Comptes Rendus
Short paper
FFT-based computation of homogenized interface parameters
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.

Published online:
DOI: 10.5802/crmeca.119
Keywords: 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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {R\'emi Cornaggia and Marie Touboul and C\'edric Bellis},
     title = {FFT-based computation of homogenized interface parameters},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {297--307},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {350},
     year = {2022},
     doi = {10.5802/crmeca.119},
     language = {en},
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PB  - Académie des sciences, Paris
DO  - 10.5802/crmeca.119
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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.

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