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FFT-based computation of homogenized interface parameters
Rémi Cornaggia1   ; Marie Touboul2  ; Cédric Bellis3 
1 Sorbonne Université, CNRS, UMR 7190, Institut Jean Le Rond ∂’Alembert, F-75005 Paris, France
2 School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
3 Aix Marseille Univ, CNRS, Centrale Marseille, LMA UMR 7031, Marseille, France
Comptes Rendus. Mécanique, Volume 350 (2022), pp. 297-307.

The homogenization of microstructured interfaces requires solving specific problems posed on semi-infinite bands. To tackle these problems with existing FFT-based algorithms, a reformulation of these band problems into fully periodic cell problems, posed on bounded domains, is established. This is performed thanks to a Dirichlet-to-Neumann operator and a decomposition of the solution involving a boundary corrector, in a Fourier framework. A fixed-point algorithm and an example choice of corrector are proposed. Comparisons with other computational methods support this proposition.

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DOI : 10.5802/crmeca.119
Mots clés : Homogenization, Dirichlet-to-Neumann, Cell problems, Band problems, FFT-based solvers

Rémi Cornaggia 1 ; Marie Touboul 2 ; Cédric Bellis 3

1 Sorbonne Université, CNRS, UMR 7190, Institut Jean Le Rond ∂’Alembert, F-75005 Paris, France
2 School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
3 Aix Marseille Univ, CNRS, Centrale Marseille, LMA UMR 7031, Marseille, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {FFT-based computation of homogenized interface parameters},
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Rémi Cornaggia; Marie Touboul; Cédric Bellis. FFT-based computation of homogenized interface parameters. Comptes Rendus. Mécanique, Volume 350 (2022), pp. 297-307. doi : 10.5802/crmeca.119. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.119/

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