Comptes Rendus. M\'ecanique},
pages = {251--267},
publisher = {Acad\'emie des sciences, Paris},
volume = {352},
year = {2024},
doi = {10.5802/crmeca.269},
language = {en},
}
TY - JOUR AU - Martin Dolbeau AU - Jérémy Bleyer AU - Karam Sab TI - Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media JO - Comptes Rendus. Mécanique PY - 2024 SP - 251 EP - 267 VL - 352 PB - Académie des sciences, Paris DO - 10.5802/crmeca.269 LA - en ID - CRMECA_2024__352_G1_251_0 ER -
%0 Journal Article %A Martin Dolbeau %A Jérémy Bleyer %A Karam Sab %T Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media %J Comptes Rendus. Mécanique %D 2024 %P 251-267 %V 352 %I Académie des sciences, Paris %R 10.5802/crmeca.269 %G en %F CRMECA_2024__352_G1_251_0
Martin Dolbeau; Jérémy Bleyer; Karam Sab. Accelerating the Adaptive Eyre–Milton FFT-based method for infinitely double contrasted media. Comptes Rendus. Mécanique, Volume 352 (2024), pp. 251-267. doi : 10.5802/crmeca.269. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.269/
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