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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/

[1] J.-J. Marigo; A. Maurel; K. Pham; A. Sbitti Effective dynamic properties of a row of elastic inclusions: The case of scalar shear waves, J. Elast., Volume 128 (2017) no. 2, pp. 265-289 | DOI | MR | Zbl

[2] M. Touboul Acoustic and elastic wave propagation in microstructured media with interfaces: homogenization, simulation and optimization, Ph. D. Thesis, Aix-Marseille Université (2021) https://tel.archives-ouvertes.fr/tel-03411353/

[3] R. Cornaggia; C. Bellis Tuning effective dynamical properties of periodic media by FFT-accelerated topological optimization, Int. J. Numer. Methods Eng., Volume 121 (2020) no. 14, pp. 3178-3205 | DOI | MR

[4] I. Harari; I. Patlashenko; D. Givoli Dirichlet-to-Neumann maps for unbounded wave guides, J. Comput. Phys., Volume 143 (1998) no. 1, pp. 200-223 | DOI | MR | Zbl

[5] A.-S. Bonnet-Ben Dhia; G. Legendre An alternative to Dirichlet-to-Neumann maps for waveguides, C. R. Mat., Volume 349 (2011) no. 17–18, pp. 1005-1009 | MR | Zbl

[6] H. Moulinec; P. Suquet A numerical method for computing the overall response of nonlinear composites with complex microstructure, Comput. Meth. Appl. Mech. Eng., Volume 157 (1998) no. 1, pp. 69-94 | DOI | MR | Zbl

[7] M. Schneider A review of nonlinear FFT-based computational homogenization methods, Acta Mech., Volume 232 (2021) no. 6, pp. 2051-2100 | DOI | MR | Zbl

[8] L. Gélébart A modified FFT-based solver for the mechanical simulation of heterogeneous materials with Dirichlet boundary conditions, C. R. Méc., Volume 348 (2020) no. 8–9, pp. 693-704

[9] H. Moulinec; F. Silva Comparison of three accelerated FFT-based schemes for computing the mechanical response of composite materials, Int. J. Numer. Methods Eng., Volume 97 (2014) no. 13, pp. 960-985 | DOI | MR | Zbl

[10] F. Hecht New development in FreeFem++, J. Numer. Math., Volume 20 (2012) no. 3–4, pp. 251-265 | MR | Zbl

[11] A. Maurel; J.-J. Marigo; K. Pham Effective boundary condition for the reflection of shear waves at the periodic rough boundary of an elastic body, Vietnam J. Mech., Volume 40 (2018) no. 4, pp. 303-323 | DOI

[12] S. Fliss Wave propagation in periodic media: mathematical analysis and numerical simulation, 2019 https://hal.archives-ouvertes.fr/tel-02394976 Habilitation à diriger des recherches, Université Paris Sud (Paris 11)

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