R. Abdelkhalek, ´ Evaluation des accélérateurs de calcul GPGPU pour la modélisation sismique, Master's thesis, ENSEIRB, 2007.

R. Abdelkhalek, H. Calandra, O. Coulaud, J. Roman, and G. Latu, Fast seismic modeling and Reverse Time Migration on a GPU cluster, 2009 International Conference on High Performance Computing & Simulation, pp.36-44, 2009.
DOI : 10.1109/HPCSIM.2009.5192786

URL : https://hal.archives-ouvertes.fr/inria-00403933

S. Adams, J. Payne, and R. Boppana, Finite Difference Time Domain (FDTD) Simulations Using Graphics Processors, 2007 DoD High Performance Computing Modernization Program Users Group Conference, pp.334-338, 2007.
DOI : 10.1109/HPCMP-UGC.2007.34

Z. Alterman and F. C. Karal, Propagation of elastic waves in layered media by finite difference methods, Bull. Seismol. Soc. Am, vol.58, pp.367-398, 1968.

J. A. Anderson, C. D. Lorenz, and A. Travesset, General purpose molecular dynamics simulations fully implemented on graphics processing units, Journal of Computational Physics, vol.227, issue.10, pp.5342-5359, 2008.
DOI : 10.1016/j.jcp.2008.01.047

H. Aochi and J. Douglas, Testing the Validity of Simulated Strong Ground Motion from the Dynamic Rupture of a Finite Fault, by Using Empirical Equations, Bulletin of Earthquake Engineering, vol.65, issue.3, pp.211-229, 2006.
DOI : 10.1007/s10518-006-0001-3

URL : https://hal.archives-ouvertes.fr/hal-00557619

C. Augonnet, S. Thibault, R. Namyst, and P. Wacrenier, StarPU: A Unified Platform for Task Scheduling on Heterogeneous Multicore Architectures, Proceedings of the 15th EuroPar Conference, pp.863-874, 2009.
DOI : 10.1111/j.1467-8659.2007.01012.x

URL : https://hal.archives-ouvertes.fr/inria-00384363

A. Balevic, L. Rockstroh, W. Li, J. Hillebrand, S. Simon et al., Acceleration of a finite-difference method with general purpose GPUs - Lesson learned, 2008 8th IEEE International Conference on Computer and Information Technology, pp.291-294, 2008.
DOI : 10.1109/CIT.2008.4594689

A. Balevic, L. Rockstroh, A. Tausendfreund, S. Patzelt, G. Goch et al., Accelerating simulations of light scattering based on a finitedifference time-domain method with general purpose GPUs, Proceedings of the 11th IEEE International Conference on Computational Science and Engineering, pp.327-334, 2008.

G. S. Baron, C. D. Sarris, E. Fiume, R. Sr, and E. S. , Fast and Accurate Time-Domain Simulations with Commodity Graphics Hardware, 2005 IEEE Antennas and Propagation Society International Symposium, pp.193-196, 2005.
DOI : 10.1109/APS.2005.1552619

N. Bell and M. Garland, Implementing sparse matrix-vector multiplication on throughput-oriented processors, Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis, SC '09, pp.1-11, 2009.
DOI : 10.1145/1654059.1654078

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.174.1350

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

M. Bernacki, S. Lanteri, and S. Piperno, TIME-DOMAIN PARALLEL SIMULATION OF HETEROGENEOUS WAVE PROPAGATION ON UNSTRUCTURED GRIDS USING EXPLICIT, NONDIFFUSIVE, DISCONTINUOUS GALERKIN METHODS, Journal of Computational Acoustics, vol.14, issue.01, pp.57-81, 2006.
DOI : 10.1142/S0218396X06002937

URL : https://hal.archives-ouvertes.fr/hal-00607725

T. Brandvik and G. Pullan, Acceleration of a two-dimensional Euler flow solver using commodity graphics hardware, Proceedings of the Institution of Mechanical Engineers, pp.221-1745, 2007.
DOI : 10.1243/09544062JMES813FT

J. M. Carcione and P. J. Wang, A Chebyshev collocation method for the wave equation in generalized coordinates, Comp. Fluid Dyn. J, vol.2, pp.269-290, 1993.

E. Chaljub, D. Komatitsch, J. P. Vilotte, Y. Capdeville, B. Valette et al., Spectral-element analysis in seismology, Advances in wave propagation in heterogeneous media, pp.365-419, 2007.
DOI : 10.1016/S0065-2687(06)48007-9

URL : https://hal.archives-ouvertes.fr/insu-00345810

W. C. Chew and Q. Liu, PERFECTLY MATCHED LAYERS FOR ELASTODYNAMICS: A NEW ABSORBING BOUNDARY CONDITION, Journal of Computational Acoustics, vol.04, issue.04, pp.341-359, 1996.
DOI : 10.1142/S0218396X96000118

A. J. Chorin, Numerical solution of the Navier-Stokes equations, Mathematics of Computation, vol.22, issue.104, pp.745-762, 1968.
DOI : 10.1090/S0025-5718-1968-0242392-2

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

K. T. Danielson and R. R. Namburu, Nonlinear dynamic finite element analysis on parallel computers using Fortran90 and MPI, Advances in Engineering Software, vol.29, pp.3-6, 1998.

R. Dolbeau, S. Bihan, and F. Bodin, HMPP: A hybrid multi-core parallel programming environment, Proceedings of the Workshop on General Purpose Processing on Graphics Processing Units (GPGPU'2007), pp.1-5, 2007.

F. H. Drossaert and A. Giannopoulos, A nonsplit complex frequency-shifted PML based on recursive integration for FDTD modeling of elastic waves, GEOPHYSICS, vol.72, issue.2, pp.72-81, 2007.
DOI : 10.1190/1.2424888

M. Dumbser and M. Käser, An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes - II. The three-dimensional isotropic case, Geophysical Journal International, vol.167, issue.1, pp.319-336, 2006.
DOI : 10.1111/j.1365-246X.2006.03120.x

E. Elsen, P. Legresley, and E. Darve, Large calculation of the flow over a hypersonic vehicle using a GPU, Journal of Computational Physics, vol.227, issue.24, pp.10148-10161, 2008.
DOI : 10.1016/j.jcp.2008.08.023

R. S. Falk and G. R. Richter, Explicit Finite Element Methods for Symmetric Hyperbolic Equations, SIAM Journal on Numerical Analysis, vol.36, issue.3, pp.935-952, 1999.
DOI : 10.1137/S0036142997329463

G. Festa and J. P. Vilotte, The Newmark scheme as velocity-stress time-staggering: an efficient PML implementation for spectral element simulations of elastodynamics, Geophysical Journal International, vol.161, issue.3, pp.789-812, 2005.
DOI : 10.1111/j.1365-246X.2005.02601.x

G. Festa, E. Delavaud, and J. P. Vilotte, Interaction between surface waves and absorbing boundaries for wave propagation in geological basins: 2D numerical simulations, Geophysical Research Letters, vol.13, issue.5, pp.32-20306, 2005.
DOI : 10.1029/2005GL024091

S. D. Gedney and B. Zhao, An Auxiliary Differential Equation Formulation for the Complex-Frequency Shifted PML, IEEE Transactions on Antennas and Propagation, vol.58, issue.3, pp.838-847, 2010.
DOI : 10.1109/TAP.2009.2037765

L. Genovese, M. Ospici, T. Deutsch, J. Méhaut, A. Neelov et al., Density functional theory calculation on many-cores hybrid central processing unit-graphic processing unit architectures, The Journal of Chemical Physics, vol.131, issue.3, p.34103, 2009.
DOI : 10.1063/1.3166140

F. X. Giraldo, J. S. Hesthaven, and T. Warburton, Nodal High-Order Discontinuous Galerkin Methods for the Spherical Shallow Water Equations, Journal of Computational Physics, vol.181, issue.2, pp.499-525, 2002.
DOI : 10.1006/jcph.2002.7139

R. W. Graves, Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences, Bull. Seismol. Soc. Am, vol.86, issue.4, pp.1091-1106, 1996.

W. Gropp, E. Lusk, and A. Skjellum, Using MPI, portable parallel programming with the Message-Passing Interface, 1994.

M. J. Grote, A. Schneebeli, and D. Schötzau, Discontinuous Galerkin Finite Element Method for the Wave Equation, SIAM Journal on Numerical Analysis, vol.44, issue.6, pp.2408-2431, 2006.
DOI : 10.1137/05063194X

URL : https://hal.archives-ouvertes.fr/hal-01443184

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, pp.3061-3069, 1996.
DOI : 10.1121/1.417118

O. Holberg, COMPUTATIONAL ASPECTS OF THE CHOICE OF OPERATOR AND SAMPLING INTERVAL FOR NUMERICAL DIFFERENTIATION IN LARGE-SCALE SIMULATION OF WAVE PHENOMENA*, Geophysical Prospecting, vol.24, issue.6, pp.629-655, 1987.
DOI : 10.1016/0021-9991(80)90005-4

F. Q. Hu, M. Y. Hussaini, and P. Rasetarinera, An Analysis of the Discontinuous Galerkin Method for Wave Propagation Problems, Journal of Computational Physics, vol.151, issue.2, pp.921-946, 1999.
DOI : 10.1006/jcph.1999.6227

M. J. Inman and A. Z. Elsherbeni, Optimization and parameter exploration using GPU based FDTD solvers, 2008 IEEE MTT-S International Microwave Symposium Digest, pp.149-152, 2008.
DOI : 10.1109/MWSYM.2008.4633125

M. J. Inman, A. Z. Elsherbeni, J. G. Maloney, and B. N. Baker, GPU based FDTD solver with CPML boundaries, 2007 IEEE Antennas and Propagation International Symposium, pp.5255-5258, 2007.
DOI : 10.1109/APS.2007.4396732

H. Kawase, Time-domain response of a semi-circular canyon for incident SV, P and Rayleigh waves calculated by the discrete wavenumber boundary element method, Bull. Seismol. Soc. Am, vol.78, pp.1415-1437, 1988.

D. B. Kirk and W. W. Hwu, Programming Massively Parallel Processors: A Hands-on Approach, 2010.

A. Klöckner, T. Warburton, J. Bridge, and J. S. Hesthaven, Nodal discontinuous Galerkin methods on graphics processors, Journal of Computational Physics, vol.228, issue.21, pp.7863-7882, 2009.
DOI : 10.1016/j.jcp.2009.06.041

D. Komatitsch and R. Martin, An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation, GEOPHYSICS, vol.72, issue.5, pp.72-155, 2007.
DOI : 10.1190/1.2757586

URL : https://hal.archives-ouvertes.fr/inria-00528418

D. Komatitsch and J. Tromp, Introduction to the spectral element method for three-dimensional seismic wave propagation, Geophysical Journal International, vol.139, issue.3, pp.806-822, 1999.
DOI : 10.1046/j.1365-246x.1999.00967.x

D. Komatitsch, F. Coutel, and P. Mora, Tensorial formulation of the wave equation for modelling curved interfaces, Geophys, J. Int, vol.127, issue.1, pp.156-168, 1996.

D. Komatitsch, D. Michéa, and G. Erlebacher, Porting a high-order finite-element earthquake modeling application to NVIDIA graphics cards using CUDA, Journal of Parallel and Distributed Computing, vol.69, issue.5, pp.451-460, 2009.
DOI : 10.1016/j.jpdc.2009.01.006

URL : https://hal.archives-ouvertes.fr/inria-00436426

D. Komatitsch, G. Erlebacher, D. Göddeke, and D. Michéa, High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster, Journal of Computational Physics, vol.229, issue.20, pp.229-7692, 2010.
DOI : 10.1016/j.jcp.2010.06.024

URL : https://hal.archives-ouvertes.fr/inria-00528481

D. Komatitsch, D. Göddeke, G. Erlebacher, and D. Michéa, Modeling the propagation of elastic waves using spectral elements on??a??cluster of??192 GPUs, Computer Science - Research and Development, vol.115, issue.3, 2010.
DOI : 10.1007/s00450-010-0109-1

URL : https://hal.archives-ouvertes.fr/inria-00528482

S. E. Krakiwsky, L. E. Turner, and M. M. Okoniewski, Graphics processor unit (GPU) acceleration of finite-difference time-domain (FDTD) algorithm, 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512), pp.265-268, 2004.
DOI : 10.1109/ISCAS.2004.1329513

S. E. Krakiwsky, L. E. Turner, and M. M. Okoniewski, Acceleration of finite-difference time-domain (FDTD) using graphics processor units (GPU), 2004 IEEE MTT-S International Microwave Symposium Digest (IEEE Cat. No.04CH37535), pp.1033-1036, 2004.
DOI : 10.1109/MWSYM.2004.1339160

J. Kristek and P. Moczo, Seismic-Wave Propagation in Viscoelastic Media with Material Discontinuities: A 3D Fourth-Order Staggered-Grid Finite-Difference Modeling, Bulletin of the Seismological Society of America, vol.93, issue.5, pp.2273-2280, 2003.
DOI : 10.1785/0120030023

J. Kristek, P. Moczo, and M. Galis, A brief summary of some PML formulations and discretizations for the velocity-stress equation of seismic motion, Studia Geophysica et Geodaetica, vol.68, issue.4, pp.459-474, 2009.
DOI : 10.1007/s11200-009-0034-6

Q. Liu, J. Polet, D. Komatitsch, and J. Tromp, Spectral-Element Moment Tensor Inversions for Earthquakes in Southern California, Bulletin of the Seismological Society of America, vol.94, issue.5, pp.1748-1761, 2004.
DOI : 10.1785/012004038

URL : https://hal.archives-ouvertes.fr/hal-00669069

R. Madariaga, Dynamics of an expanding circular fault, Bull. Seismol. Soc. Am, vol.66, issue.3, pp.639-666, 1976.

R. Martin and D. Komatitsch, An optimized convolution-perfectly matched layer (C-PML) absorbing technique for 3D seismic wave simulation based on a finite-difference method, Geophysical Research Abstracts, p.3988, 2006.

R. Martin and D. Komatitsch, An unsplit convolutional perfectly matched layer technique improved at grazing incidence for the viscoelastic wave equation, Geophys, J. Int, vol.179, issue.1, pp.333-344, 2009.

R. Martin, D. Komatitsch, and H. Barucq, An optimized convolution-perfectly matched layer (C-PML) absorbing technique for 3D seismic wave simulation based on a finite-difference method, Fall Meet, 2005.

R. Martin, D. Komatitsch, and A. Ezziani, An unsplit convolutional perfectly matched layer improved at grazing incidence for seismic wave propagation in poroelastic media, GEOPHYSICS, vol.73, issue.4, pp.51-61, 2008.
DOI : 10.1190/1.2939484

R. Martin, D. Komatitsch, and S. D. Gedney, A variational formulation of a stabilized unsplit convolutional perfectly matched layer for the isotropic or anisotropic seismic wave equation, Comput. Model. Eng. Sci, vol.37, issue.3, pp.274-304, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00528432

R. Martin, D. Komatitsch, S. D. Gedney, and E. Bruthiaux, A high-order time and space formulation of the unsplit perfectly matched layer for the seismic wave equation using Auxiliary Differential Equations (ADE-PML), Comput. Model. Eng. Sci, vol.56, issue.1, pp.17-42, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00528456

K. C. Meza-fajardo and A. S. Papageorgiou, A Nonconvolutional, Split-Field, Perfectly Matched Layer for Wave Propagation in Isotropic and Anisotropic Elastic Media: Stability Analysis, Bulletin of the Seismological Society of America, vol.98, issue.4, pp.1811-1836, 2008.
DOI : 10.1785/0120070223

P. Micikevicius, 3D finite difference computation on GPUs using CUDA, Proceedings of 2nd Workshop on General Purpose Processing on Graphics Processing Units, GPGPU-2, pp.79-84, 2009.
DOI : 10.1145/1513895.1513905

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.472.447

P. Moczo and J. Kristek, On the rheological models used for time-domain methods of seismic wave propagation, Geophysical Research Letters, vol.121, issue.1, p.1306, 2005.
DOI : 10.1029/2004GL021598

P. Moczo, J. Robertsson, and L. Eisner, The finite-difference time-domain method for modeling of seismic wave propagation, in Advances in wave propagation in heterogeneous media, of Advances in Geophysics, pp.421-516, 2007.

P. Monk, G. R. Richter, L. Nyland, M. Harris, and J. Prins, A discontinuous Galerkin method for linear symmetric hyperbolic systems in inhomogeneous media NVIDIA Corporation NVIDIA CUDA Programming Guide version 2.3, Santa Clara, California, USA, 139 pages. NVIDIA Corporation NVIDIA's next generation CUDA compute architecture: FERMI, Tech. rep Fast N-body simulation with CUDA, Journal of Scientific Computing, vol.13, issue.22, pp.22-23, 2005.

J. D. Owens, D. P. Luebke, N. K. Govindaraju, M. J. Harris, J. Krüger et al., A Survey of General-Purpose Computation on Graphics Hardware, Computer Graphics Forum, vol.7, issue.4, pp.80-113, 2007.
DOI : 10.1016/j.rti.2005.04.002

J. Planas, R. M. Badia, E. Ayguadé, and J. Labarta, Hierarchical Task-Based Programming With StarSs, International Journal of High Performance Computing Applications, vol.23, issue.3, pp.284-299, 2009.
DOI : 10.1177/1094342009106195

URL : http://hdl.handle.net/2117/28379

D. K. Price, J. R. Humphrey, and E. J. Kelmelis, GPU-based accelerated 2D and 3D FDTD solvers, Physics and Simulation of Optoelectronic Devices XV, 2007.
DOI : 10.1117/12.715044

W. H. Reed and T. R. Hill, Triangular mesh methods for the neutron transport equation, Tech. Rep. LA-UR-73-479 Discontinuous finite element methods for acoustic and elastic wave problems, Los Alamos Scientific Laboratory Contemporary Mathematics, vol.329, pp.271-282, 1973.

J. A. Roden and S. D. Gedney, Convolution PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media, Microwave and Optical Technology Letters, pp.334-339, 2000.

J. Tromp, D. Komatitsch, and Q. Liu, Spectral-element and adjoint methods in seismology, Communications in Computational Physics, vol.3, issue.1, pp.1-32, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00721213

R. Vai, J. M. Castillo-covarrubias, F. J. Sánchez-sesma, D. Komatitsch, and J. P. Vilotte, Elastic wave propagation in an irregularly layered medium, Soil Dynamics and Earthquake Engineering, vol.18, issue.1, pp.11-18, 1999.
DOI : 10.1016/S0267-7261(98)00027-X

URL : https://hal.archives-ouvertes.fr/hal-00669057

A. Valcarce, G. De-la-roche, and J. Zhang, A GPU approach to FDTD for radio coverage prediction, in Proceedings of the 11th IEEE International Figure 3. (Left) Three-dimensional block of 8 × 8 × 8 = 512 grid points (dark gray) and its 'halo' of 6 × 8 × 8 × 2 = 768 grid points (light gray) that need to be loaded from global memory to shared memory to implement a finite-difference calculation on the GPU by a block of 512 CUDA threads based on the stencil of Figure 2 and on an intuitive decomposition into a cubic distribution of threads. (Right) Two-dimensional tile of 8 × 16 = 128 grid points (dark gray) and its two-dimensional 'halo' of grid points (light gray) that need to be loaded from global memory to shared memory by this block of 128 threads when the more efficient two-dimensional approach introduced by Micikevicius (2009) is used, We have not drawn the additional halo of 8 × 16 × 2 × 2 = 512 grid points located in front and behind this tile because it does not need to be stored in shared memory, it can much more efficiently be stored in registers organized in a pipeline fashion, taking advantage of the fact that access to these registers is extremely fast, 2008.