]. S. Références1, D. Abarbanel, and . Gottlieb, A mathematical analysis of the PML method, J. Comput. Phys, vol.134, issue.2, pp.357-363, 1997.

S. Abarbanel, D. Gottlieb, and J. S. Hesthaven, Long time behavior of the perfectly matched layer equations in computational electromagnetics, SIAM J. Scientific Comp, vol.17, pp.1-4, 2002.

Y. Achdou, C. Japhet, Y. Maday, and F. Nataf, A new cement to glue non-conforming grids with Robin interface conditions: The finite volume case, Numerische Mathematik, vol.92, issue.4, pp.593-620, 2002.
DOI : 10.1007/s002110100336

B. Alpert, L. Greengard, and T. Hagström, Rapid Evaluation of Nonreflecting Boundary Kernels for Time-Domain Wave Propagation, SIAM Journal on Numerical Analysis, vol.37, issue.4, pp.1138-1164, 2000.
DOI : 10.1137/S0036142998336916

B. Alpert, L. Greengard, and T. Hagström, Nonreflecting Boundary Conditions for the Time-Dependent Wave Equation, Journal of Computational Physics, vol.180, issue.1, pp.270-296, 2002.
DOI : 10.1006/jcph.2002.7093

G. Baker, Essentials of Padé approximants, 1975.

H. Barucq, A new family of first-order boundary conditions for the Maxwell system: derivation, well-posedness and long-time behavior, Journal de Math??matiques Pures et Appliqu??es, vol.82, issue.1, pp.67-88, 2003.
DOI : 10.1016/S0021-7824(02)00002-8

E. Bécache, A. Bonnet-ben-dhia, and G. Legendre, Perfectly Matched Layers for the Convected Helmholtz Equation, SIAM Journal on Numerical Analysis, vol.42, issue.1, pp.409-433, 2004.
DOI : 10.1137/S0036142903420984

E. Bécache, S. Fauqueux, and P. Joly, Stability of perfectly matched layers, group velocities and anisotropic waves, Journal of Computational Physics, vol.188, issue.2, pp.399-433, 2003.
DOI : 10.1016/S0021-9991(03)00184-0

E. Bécache and P. Joly, On the analysis of B??renger's Perfectly Matched Layers for Maxwell's equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.36, issue.1, pp.87-119, 2002.
DOI : 10.1051/m2an:2002004

E. Bécache, P. G. Petropoulos, and S. Gedney, On the Long-Time Behavior of Unsplit Perfectly Matched Layers, IEEE Transactions on Antennas and Propagation, vol.52, issue.5, 2002.
DOI : 10.1109/TAP.2004.827253

F. and B. Belgacem, The Mortar finite element method with Lagrange multipliers, Numerische Mathematik, vol.84, issue.2, pp.173-197, 1999.
DOI : 10.1007/s002110050468

J. P. Bérenger, A perfectly matched layer for the absorption of electromagnetic waves, Journal of Computational Physics, vol.114, issue.2, pp.185-200, 1994.
DOI : 10.1006/jcph.1994.1159

J. P. Bérenger, Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic Waves, Journal of Computational Physics, vol.127, issue.2, pp.363-379, 1996.
DOI : 10.1006/jcph.1996.0181

C. Bernardi, Y. Maday, and A. T. Patera, A new nonconforming approach to domain decomposition: the mortar element method In Nonlinear partial differential equations and their applications, Colì ege de France Seminar Pitman Res. Notes Math. Ser. Longman Sci. Tech, vol.299, pp.13-51, 1989.

C. Bescond and M. Deschamps, Dynamical surface response of a semi-infinite anisotropic elastic medium to an impulsive force, The Journal of the Acoustical Society of America, vol.103, issue.1, pp.114-138, 1998.
DOI : 10.1121/1.421071

E. Bossy, Evaluation ultrasonore de l'os cortical par transmission axiale : modélisation et expérimentation in vitro et in vivo, Thèse de doctorat, 2003.

E. Bossy, M. Talmant, and P. Laugier, Effect of bone cortical thickness on velocity measurements using ultrasonic axial transmission: A 2D simulation study, The Journal of the Acoustical Society of America, vol.112, issue.1
DOI : 10.1121/1.1480836

L. Cagniard, Réflexion et réfraction des ondes sismiques progressives, 1939.

P. G. Ciarlet, The finite element method for elliptic problems, Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.40, 2002.

G. C. Cohen, Higher-Order Numerical Methods for Transient Wave Equations. Scientific Computation, Applied Mechanics Reviews, vol.55, issue.5, 2002.
DOI : 10.1115/1.1497470
URL : https://hal.archives-ouvertes.fr/hal-01166961

G. C. Cohen and S. Fauqueux, MIXED FINITE ELEMENTS WITH MASS-LUMPING FOR THE TRANSIENT WAVE EQUATION, Journal of Computational Acoustics, vol.08, issue.01, pp.171-188, 1999.
DOI : 10.1142/S0218396X0000011X

F. Collino, T. Fouquet, and P. Joly, Conservative space-time mesh refinement methods for the FDTD solution of Maxwell???s equations, Journal of Computational Physics, vol.211, issue.1
DOI : 10.1016/j.jcp.2005.03.035

F. Collino and B. Lavaud, Peut-on obtenir des amplitudes correctes avec leséquationsleséquations paraxiales ? 3004, 1996.

F. Collino and P. Monk, Conditions et couches absorbantes pour leséquationsleséquations de Maxwell In Aspects récents en méthodes numériques pour leséquationsleséquations, 1998.

F. Collino and P. Monk, The Perfectly Matched Layer in Curvilinear Coordinates, SIAM Journal on Scientific Computing, vol.19, issue.6, pp.157-171, 1998.
DOI : 10.1137/S1064827596301406
URL : https://hal.archives-ouvertes.fr/inria-00073643

F. Collino and C. Tsogka, Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media, GEOPHYSICS, vol.66, issue.1, pp.294-307, 2001.
DOI : 10.1190/1.1444908

G. Derveaux, Modélisation numérique de la guitare acoustique, Thèse de doctorat, Ecole Polytechnique, 2002.

J. Diaz and P. Joly, An Analysis of Higher Order Boundary Conditions for the Wave Equation, SIAM Journal on Applied Mathematics, vol.65, issue.5
DOI : 10.1137/S0036139903436145
URL : https://hal.archives-ouvertes.fr/inria-00071617

J. Diaz and P. Joly, ROBUST HIGH ORDER NON-CONFORMING FINITE ELEMENT FORMULATION FOR TIME DOMAIN FLUID-STRUCTURE INTERACTION, Journal of Computational Acoustics, vol.13, issue.03
DOI : 10.1142/S0218396X05002736
URL : https://hal.archives-ouvertes.fr/inria-00409201

J. Diaz and P. Joly, A time domain analysis of PML models in acoustics, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.29-32
DOI : 10.1016/j.cma.2005.02.031
URL : https://hal.archives-ouvertes.fr/inria-00410313

J. Diaz and P. Joly, ´ Eléments finis d'ordré elevé pour le couplage fluide-structure. InÉtude In´InÉtude de la propagation ultrasonore en milieux non homogènes en vue du contrôle non destructif, GDR-US 2501, pp.71-80, 2003.

J. Diaz and P. Joly, Stabilized Perfectly Matched Layer for Advective Acoustics, The Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation, pp.115-119, 2003.
DOI : 10.1007/978-3-642-55856-6_18

T. H. Duong and P. Joly, On the stability analysis of boundary conditions for the wave equation by energy methods; Part I : The homogeneous case, Math. of Comp, vol.62, pp.206-539, 1994.
URL : https://hal.archives-ouvertes.fr/inria-00075253

V. Duwig, Raffinement de maillage pour le couplage fluide-structure, 2001.

B. Engquist and L. Halpern, Far field boundary conditions for computation over long time, Applied Numerical Mathematics, vol.4, issue.1, pp.21-45, 1988.
DOI : 10.1016/S0168-9274(88)80004-7

B. Engquist and L. Halpern, Long-time behaviour of absorbing boundary conditions, Mathematical Methods in the Applied Sciences, vol.20, issue.3, pp.3-189, 1990.
DOI : 10.1002/mma.1670130302

B. Engquist and A. Majda, Absorbing boundary conditions for the numerical simulation of waves, Mathematics of Computation, vol.31, issue.139, pp.629-651, 1977.
DOI : 10.1090/S0025-5718-1977-0436612-4

B. Engquist and A. Majda, Radiation boundary conditions for acoustic and elastic wave calculations, Communications on Pure and Applied Mathematics, vol.28, issue.3, pp.314-358, 1979.
DOI : 10.1002/cpa.3160320303

A. Ezziani, Modélisation mathématique et numérique de la propagation d'ondes dans les milieux viscoélastiques et poroélastiques, Thèse de doctorat, 2005.

S. Fauqueux, Eléments finis spectraux et couches absorbantes parfaitement adaptées pour la propagation d'ondesélastiquesondesélastiques en milieu transitoire, Thèse de doctorat, 2003.

M. J. Gander, L. Halpern, and F. Nataf, Optimal Schwarz Waveform Relaxation for the One Dimensional Wave Equation, SIAM Journal on Numerical Analysis, vol.41, issue.5, pp.1643-1681, 2003.
DOI : 10.1137/S003614290139559X

D. Givoli, Exact and High-Order Non-Reflecting Computational Boundaries, Mathematical and Numerical Aspects of Wave Propagation, pp.1-42, 2003.
DOI : 10.1007/978-3-642-55856-6_4

M. J. Gröte and J. B. Keller, Exact Nonreflecting Boundary Conditions for the Time Dependent Wave Equation, SIAM Journal on Applied Mathematics, vol.55, issue.2, pp.280-297, 1995.
DOI : 10.1137/S0036139993269266

M. J. Gröte and J. B. Keller, Nonreflecting Boundary Conditions for Time-Dependent Scattering, Journal of Computational Physics, vol.127, issue.1, pp.52-81, 1996.
DOI : 10.1006/jcph.1996.0157

T. Hagström, E. Bécache, G. Cohen, and P. Joly, On the convergence of local approximations to pseudo-differentials operators, Proceedings of the 3rd Int. Conference on Mathematical and Numerical spects of Wave Propagation Phenomena, pp.474-482, 1995.

T. Hagström, On High-Order Radiation Boundary Conditions, Computational Wave Propagation, B. Engquist et, pp.1-21, 1996.
DOI : 10.1007/978-1-4612-2422-8_1

T. Hagström, Radiation boundary conditions for the numerical simulation of waves, Acta Numerica, vol.33, pp.47-106, 1999.
DOI : 10.2307/2008250

T. Hagström, New Results on Absorbing Layers and Radiation Boundary Conditions, Topics in Computational Wave Propagation -Direct and Inverse Problems, pp.1-42, 2003.
DOI : 10.1007/978-3-642-55483-4_1

T. Hagström and I. Nazarov, Absorbing Layers and Radiation Boundary Conditions for Jet Flow Simulations, 8th AIAA/CEAS Aeroacoustics Conference & Exhibit, 2002.
DOI : 10.2514/6.2002-2606

L. Halpern, Approximation paraxiales et conditions aux limites absorbantes, Thèse d'´ etat, 1986.

L. Halpern and J. Rauch, Error analysis for absorbing boundary conditions, Numerische Mathematik, vol.176, issue.4, pp.459-467, 1987.
DOI : 10.1007/BF01397547

M. Hamdi, Y. Ousset, and G. Verchery, A displacement method for the analysis of vibrations of coupled fluid-structure systems, International Journal for Numerical Methods in Engineering, vol.12, issue.1, pp.139-150, 1978.
DOI : 10.1002/nme.1620130110

J. S. Hesthaven, On the Analysis and Construction of Perfectly Matched Layers for the Linearized Euler Equations, Journal of Computational Physics, vol.142, issue.1, pp.129-147, 1998.
DOI : 10.1006/jcph.1998.5938

R. L. Higdon, Initial-Boundary Value Problems for Linear Hyperbolic System, SIAM Review, vol.28, issue.2, pp.177-217, 1986.
DOI : 10.1137/1028050

R. L. Higdon, Numerical absorbing boundary conditions for the wave equation, Mathematics of Computation, vol.49, issue.179, pp.65-90, 1987.
DOI : 10.1090/S0025-5718-1987-0890254-1

J. H. Van-der-hijden, Propagation of transient elastic waves in stratified anisotropic media, of North Holland Series in Applied Mathematics and Mechanics, 1987.

T. Hohage, F. Schmidt, and L. Zschiedrich, Solving Time-Harmonic Scattering Problems Based on the Pole Condition II: Convergence of the PML Method, SIAM Journal on Mathematical Analysis, vol.35, issue.3
DOI : 10.1137/S0036141002406485

A. T. De-hoop, A modification of cagniard???s method for solving seismic pulse problems, Applied Scientific Research, Section B, vol.34, issue.1, pp.349-356, 1959.
DOI : 10.1007/BF02920068

A. T. De-hoop, P. Van-den-berg, and F. Remis, Analytic time-domain performance analysis of absorbing boundary conditions and perfectly matched layers, IEEE Antennas and Propagation Society International Symposium. 2001 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.01CH37229), pp.502-505, 2001.
DOI : 10.1109/APS.2001.959509

F. Q. Hu, On Absorbing Boundary Conditions for Linearized Euler Equations by a Perfectly Matched Layer, Journal of Computational Physics, vol.129, issue.1, p.201, 1996.
DOI : 10.1006/jcph.1996.0244

F. Q. Hu, A Stable, Perfectly Matched Layer for Linearized Euler Equations in Unsplit Physical Variables, Journal of Computational Physics, vol.173, issue.2, pp.455-480, 2001.
DOI : 10.1006/jcph.2001.6887

P. Joly, Variational Methods for Time-Dependent Wave Propagation Problems, Topics in Computational Wave Propagation, Direct and Inverse Problems, pp.201-264, 2003.
DOI : 10.1007/978-3-642-55483-4_6

C. Jordan, Cours d'analyse de l'´ ecole polytechnique, pp.285-286, 1909.

D. Komatitsch, C. Barnes, and J. Tromp, Wave propagation near a fluid???solid interface: A spectral???element approach, GEOPHYSICS, vol.65, issue.2, pp.623-631, 2000.
DOI : 10.1190/1.1444758
URL : https://hal.archives-ouvertes.fr/hal-00669051

H. O. Kreiss, Initial boundary value problems for hyperbolic systems, Communications on Pure and Applied Mathematics, vol.19, issue.3, pp.277-298, 1970.
DOI : 10.1002/cpa.3160230304

H. Kreiss and J. Lorenz, Initial boundary value problems and the Navier-Stokes equations, 1989.
DOI : 10.1137/1.9780898719130

M. Lassas and E. Somersalo, On the existence and convergence of the solution of PML equations, Computing, vol.114, issue.3, pp.229-241, 1998.
DOI : 10.1007/BF02684334

J. Lions, J. Métral, and O. Vacus, Well-posed absorbing layer for hyperbolic problems, Numerische Mathematik, vol.92, issue.3, pp.535-562, 2002.
DOI : 10.1007/s002110100263

Y. Lu and J. Mclaughlin, Spectral analysis of the parabolic equation method, 1995.

A. Mourad and M. Deschamps, Lamb???s problem for an anisotropic half???space studied by the Cagniard de Hoop method, The Journal of the Acoustical Society of America, vol.97, issue.5, pp.3194-3201, 1995.
DOI : 10.1121/1.411823

Y. Pao and R. Gajewski, The generalized ray theory and transient respons of layered elastic solids, 1977.

O. Poncelet, Réponse transitoirè a une source impulsionnelle en espace en milieu anisotrope. Calcul de fonctions de Green par la méthode de Cagniard-de Hoop, Ondesélastiques Ondesélastiques dans les solides, pp.277-330, 2001.

S. Rienstra and A. Hirschberg, An introduction to acoustics Disponible en ligne sur http

]. J. Rodríguez, Raffinement de maillage spatio-temporel pour les equations de l'elastodynamique, Thèse de doctorat

L. Saas, I. Faille, F. Nataf, and F. Willien, Domain decomposition for a finite volume method on non-matching grids, Comptes Rendus Mathematique, vol.338, issue.5, pp.407-412, 2004.
DOI : 10.1016/j.crma.2003.12.014
URL : https://hal.archives-ouvertes.fr/hal-00017517

P. Solín and K. , Segeth et I. Dole?el. Higher-order finite element methods, Studies in Advanced Mathematics. Chapman & Hall/CRC, 2004.

C. K. Tam, L. Auriault, and F. Cambuli, Perfectly Matched Layer as an Absorbing Boundary Condition for the Linearized Euler Equations in Open and Ducted Domains, Journal of Computational Physics, vol.144, issue.1, pp.213-234, 1998.
DOI : 10.1006/jcph.1998.5997

L. N. Trefethen and L. Halpern, Well-posedness of one-way wave equations and absorbing boundary conditions, Mathematics of Computation, vol.47, issue.176, pp.176-421, 1986.
DOI : 10.1090/S0025-5718-1986-0856695-2

C. Tsogka, Modélisation mathématique et numérique de la propagation des ondesélastiques ondesélastiques tridimensionnelles dans des milieux fissurés, Thèse de doctorat, 1999.

J. Virieux, -wave propagation in heterogeneous media: Velocity???stress finite???difference method, GEOPHYSICS, vol.49, issue.11, pp.1933-1957, 1984.
DOI : 10.1190/1.1441605
URL : https://hal.archives-ouvertes.fr/hal-00408480

J. Virieux, wave propagation in heterogeneous media: Velocity???stress finite???difference method, GEOPHYSICS, vol.51, issue.4, pp.889-901, 1986.
DOI : 10.1190/1.1442147

E. T. Whittaker and G. N. Watson, A course in modern analysis, pp.115-117, 1990.

L. Zhao and A. C. Cangellaris, A general approach for the development of unsplitfield time-domain implementations of perfectly matched layers for FDTD grid truncation, IEEE Microwave and Guided Letters, vol.6, p.5, 1996.