P. Chevret and J. Chatillon, Implementation of diffraction in a ray-tracing model for the prediction of noise in open-plan offices, The Journal of the Acoustical Society of America, vol.132, issue.5, pp.3125-3137, 2012.
DOI : 10.1121/1.4754554

P. Chevret and J. Chatillon, Sound level prediction in open-spaces : implementation of diffraction in RAYPLUS software, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00810684

J. Ducourneau, V. Planeau, J. Chatillon, and A. Nejade, Measurement of sound absorption coefficients of flat surfaces in a workshop, Applied Acoustics, vol.70, issue.5, pp.710-721, 2009.
DOI : 10.1016/j.apacoust.2008.09.001

J. Ducourneau, A. Faiz, A. Khanfir, and J. Chatillon, Measuring sound scattering coefficients of uneven surfaces in a reverberant workplace ??? Principle and validation of the method, Applied Acoustics, vol.74, issue.5, pp.653-660, 2013.
DOI : 10.1016/j.apacoust.2012.11.012
URL : https://hal.archives-ouvertes.fr/hal-00968687

A. Faiz, J. Ducourneau, A. Khanfir, and J. Chatillon, Nouveau dispositif de mesure du coefficient de diffusion acoustique de parois à relief verticales présentes dans les locaux industriels, 2014.

J. Ducourneau, A. Faiz, and J. Chatillon, New device for measuring mapping of sound scattering coefficients of vertical uneven surfaces in a reverberant workplace, Applied Acoustics, vol.90, pp.21-30, 2015.
DOI : 10.1016/j.apacoust.2014.10.004
URL : https://hal.archives-ouvertes.fr/hal-01417342

J. Ducourneau, A. Faiz, K. Rabisse, and N. Trompette, Validation et limites d'un dispositif de mesure du coefficient de diffusion acoustique des parois à relief dans les bâtiments, 2016.

L. Bos, Caractérisation acoustique des parois épaisses périodiques dans les locaux industriels, 2006.

J. Ducourneau, L. Bos, V. Planeau, A. Faiz, S. Skali-lami et al., Prediction of the acoustic pressure above periodically uneven facings in industrial workplaces, Journal of Sound and Vibration, vol.329, issue.11, pp.2276-2290, 2010.
DOI : 10.1016/j.jsv.2009.12.028

A. Khanfir, A. Faiz, J. Ducourneau, J. Chatillon, and S. Skali-lami, Scattered acoustic field above a grating of parallel rectangular cavities, Journal of Sound and Vibration, vol.332, issue.4, pp.1047-1060, 2013.
DOI : 10.1016/j.jsv.2012.10.023
URL : https://hal.archives-ouvertes.fr/hal-01431066

A. Khanfir, A. Faiz, J. Ducourneau, J. Chatillon, and S. Skali-lami, Scattered acoustic field above a grating of non-parallel rectangular cavities, Journal of Sound and Vibration, vol.361, pp.251-260, 2016.
DOI : 10.1016/j.jsv.2015.09.039
URL : https://hal.archives-ouvertes.fr/hal-01273336

A. Khanfir, Étude des mécanismes de diffusion acoustique d'une cavité et d'un réseau à relief périodique et apériodique

A. Imran, Q. A. Naqvi, and K. Hongo, DIFFRACTION OF ELECTROMAGNETIC PLANE WAVE BY AN IMPEDANCE STRIP, Progress In Electromagnetics Research, vol.75, pp.303-318, 2007.
DOI : 10.2528/PIER07053104

J. Ducourneau and V. Planeau, The average absorption coefficient for enclosed spaces with non uniformly distributed absorption, Applied Acoustics, vol.64, issue.9, pp.845-862, 2003.
DOI : 10.1016/S0003-682X(03)00047-1

A. Faiz, J. Ducourneau, and J. Chatillon, Mesure du coefficient d'absorption acoustique apparent de parois à reliefs périodiques et apériodiques, 2012.

M. Bruneau, Manuel d'acoustique fondamentale, Hermes, 1998.

F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces : International Series in Natural Philosophy, 2013.

E. I. Thorsos, The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum, The Journal of the Acoustical Society of America, vol.83, issue.1, pp.78-92, 1988.
DOI : 10.1121/1.396188

S. Hu, L. Fu, and Z. Yao, Comparison of various approximation theories for randomly rough surface scattering, Wave Motion, vol.46, issue.5, pp.281-292, 2009.
DOI : 10.1016/j.wavemoti.2009.03.001

A. De-bruijn, The Sound Absorption of an Absorbing Periodically Uneven Surface of Rectangular Profile, Acta Acustica united with Acustica, vol.18, issue.3, pp.123-131, 1967.

Y. Ando and K. Kato, Calculations on the Sound Reflection from Periodically Uneven Surfaces of Arbitrary Profile, Acta Acustica united with Acustica, vol.35, issue.5, pp.321-329, 1976.

K. Hongo and H. Serizawa, Diffraction of electromagnetic plane wave by a rectangular plate and a rectangular hole in the conducting plate, IEEE Transactions on Antennas and Propagation, vol.47, issue.6, pp.1029-1041, 1999.
DOI : 10.1109/8.777128

K. Hongo and H. Serizawa, Diffraction of an acoustic plane wave by a rectangular hole in an infinitely large rigid screen, The Journal of the Acoustical Society of America, vol.106, issue.1, pp.29-35, 1999.
DOI : 10.1121/1.427033

H. Kuttruff, Room Acoustics, Fifth Edition, 2009.
DOI : 10.3397/1.3455049

P. De-fermat, Oeuvres de Fermat / publ. par les soins de MM, p.1896

V. O. Knudsen, Architectural Acoustics, Scientific American, vol.209, issue.5, 1932.
DOI : 10.1038/scientificamerican1163-78

A. Toepler, Beobachtungen nach einer neuen optischen Methode, p.1864

L. Foucault, Recueil des travaux scientifiques de Léon Foucault, 12148.

A. H. Davis and G. W. Kaye, The acoustics of buildings. London : G. Bell and sons, ltd, 1927.

F. Jacobsen, The Diffuse Sound Field : Statistical Considerations Concerning the Reverberant Field in the Steady State, 1979.

M. Hodgson, When is diffuse-field theory applicable ? Applied Acoustics, pp.197-207, 1996.
DOI : 10.1016/s0003-682x(96)00010-2

J. B. Moreland and R. S. Musa, The Performance of Acoustic Barriers, Noise Control Engineering, vol.1, issue.2, pp.98-101, 1973.
DOI : 10.3397/1.2831948

J. B. Moreland and R. F. Minto, An example of in-plant noise reduction with an acoustical barrier, Applied Acoustics, vol.9, issue.3, pp.205-214, 1976.
DOI : 10.1016/0003-682X(76)90018-9

S. K. Lau and S. K. Tang, Performance of a noise barrier within an enclosed space, Applied Acoustics, vol.70, issue.1, pp.50-57, 2009.
DOI : 10.1016/j.apacoust.2008.01.006

H. J. Steeneken and T. Houtgast, A physical method for measuring speech???transmission quality, The Journal of the Acoustical Society of America, vol.67, issue.1, pp.318-326, 1980.
DOI : 10.1121/1.384464

W. Reichardt, O. A. Alim, and W. Schmidt, Abh??ngigkeit der grenzen zwischen brauchbarer und unbrauchbarer durchsichtigkeit von der art des musikmotives, der nachhallzeit und der nachhalleinsatzzeit, Applied Acoustics, vol.7, issue.4, pp.243-264, 1974.
DOI : 10.1016/0003-682X(74)90033-4

W. C. Sabine, Collected Papers on Acoustics, 1922.

C. F. Eyring, REVERBERATION TIME IN ???DEAD??? ROOMS, The Journal of the Acoustical Society of America, vol.1, issue.2A, pp.217-241, 1930.
DOI : 10.1121/1.1915175

C. F. Eyring, METHODS OF CALCULATING THE AVERAGE COEFFICIENT OF SOUND ABSORPTION, The Journal of the Acoustical Society of America, vol.4, issue.3, pp.178-192, 1933.
DOI : 10.1121/1.1915599

L. L. Beranek, Analysis of Sabine and Eyring equations and their application to concert hall audience and chair absorption, The Journal of the Acoustical Society of America, vol.120, issue.3, pp.1399-1410, 2006.
DOI : 10.1121/1.2221392

G. Millington, A MODIFIED FORMULA FOR REVERBERATION, The Journal of the Acoustical Society of America, vol.4, issue.1A, pp.69-82, 1932.
DOI : 10.1121/1.1915588

A. Krokstad, S. Strom, and S. Sørsdal, Calculating the acoustical room response by the use of a ray tracing technique, Journal of Sound and Vibration, vol.8, issue.1, pp.118-125, 1968.
DOI : 10.1016/0022-460X(68)90198-3

H. Lehnert, Systematic errors of the ray-tracing algorithm, Applied Acoustics, vol.38, issue.2-4, pp.207-221, 1993.
DOI : 10.1016/0003-682X(93)90052-8

M. Hodgson, Evidence of diffuse surface reflections in rooms, The Journal of the Acoustical Society of America, vol.89, issue.2, pp.765-771, 1991.
DOI : 10.1121/1.1894636

X. Zeng, C. L. Christensen, and J. H. , Practical methods to define scattering coefficients in a room acoustics computer model, Applied Acoustics, vol.67, issue.8, pp.771-786, 2006.
DOI : 10.1016/j.apacoust.2005.12.001

E. R. Freniere, G. G. Gregory, and R. A. Hassler, Edge diffraction in Monte Carlo ray tracing, pp.151-157, 1999.

A. M. Ondet and J. L. Barbry, Modeling of sound propagation in fitted workshops using ray tracing, The Journal of the Acoustical Society of America, vol.85, issue.2, pp.787-796, 1989.
DOI : 10.1121/1.397551

A. M. Ondet and J. L. Barbry, Prévision des niveaux sonores dans les locaux industriels encombrés à l'aide du logiciel d'acoustique prévisionnelle RAYSCAT, INRS, 1991.

R. G. Kouyoumjian and P. H. Pathak, A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface, Proceedings of the IEEE, vol.62, issue.11, pp.1448-1461, 1974.
DOI : 10.1109/PROC.1974.9651

P. S. Heckbert and P. Hanrahan, Beam Tracing Polygonal Objects, Proceedings of the 11th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH '84, pp.119-127, 1984.

N. Dadoun, D. G. Kirkpatrick, and J. P. Walsh, The geometry of beam tracing, Proceedings of the first annual symposium on Computational geometry , SCG '85, pp.55-61, 1985.
DOI : 10.1145/323233.323241

M. Monks, B. M. Oh, and J. Dorsey, Acoustic Simulation and Visualization using a New Unified Beam Tracing and Image Source Approach, 1996.

T. Funkhouser, I. Carlbom, G. Elko, G. Pingali, M. Sondhi et al., A beam tracing approach to acoustic modeling for interactive virtual environments, Proceedings of the 25th annual conference on Computer graphics and interactive techniques , SIGGRAPH '98, pp.21-32, 1998.
DOI : 10.1145/280814.280818

T. Funkhouser, N. Tsingos, I. Carlbom, G. Elko, M. Sondhi et al., A beam tracing method for interactive architectural acoustics, The Journal of the Acoustical Society of America, vol.115, issue.2, pp.739-756, 2004.
DOI : 10.1121/1.1641020
URL : https://hal.archives-ouvertes.fr/inria-00606736

B. M. Gibbs and D. K. Jones, A Simple Image Method for Calculating the Distribution of Sound Pressure Levels within an Enclosure, Acta Acustica united with Acustica, vol.26, issue.1, pp.24-32, 1972.

J. B. Allen and D. A. Berkley, Image method for efficiently simulating small???room acoustics, The Journal of the Acoustical Society of America, vol.65, issue.4, pp.943-950, 1979.
DOI : 10.1121/1.382599

J. Borish, Extension of the image model to arbitrary polyhedra, The Journal of the Acoustical Society of America, vol.75, issue.6, pp.1827-1836, 1984.
DOI : 10.1121/1.390983

M. Vorländer, Simulation of the transient and steady???state sound propagation in rooms using a new combined ray???tracing/image???source algorithm, The Journal of the Acoustical Society of America, vol.86, issue.1, pp.172-178, 1989.
DOI : 10.1121/1.398336

S. G. Mcgovern, Fast image method for impulse response calculations of box-shaped rooms, Applied Acoustics, vol.70, issue.1, pp.182-189, 2009.
DOI : 10.1016/j.apacoust.2008.02.003

S. M. Dance and B. M. Shield, THE COMPLETE IMAGE-SOURCE METHOD FOR THE PREDICTION OF SOUND DISTRIBUTION IN NON-DIFFUSE ENCLOSED SPACES, Journal of Sound and Vibration, vol.201, issue.4, pp.473-489, 1997.
DOI : 10.1006/jsvi.1996.0770

S. Kopuz and N. Lalor, Analysis of interior acoustic fields using the finite element method and the boundary element method, Applied Acoustics, vol.45, issue.3, pp.193-210, 1995.
DOI : 10.1016/0003-682X(94)00045-W

F. Ihlenburg, Finite element analysis of acoustic scattering. Number v. 132 in Applied mathematical sciences, 1998.

D. J. Nefske, J. A. Wolf, and L. J. Howell, Structural-acoustic finite element analysis of the automobile passenger compartment: A review of current practice, Journal of Sound and Vibration, vol.80, issue.2, pp.247-266, 1982.
DOI : 10.1016/0022-460X(82)90194-8

N. González-salido, A. Islas-cital, F. Camarena, R. Pico, and P. R. Atkins, Scattering of complex geometries by Finite Element Method, p.2012

K. S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Transactions on Antennas and Propagation, vol.14, issue.3, pp.302-307, 1966.

R. A. Stephen, Modeling sea surface scattering by the time???domain finite???difference method, The Journal of the Acoustical Society of America, vol.100, issue.4, pp.2070-2078, 1996.
DOI : 10.1121/1.417917

S. Wang, Finite???difference time???domain approach to underwater acoustic scattering problems, The Journal of the Acoustical Society of America, vol.99, issue.4, pp.1924-1931, 1996.
DOI : 10.1121/1.415375

T. Yokota, S. Sakamoto, and H. Tachibana, Visualization of sound propagation and scattering in rooms, Acoustical Science and Technology, vol.23, issue.1, pp.40-46, 2002.
DOI : 10.1250/ast.23.40

T. Yokota, S. Sakamoto, and H. Tachibana, Sound field simulation method by combining finite difference time domain calculation and multi-channel reproduction technique, Acoustical Science and Technology, vol.25, issue.1, pp.15-23, 2004.
DOI : 10.1250/ast.25.15

L. Savioja, T. Rinne, and T. Takala, Simulation of room acoustics with a 3-D finite difference mesh, pp.463-466, 1994.

S. Sakamoto, H. Nagatomo, A. Ushiyama, and H. Tachibana, Calculation of impulse responses and acoustic parameters in a hall by the finite-difference time-domain method, Acoustical Science and Technology, vol.29, issue.4, pp.256-265, 2008.
DOI : 10.1250/ast.29.256

S. Sakamoto, T. Seimiya, and H. Tachibana, Visualization of sound reflection and diffraction using finite difference time domain method, Acoustical Science and Technology, vol.23, issue.1, pp.34-39, 2002.
DOI : 10.1250/ast.23.34

D. Botteldooren, Finite???difference time???domain simulation of low???frequency room acoustic problems, The Journal of the Acoustical Society of America, vol.98, issue.6, pp.3302-3308, 1995.
DOI : 10.1121/1.413817

J. Theodore, B. G. Schultz, and . Watters, Propagation of sound across audience seating, The Journal of the Acoustical Society of America, vol.36, issue.5, pp.885-896, 1964.

J. Lovetri, D. Mardare, and G. Soulodre, Modeling of the seat dip effect using the finite???difference time???domain method, The Journal of the Acoustical Society of America, vol.100, issue.4, pp.2204-2212, 1996.
DOI : 10.1121/1.417929

T. Lokki, A. Southern, and L. Savioja, Studies on seat dip effect with 3d FDTD modeling, Proc. Forum Acusticum, pp.1517-1522, 2011.

T. G. Jurgens, A. Taflove, K. Umashankar, and T. G. Moore, Finite-difference time-domain modeling of curved surfaces (EM scattering), IEEE Transactions on Antennas and Propagation, vol.40, issue.4, pp.357-366, 1992.
DOI : 10.1109/8.138836

J. Häggblad and B. Engquist, Consistent modeling of boundaries in acoustic finite-difference time-domain simulations, The Journal of the Acoustical Society of America, vol.132, issue.3, pp.1303-1310, 2012.
DOI : 10.1121/1.4740490

N. Raghuvanshi, R. Narain, and M. C. Lin, Efficient and Accurate Sound Propagation Using Adaptive Rectangular Decomposition, IEEE Transactions on Visualization and Computer Graphics, vol.15, issue.5, pp.789-801, 2009.
DOI : 10.1109/TVCG.2009.28

N. Raghuvanshi, Interactive physically-based sound simulation, 2013.

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to algorithms, 2007.

R. Mehra, N. Raghuvanshi, L. Savioja, M. C. Lin, and D. Manocha, An efficient GPU-based time domain solver for the acoustic wave equation, Applied Acoustics, vol.73, issue.2, pp.83-94, 2012.
DOI : 10.1016/j.apacoust.2011.05.012

R. Mehra, Efficient techniques for wave-based sound propagation in interactive applications, 2015.

R. Mehra, N. Raghuvanshi, A. Chandak, D. G. Albert, D. K. Wilson et al., Acoustic pulse propagation in an urban environment using a three-dimensional numerical simulation, The Journal of the Acoustical Society of America, vol.135, issue.6, pp.3231-3242, 2014.
DOI : 10.1121/1.4874495

N. Morales, R. Mehra, and D. Manocha, A parallel time-domain wave simulator based on rectangular decomposition for distributed memory architectures, Applied Acoustics, vol.97, pp.104-114, 2015.
DOI : 10.1016/j.apacoust.2015.03.017

N. Morales, V. Chavda, R. Mehra, and D. Manocha, MPARD: A high-frequency wave-based acoustic solver for very large compute clusters, Applied Acoustics, vol.121, pp.82-94, 2017.
DOI : 10.1016/j.apacoust.2017.01.009

R. Courant, K. Friedrichs, and H. Lewy, On the Partial Difference Equations of Mathematical Physics, IBM Journal of Research and Development, vol.11, issue.2, pp.215-234, 1967.
DOI : 10.1147/rd.112.0215

K. Kowalczyk, Boundary and medium modelling using compact finite difference schemes in simulations of room acoustics for audio and architectural design applications, 2008.

K. Kowalczyk and M. Van-walstijn, Virtual room acoustics using finite difference methods. How to model and analyse frequency-dependent boundaries?, 2008 3rd International Symposium on Communications, Control and Signal Processing, pp.1504-1509, 2008.
DOI : 10.1109/ISCCSP.2008.4537465

K. Kowalczyk and M. Van-walstijn, Wideband and Isotropic Room Acoustics Simulation Using 2-D Interpolated FDTD Schemes, IEEE Transactions on Audio, Speech, and Language Processing, vol.18, issue.1, pp.78-89, 2010.
DOI : 10.1109/TASL.2009.2023645

K. Kowalczyk and M. Van-walstijn, Room Acoustics Simulation Using 3-D Compact Explicit FDTD Schemes, IEEE Transactions on Audio, Speech, and Language Processing, vol.19, issue.1, pp.34-46, 2011.
DOI : 10.1109/TASL.2010.2045179

J. Huopaniemi, L. Savioja, and M. Karjalainen, Modeling of reflections and air absorption in acoustical spaces a digital filter design approach, Proceedings of 1997 Workshop on Applications of Signal Processing to Audio and Acoustics, 1997.
DOI : 10.1109/ASPAA.1997.625594

K. Kowalczyk and M. Van-walstijn, Modeling Frequency-Dependent Boundaries as Digital Impedance Filters in FDTD and K-DWM Room Acoustics Simulations, Journal of the Audio Engineering Society, vol.56, issue.78, pp.569-583, 2008.

K. Kowalczyk and M. Van-walstijn, Formulation of Locally Reacting Surfaces in FDTD/K-DWM Modelling of Acoustic Spaces, Acta Acustica united with Acustica, vol.94, issue.6, pp.891-906, 2008.
DOI : 10.3813/AAA.918107

H. Bourlès, Linear systems Control systems, robotics and manufacturing series, ISTE, 2010.

J. Berenger, 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. Berenger, 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

F. D. Hastings, J. B. Schneider, and S. L. Broschat, Application of the perfectly matched layer (PML) absorbing boundary condition to elastic wave propagation, The Journal of the Acoustical Society of America, vol.100, issue.5
DOI : 10.1121/1.417118

F. Q. Hu, On Absorbing Boundary Conditions for Linearized Euler Equations by a Perfectly Matched Layer, Journal of Computational Physics, vol.129, issue.1, pp.201-219, 1996.
DOI : 10.1006/jcph.1996.0244

D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method, 2000.

Q. Liu and J. Tao, The perfectly matched layer for acoustic waves in absorptive media, The Journal of the Acoustical Society of America, vol.102, issue.4, pp.2072-2082, 1997.
DOI : 10.1121/1.419657

Y. S. Rickard, N. K. Georgieva, and W. Huang, Application and optimization of PML ABC for the 3-D wave equation in the time domain, IEEE Transactions on Antennas and Propagation, vol.51, issue.2, pp.286-295, 2003.
DOI : 10.1109/TAP.2003.809093

S. Jie, Z. Weisong, J. Xiangjun, Z. Xin, and R. Malekian, Underwater Broadband Acoustic Scattering Modelling Based on FDTD, Elektronika ir Elektrotechnika, vol.21, issue.2, pp.58-64, 2015.
DOI : 10.5755/j01.eee.21.2.11513

T. W. Parks and C. S. Burrus, Digital filter design. Topics in digital signal processing, 1987.

T. Parks and J. Mcclellan, Chebyshev Approximation for Nonrecursive Digital Filters with Linear Phase, IEEE Transactions on Circuit Theory, vol.19, issue.2, pp.189-194, 1972.
DOI : 10.1109/TCT.1972.1083419

G. U. Yule, On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer's Sunspot Numbers, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.226, issue.636-646, pp.636-646267, 1927.
DOI : 10.1098/rsta.1927.0007

J. S. Suh and P. A. Nelson, Measurement of transient response of rooms and comparison with geometrical acoustic models, The Journal of the Acoustical Society of America, vol.105, issue.4, pp.2304-2317, 1999.
DOI : 10.1121/1.426837

M. R. Schroeder, New Method of Measuring Reverberation Time, The Journal of the Acoustical Society of America, vol.37, issue.3, pp.409-412, 1965.
DOI : 10.1121/1.1909343