A. Bensoussan, J. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, 1978.

M. Bonnet, R. Cornaggia, and B. B. Guzina, Microstructural topological sensitivities of the second-order macroscopic model for waves in periodic media, SIAM Journal on Applied Mathematics, vol.78, issue.4, pp.2057-2082, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01742396

A. Bonnet-bendhia, D. Drissi, and N. Gmati, Simulation of a muffler's transmission losses by a homogenized finite element method, Journal of Computational Acoustics, vol.12, issue.3, pp.447-474, 2004.

J. P. Cassier, M. Kachanovska, and M. , Mathematical models for dispersive electromagnetic waves: An overview, Computers & Mathematics with Applications, vol.74, issue.11, pp.2792-2830, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01647185

G. Chiavassa and B. Lombard, Time domain numerical modeling of wave propagation in 2D heterogeneous porous media, Journal of Computational Physics, vol.230, issue.13, pp.5288-5309, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00547008

M. David, C. Pideri, and J. Marigo, Homogenized interface model describing inhomogeneities located on a surface, Journal of Elasticity, vol.109, issue.2, pp.153-187, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00655496

B. Delourme, Modèles asymptotiques des interfaces fines et périodiques e? electromagnétisme, 2010.

B. Bojan, M. Guzina, and . Bonnet, Small-inclusion asymptotic of misfit functionals for inverse problems in acoustics, Inverse Problems, vol.22, issue.5, pp.1761-1785, 2006.

R. B. Harvey, P. M. Morse, and H. Feschbach, Methods of theoretical physics, The Mathematical Gazette, vol.39, issue.327, p.80, 1955.

B. Lombard, Modélisation numérique de la propagation et de la diffraction d'ondes mécaniques, Habilitationà Diriger des Recherches de l'Université, 2010.

B. Lombard, A. Maurel, and J. Marigo, Numerical modeling of the acoustic wave propagation across an homogenized rigid microstructure in the time domain, Journal of Computational Physics, vol.335, pp.558-577, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01348416

B. Lombard, J. Piraux, C. Gélis, and J. Virieux, Free and smooth boundaries in 2-d finite-difference schemes for transient elastic waves, Geophysical Journal International, vol.172, issue.1, pp.252-261, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00157508

B. Lombard and J. Piraux, How to incorporate the spring-mass conditions in finitedifference schemes, SIAM Journal of Scientific Computing, vol.24, issue.4, pp.1379-1407, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00004812

B. Lombard and J. Piraux, Numerical treatment of two-dimensional interfaces for acoustic and elastic waves, Journal of Computational Physics, vol.195, issue.1, pp.90-116, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00004813

B. Lombard and J. Piraux, Numerical modeling of elastic waves across imperfect contacts, SIAM Journal on Scientific Computing, vol.28, issue.1, pp.172-205, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00004815

F. Lorcher and C. Munz, Lax-wendroff-type schemes of arbitrary order in several space dimensions, IMA Journal of Numerical Analysis, vol.27, issue.3, pp.593-615, 2006.

G. Ma, M. Yang, S. Xiao, Z. Yang, and P. Sheng, Acoustic metasurface with hybrid resonances, Nature Materials, vol.13, pp.873-879, 2014.

J. Marigo and A. Maurel, Homogenization models for thin rigid structured surfaces and films, The Journal of the Acoustical Society of America, vol.140, issue.1, pp.260-273, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01657581

J. Marigo, A. Maurel, K. Pham, and A. Sbitti, Effective dynamic properites of a row of elastic inclusions: The case of scalar shear waves, Journal of Elasticity, vol.128, issue.2, pp.265-289, 2017.

J. Marigo and C. Pideri, The effective behaviour of elastic bodies containing microcracks or microholes localized on a surface, International Journal of Damage Mechanics, vol.20, pp.1151-1177, 2011.

K. Pham, A. Maurel, and J. Marigo, Two scale homogenization of a row of locally resonant inclusions -the case of shear waves, Journal of the Mechanics and Physics of Solids, vol.106, pp.80-94, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01657086

J. Sanchez-hubert and E. Sanchez-palencia, Introduction aux Méthodes Asymptotiques et a l'Homogénéisation. Collection Mathématiques Appliquées pour la Maîtrise, 1992.

L. Schwan, O. Umnova, and C. Boutin, Sound absorption and reflection from a resonant metasurface: Homogenisation model with experimental validation, Wave Motion, vol.72, pp.154-172, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01773728

T. Schwartzkopff, M. Dumbser, and C. Munz, Fast high order ADER schemes for linear hyperbolic equations, Journal of Computational Physics, vol.197, issue.2, pp.532-539, 2004.

X. Su, Z. Lu, and A. N. Norris, Elastic metasurfaces for splitting sv-and p-waves in elastic solids, Journal of Applied Physics, vol.123, p.91701, 2018.

W. T. Vetterling, W. H. Press, S. A. Teukolskyn, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 1992.

C. Zhang and R. J. Leveque, The immersed interface method for acoustic wave equations with discontinuous coefficients, Wave Motion, vol.25, pp.237-263, 1997.