Open Access
Issue
ESAIM: M2AN
Volume 57, Number 3, May-June 2023
Page(s) 1413 - 1444
DOI https://doi.org/10.1051/m2an/2023027
Published online 18 May 2023
  1. A. Abdulle and T. Pouchon, A priori error analysis of the finite element heterogeneous multiscale method for the wave equation over long time. SIAM J. Numer. Anal. 54 (2016) 1507–1534. [Google Scholar]
  2. G. Allaire and T. Yamada, Optimization of dispersive coefficients in the homogenization of the wave equation in periodic structures. Numer. Math. 140 (2018) 265–326. [CrossRef] [MathSciNet] [Google Scholar]
  3. G. Allaire, M. Briane and M. Vanninathan, A comparison between two-scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures. SeMA J. 73 (2016) 237–259. [CrossRef] [MathSciNet] [Google Scholar]
  4. G. Allaire, A. Lamacz-Keymling and J. Rauch, Crime pays: homogenized wave equations for long times. Asymptot. Anal. (2021) 1–42. [Google Scholar]
  5. I. Andrianov, V. Bolshakov, V. Danishevs and D. Weichert, Higher order asymptotic homogenization and wave propagation in periodic composite materials. Proc. R. Soc. London A Math. Phys. Eng. Sci. 464 (2008) 1181–1201. [Google Scholar]
  6. S. Armstrong, T. Kuusi, J.C. Mourrat and C. Prange, Quantitative analysis of boundary layers in periodic homogenization. Arch. Ration. Mech. Anal. 226 (2017) 695–741. [CrossRef] [MathSciNet] [Google Scholar]
  7. C. Bellis and B. Lombard, Simulating transient wave phenomena in acoustic metamaterials using auxiliary fields. Wave Motion 86 (2019) 175–194. [CrossRef] [Google Scholar]
  8. C. Beneteau, Modèles homogénéisés enrichis en présence de bords: analyse et traitement numérique. Ph.D. Thesis, Institut Polytechnique de Paris (2021). [Google Scholar]
  9. A. Bensoussan, J.L. Lions and G. Papanicolau, Asymptotic Analysis for Periodic Structures, North-Holland (1978). [Google Scholar]
  10. F. Cakoni, B. Guzina and S. Moskow, On the homogenization of a scalar scattering problem for highly oscillating anisotropic media. SIAM J. Math. Anal. 48 (2016) 2532–2560. [CrossRef] [MathSciNet] [Google Scholar]
  11. F. Cakoni, B. Guzina, S. Moskow and T. Pangburn, Scattering by a bounded highly oscillating periodic medium and the effect of boundary correctors. SIAM J. Appl. Math. 79 (2019) 1448–1474. [CrossRef] [MathSciNet] [Google Scholar]
  12. Y. Capdeville, Homogenization of seismic point and extended sources. Geophys. J. Int. 226 (2021) 1390–1416. [CrossRef] [Google Scholar]
  13. Y. Capdeville, L. Guillot and J.J. Marigo, 1-D non-periodic homogenization for the seismic wave equation. Geophys. J. Int. 181 (2010) 897–910. [Google Scholar]
  14. R. Cornaggia and C. Bellis, Tuning effective dynamical properties of periodic media by FFT-accelerated topological optimization. Int. J. Numer. Methods Eng. 121 (2020) 3178–3205. [CrossRef] [Google Scholar]
  15. R. Cornaggia and B. Guzina, Second-order homogenization of boundary and transmission conditions for one-dimensional waves in periodic media. Int. J. Solids Struct. 188–189 (2020) 88–102. [CrossRef] [Google Scholar]
  16. R.V. Craster, J. Kaplunov and A.V. Pichugin, High-frequency homogenization for periodic media. Proc. R. Soc. London A: Math. Phys. Eng. Sci. 466 (2010) 2341–2362. [Google Scholar]
  17. B. Delourme, H. Haddar and P. Joly, Approximate models for wave propagation across thin periodic interfaces. J. Math. Pures Appl. 98 (2012) 28–71. [Google Scholar]
  18. J. Fish and W. Chen, Higher-order homogenization of initial/boundary-value problem. J. Eng. Mech. 127 (2001) 1223–1230. [Google Scholar]
  19. J. Fish, W. Chen and G. Nagai, Non-local dispersive model for wave propagation in heterogeneous media: one-dimensional case. Int. J. Numer. Methods Eng. 54 (2002) 331–346. [CrossRef] [Google Scholar]
  20. S. Fliss, Wave propagation in periodic media: mathematical analysis and numerical simulation, Habilitation à diriger des recherches, Université Paris Sud, Paris 11 (2019). [Google Scholar]
  21. S. Forest and K. Sab, Finite-deformation second-order micromorphic theory and its relations to strain and stress gradient models. Math. Mech. Solids (2017) 1–21. [Google Scholar]
  22. D. Gérard-Varet and N. Masmoudi, Homogenization and boundary layers. Acta Math. 209 (2012) 133–178. [CrossRef] [MathSciNet] [Google Scholar]
  23. E. Godlewski and P.A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws, Springer (1996). [CrossRef] [Google Scholar]
  24. B. Guzina, S. Meng and O. Oudghiri-Idrissi, A rational framework for dynamic homogenization at finite wavelengths and frequencies. Proc. R. Soc. A: Math. Phys. Eng. Sci. 475 (2019) 20180547. [Google Scholar]
  25. D. Harutyunyan, G.W. Milton and R.V. Craster, High-frequency homogenization for travelling waves in periodic media. Proc. R. Soc. London A: Math. Phys. Eng. Sci. 472 (2016) 20160066. [Google Scholar]
  26. M. Josien, Some quantitative homogenization results in a simple case of interface. Commun. Partial. Differ. Equ. 44 (2019) 907–939. [CrossRef] [Google Scholar]
  27. A. Lamacz, Dispersive effective models for waves in heterogeneous media. Math. Models Methods Appl. Sci. 21 (2011) 1871–1899. [CrossRef] [MathSciNet] [Google Scholar]
  28. V. Laude, Phononic Crystals, De Gruyter (2015). [CrossRef] [Google Scholar]
  29. R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press (2002). [CrossRef] [Google Scholar]
  30. B. Lombard and J. Piraux, How to incorporate the spring-mass conditions in finite-difference schemes. SIAM J. Sci. Comput. 24 (2003) 1379–1407. [CrossRef] [MathSciNet] [Google Scholar]
  31. J.J. Marigo and A. Maurel, Second order homogenization of subwavelength stratified media including finite size effect. SIAM J. Appl. Math. 77 (2017) 721–743. [CrossRef] [MathSciNet] [Google Scholar]
  32. A. Maurel and J.J. Marigo, Sensitivity of a dielectric layered structure on a scale below the periodicity: a fully local homogenized model. Phys. Rev. B 98 (2018) 024306. [CrossRef] [Google Scholar]
  33. A. Maurel, K. Pham and J.J. Marigo, Scattering of gravity waves by a periodically structured ridge of finite extent. J. Fluid Mech. 871 (2019) 350–376. [CrossRef] [MathSciNet] [Google Scholar]
  34. S. Moskow and M. Vogelius, First-order corrections to the homogenised eigenvalues of a periodic composite medium. A convergence proof. Proc. R. Soc. Edinb. A Math. 127 (1997) 1263–1299. [CrossRef] [Google Scholar]
  35. F. Santosa and W.W. Symes, A dispersive effective medium for wave propagation in periodic composites. SIAM Journal on Applied Mathematics 51 (1991) 984–1005. [CrossRef] [MathSciNet] [Google Scholar]
  36. L. Schwan, N. Favrie, N. Cottereau and B. Lombard, Extended stress gradient elastodynamics: wave dispersion and micro-macro identification of parameters. Int. J. Solids Struct. 219–220 (2021) 34–50. [CrossRef] [Google Scholar]
  37. D.P. Shahraki and B. Guzina, Homogenization of the wave equation with non-uniformly oscillating coefficients. Math. Mech. Solids 27–11 (2022) 2341–2365. [CrossRef] [MathSciNet] [Google Scholar]
  38. D.P. Shahraki and B. Guzina, From d’Alembert to Bloch and back: a semi-analytical solution of 1D boundary value problems governed by the wave equation in periodic media. Int. J. Solids Structures 234–235 (2022) 111239. [CrossRef] [Google Scholar]
  39. M. Touboul, B. Lombard and C. Bellis, Time-domain simulation of wave propagation across resonant meta-interfaces. J. Comput. Phys. 414 (2020) 109474. [CrossRef] [MathSciNet] [Google Scholar]
  40. V. Vinoles, Interface problems with metamaterials: modelling, analysis and simulations, Ph.D. Thesis, ENSTA Paris-Saclay (2016). [Google Scholar]
  41. A. Wautier and B. Guzina, On the second-order homogenization of wave motion in periodic media and the sound of a chessboard. J. Mech. Phys. Solids 78 (2015) 382–414. [CrossRef] [MathSciNet] [Google Scholar]

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