Accelerating a three-dimensional finite-difference wave propagation code using GPU graphics cards

Geophysical Journal International

Volumn 182, Issue 1, 2010, Pages 389-402

  Michéa, David ^a   Komatitsch, Dimitri ^b,c  

^a BRGM   (France)

^b UNIVERSITÉ DE PAU ET DES PAYS DE L'ADOUR   (France)

^c INSTITUT UNIVERSITAIRE DE FRANCE   (France)

Author keywords

Computational seismology; Earthquake ground motions; Numerical approximations and analysis; Numerical solutions; Wave propagation

Indexed keywords

FINITE DIFFERENCE METHOD; GROUND MOTION; SEISMIC WAVE; SEISMOLOGY; WAVE EQUATION; WAVE PROPAGATION;

EID: 77954630975     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2010.04616.x     Document Type: Article

References (78)

1. Abdelkhalek R. Évaluation des accélérateurs de calcul GPGPU pour la modélisation sismique. 2007, Master's thesis, ENSEIRB, Bordeaux, France
2. Abdelkhalek R, Calandra H, Coulaud O, Roman J, Latu G. Fast seismic modeling and reverse time migration on a GPU cluster. High Performance Computing & Simulation 2009 2009, 36-44. http://hal.inria.fr/docs/00/40/39/33/PDF/hpcs.pdf, Leipzig, Germany
3. Adams S, Payne J, Boppana R. Finite difference time domain (FDTD) simulations using graphics processors. 2007, 334-338. IEEE Computer Society, Washington, DC, USA
4. Alterman Z, Karal FC. Propagation of elastic waves in layered media by finite difference methods. Bull. seism. Soc. Am. 1968, 58:367-398.
5. Anderson JA, Lorenz CD, Travesset A. General purpose molecular dynamics simulations fully implemented on graphics processing units. J. Comput. Phys. 2008, 227(10):5342-5359.
6. Aochi H, Douglas J. Testing the validity of simulated strong ground motion from the dynamic rupture of a finite fault by using empirical equations. Bull. Earthq. Eng. 2006, 4(3):211-229.
7. Augonnet C, Thibault S, Namyst R, Wacrenier P-A. StarPU: a unified platform for task scheduling on heterogeneous multicore architectures. 2009, 863-874. Vol. 5704 of Lecture Notes in Computer Science, Springer, Delft, The Netherlands
8. Balevic A, Rockstroh L, Li W, Hillebrand J, Simon S, Tausendfreund A, Patzelt S, Goch G. Acceleration of a finite-difference method with general purpose GPUs: lesson learned. 2008a, 291-294. IEEE Computer Society, Washington, DC, USA
9. Balevic A, Rockstroh L, Tausendfreund A, Patzelt S, Goch G, Simon S. Accelerating simulations of light scattering based on a finite-difference time-domain method with general purpose GPUs. 2008b, 327-334. IEEE Computer Society, Washington, DC, USA
10. Baron GS, Sarris CD, Fiume E, Rogers ES. Fast and accurate time-domain simulations with commodity graphics hardware. 2005, 193-196. 4A, IEEE Computer Society, Washington, DC, USA
11. Bell N, Garland M. Implementing sparse matrix-vector multiplication on throughput-oriented processors. 2009, 1-11. ACM, New York, USA
12. Bérenger JP. A Perfectly Matched Layer for the absorption of electromagnetic waves. J. Comput. Phys. 1994, 114:185-200.
13. Bernacki M, Lanteri S, Piperno S. Time-domain parallel simulation of heterogeneous wave propagation on unstructured grids using explicit, nondiffusive, discontinuous Galerkin methods. J. Comput. Acoust. 2006, 14(1):57-81.
14. Brandvik T, Pullan G. Acceleration of a two-dimensional Euler flow solver using commodity graphics hardware, in. 2007, 221(12):1745-1748.
15. Carcione JM, Wang PJ. A Chebyshev collocation method for the wave equation in generalized coordinates. Comp. Fluid Dyn. J. 1993, 2:269-290.
16. Chaljub E, Komatitsch D, Vilotte JP, Capdeville Y, Valette B, Festa G. Spectral element analysis in seismology. Advances in Wave Propagation in Heterogeneous Media 2007, 365-419. Wu R-S, Maupin V, Vol. 48 of Advances in Geophysics, eds, Elsevier/Academic Press, London, UK
17. Chew WC, Liu Q. Perfectly Matched Layers for elastodynamics: a new absorbing boundary condition. J. Comput. Acoust. 1996, 4(4):341-359.
18. Chorin AJ. Numerical solution of the Navier-Stokes equations. Math. Comput. 1968, 22:745-762.
19. Cockburn B, Karniadakis GE, Shu C-W. Discontinuous Galerkin Methods: Theory, Computation and Applications 2000, Springer, Heidelberg, Germany
20. Collino F, Tsogka C. Application of the PML absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media. Geophysics 2001, 66(1):294-307.
21. Danielson KT, Namburu RR. Nonlinear dynamic finite element analysis on parallel computers using Fortran90 and MPI. Adv. Eng. Software 1998, 29(3-6):179-186.
22. Dolbeau R, Bihan S, Bodin F. HMPP: a hybrid multi-core parallel programming environment. 2007, 1-5. Boston, Massachusetts, USA
23. Drossaert FH, Giannopoulos A. A nonsplit complex frequency-shifted PML based on recursive integration for FDTD modeling of elastic waves. Geophysics 2007, 72(2):T9-T17.
24. Dumbser M, Käser M. An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes-II. The three-dimensional isotropic case. Geophys. J. Int. 2006, 167(1):319-336.
25. Elsen E, LeGresley P, Darve E. Large calculation of the flow over a hypersonic vehicle using a GPU. J. Comput. Phys. 2008, 227(24):10 148-10 161.
26. Falk RS, Richter GR. Explicit finite element methods for symmetric hyperbolic equations. SIAM J. Numer. Anal. 1999, 36(3):935-952.
27. Festa G, Vilotte JP. The Newmark scheme as velocity-stress time-staggering: an efficient PML implementation for spectral-element simulations of elastodynamics. Geophys. J. Int. 2005, 161:789-812.
28. Festa G, Delavaud E, Vilotte JP. Interaction between surface waves and absorbing boundaries for wave propagation in geological basins: 2D numerical simulations. Geophys. Res. Lett. 2005, 32(20):L20306. 10.1029/2005GL024091, doi
29. Gedney SD, Zhao B. An auxiliary differential equation formulation for the complex-frequency shifted PML. IEEE Trans. Antenn. Propagat. 2010, 58(3):838-847.
30. Genovese L, Ospici M, Deutsch T, Méhaut J-F, Neelov A, Goedecker S. Density functional theory calculation on many-cores hybrid central processing unit-graphic processing unit architectures. J. Chem. Phys. 2009, 131(3). 10.1063/1.3166140, 034103, doi
31. Giraldo FX, Hesthaven JS, Warburton T. Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations. J. Comput. Phys. 2002, 181(2):499-525.
32. Graves RW. Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences. Bull. seism. Soc. Am. 1996, 86(4):1091-1106.
33. Gropp W, Lusk E, Skjellum A. Using MPI, Portable Parallel Programming with the Message-Passing Interface 1994, MIT Press, Cambridge, USA
34. Grote MJ, Schneebeli A, Schötzau D. Discontinuous Galerkin finite element method for the wave equation. SIAM J. Numer. Anal. 2006, 44(6):2408-2431.
35. Hastings FD, Schneider JB, Broschat SL. Application of the Perfectly Matched Layer (PML) absorbing boundary condition to elastic wave propagation. J. acoust. Soc. Am. 1996, 100(5):3061-3069.
36. Holberg O. Computational aspects of the choice of operator and sampling interval for numerical differentiation in large-scale simulation of wave phenomena. Geophys. Prospect. 1987, 35:629-655.
37. Humphrey JR, Price DK, Durbano JP, Kelmelis EJ, Martin RD. High performance 2D and 3D FDTD solvers on GPUs. 2006, 547-550. World Scientific and Engineering Academy and Society (WSEAS), Dallas, TX, USA
38. Inman MJ, Elsherbeni AZ. Optimization and parameter exploration using GPU based FDTD solvers. 2008, 149-152. Atlanta, Georgia, USA
39. Inman MJ, Elsherbeni AZ, Maloney JG, Baker BN. GPU based FDTD solver with CPML boundaries. 2007, 5255-5258. Honolulu, Hawaii, USA
40. Kawase H. Time-domain response of a semi-circular canyon for incident SV, P and Rayleigh waves calculated by the discrete wavenumber boundary element method. Bull. seism. Soc. Am. 1988, 78:1415-1437.
41. Klöckner A, Warburton T, Bridge J, Hesthaven JS. Nodal discontinuous Galerkin methods on graphics processors. J. Comput. Phys. 2009, 228:7863-7882.
42. Komatitsch D, Martin R. An unsplit convolutional Perfectly Matched Layer improved at grazing incidence for the seismic wave equation. Geophysics 2007, 72(5):SM155-SM167.
43. Komatitsch D, Tromp J. Introduction to the spectral-element method for 3-D seismic wave propagation. Geophys. J. Int. 1999, 139(3):806-822.
44. Komatitsch D, Coutel F, Mora P. Tensorial formulation of the wave equation for modelling curved interfaces. Geophys. J. Int. 1996, 127(1):156-168.
45. Komatitsch D, Michéa D, Erlebacher G. Porting a high-order finite-element earthquake modeling application to NVIDIA graphics cards using CUDA. J. Parallel Distrib. Comput. 2009, 69(5):451-460.
46. Komatitsch D, Erlebacher G, Göddeke D, Michéa D. High-order finite-element seismic wave propagation modeling with MPI on a large-scale GPU cluster. J. Comput. Phys. 2010a
47. Komatitsch D, Göddeke D, Erlebacher G, Michéa D. Modeling the propagation of elastic waves using spectral elements on a cluster of 192 GPUs. Comput. Sci. Res. Develop. 2010b, 10.1007/s00450-010-0109-1, doi
48. Krakiwsky SE, Turner LE, Okoniewski MM. Graphics processor unit (GPU) acceleration of a finite-difference time-domain (FDTD) algorithm. 2004a, 265-268. pp
49. Krakiwsky SE, Turner LE, Okoniewski MM. Acceleration of finite-difference time-domain (FDTD) using graphics processor units (GPU). IEEE 2004 MTT-S International Microwave Symposium Digest 2004b, 2:1033-1036.
50. Kristek J, Moczo P. Seismic-wave propagation in viscoelastic media with material discontinuities: A 3D fourth-order staggered-grid finite-difference modeling. Bull. seism. Soc. Am. 2003, 93(5):2273-2280.
51. Kristek J, Moczo P, Galis M. A brief summary of some PML formulations and discretizations for the velocity-stress equation of seismic motion. Stud. Geophys. Geod. 2009, 53(4):459-474.
52. Liu Q, Polet J, Komatitsch D, Tromp J. Spectral-element moment tensor inversions for earthquakes in Southern California. Bull. seism. Soc. Am. 2004, 94(5):1748-1761.
53. Madariaga R. Dynamics of an expanding circular fault. Bull. seism. Soc. Am. 1976, 66(3):639-666.
54. Martin R, Komatitsch D. An optimized convolution-perfectly matched layer (C-PML) absorbing technique for 3D seismic wave simulation based on a finite-difference method. Geophys. Res. Abstr. 2006, 8. http://www.cosis.net/abstracts/EGU06/03988/EGU06-J-03988-1.pdf, 03988, Abstract EGU06-A-03988
55. Martin R, Komatitsch D. An unsplit convolutional perfectly matched layer technique improved at grazing incidence for the viscoelastic wave equation. Geophys. J. Int. 2009, 179(1):333-344.
56. Martin R, Komatitsch D, Barucq H. An optimized convolution-perfectly matched layer (C-PML) absorbing technique for 3D seismic wave simulation based on a finite-difference method. EOS, Trans. Am. geophys. Un. 2005, 86(52). http://www.agu.org/meetings/fm05/waisfm05.html, Fall Meet. Suppl., Abstract NG43B-0574
57. Martin R, Komatitsch D, Ezziani A. An unsplit convolutional perfectly matched layer improved at grazing incidence for seismic wave equation in poroelastic media. Geophysics 2008a, 73(4):T51-T61.
58. Martin R, Komatitsch D, Gedney SD. A variational formulation of a stabilized unsplit convolutional perfectly matched layer for the isotropic or anisotropic seismic wave equation. Comput. Model. Eng. Sci. 2008b, 37(3):274-304.
59. Martin R, Komatitsch D, Gedney SD, Bruthiaux E. 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. 2010, 56(1):17-42.
60. Meza-Fajardo KC, Papageorgiou AS. A nonconvolutional, split-field, perfectly matched layer for wave propagation in isotropic and anisotropic elastic media: stability analysis. Bull. seism. Soc. Am. 2008, 98(4):1811-1836.
61. Micikevicius P. 3D finite-difference computation on GPUs using CUDA. 2009, 79-84. Washington, DC, USA
62. Moczo P, Kristek J. On the rheological models used for time-domain methods of seismic wave propagation. Geophys. Res. Lett. 2005, 32:L01306. 10.1029/2004GL021598, doi
63. Moczo P, Robertsson J, Eisner L. The finite-difference time-domain method for modeling of seismic wave propagation. Advances in Wave Propagation in Heterogeneous Media 2007, 421-516. Wu R-S, Maupin V, Vol. 48 of Advances in Geophysics, Chapter 8, eds, Elsevier/Academic Press, London, UK
64. Monk P, Richter GR. A discontinuous Galerkin method for linear symmetric hyperbolic systems in inhomogeneous media. J. Scient. Comput. 2005, 22-23(1-3):443-477.
65. NVIDIA CUDA Programming Guide Version 2.3. 2009a, 139. NVIDIA Corporation, Santa Clara, California, USA, pp
66. 2009b, 22. NVIDIA Corporation, NVIDIA's next generation CUDA compute architecture: FERMI, Tech. rep., NVIDIA, Santa Clara, California, USA, pp
67. Nyland L, Harris M, Prins J. Fast N-body simulation with CUDA. GPU Gems 3 2007, 677-695. Chapter 31, Addison-Wesley Professional, Boston, MA, USA
68. Owens JD, Luebke DP, Govindaraju NK, Harris MJ, Krüger J, Lefohn AE, Purcell TJ. A survey of general-purpose computation on graphics hardware. Comput. Graph. Forum 2007, 26(1):80-113.
69. Planas J, Badia RM, Ayguadé E, Labarta J. Hierarchical task-based programming with StarSs. Int. J. High Perform. Comput. Appl. 2009, 23(3):284-299.
70. Price DK, Humphrey JR, Kelmelis EJ. GPU-based accelerated 2D and 3D FDTD solvers. 2007, Vol. 6468. SPIE and the International Society for Optical Engineering, San Jose, California, USA
71. Reed WH, Hill TR. 1973, Triangular mesh methods for the neutron transport equation, Tech. Rep. LA-UR-73-479, Los Alamos Scientific Laboratory, Los Alamos, USA
72. Roden JA, Gedney SD. Convolution PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media. Microwave Opt. Technol. Lett. 2000, 27(5):334-339.
73. Tromp J, Komatitsch D, Liu Q. Spectral-element and adjoint methods in seismology. Commun. Comput. Phys. 2008, 3(1):1-32.
74. Vai R, Castillo-Covarrubias JM, Sánchez-Sesma FJ, Komatitsch D, Vilotte JP. Elastic wave propagation in an irregularly layered medium. Soil Dyn. Earthq. Eng. 1999, 18(1):11-18.
75. Valcarce A, De La Roche G, Zhang J. A GPU approach to FDTD for radio coverage prediction. 2008, 1585-1590. Guangzhou, China
76. Virieux J. P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method. Geophysics 1986, 51:889-901.
77. Yang J, Wang Y, Chen Y. GPU accelerated molecular dynamics simulation of thermal conductivities. J. Comput. Phys. 2007, 221:799-804.
78. Yee KS. Numerical solution of initial boundary value problems involving Maxwell's equations. IEEE Trans. Antenn. Propagat. 1966, 14:302-307.