Efficient magnetohydrodynamic simulations on graphics processing units with CUDA

Computer Physics Communications

Volumn 182, Issue 10, 2011, Pages 2132-2160

  Wong, Hon Cheng ^a   Wong, Un Hong ^a   Feng, Xueshang ^b   Tang, Zesheng ^a  

^a MACAU UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Macao)

^b CENTER FOR SPACE SCIENCE AND APPLIED RESEARCH   (China)

Author keywords

CUDA; GPUs; MHD simulations; Parallel computing

Indexed keywords

COMPUTER GRAPHICS; COMPUTER GRAPHICS EQUIPMENT; MAGNETOHYDRODYNAMICS; MAGNETOPLASMA; PARALLEL PROCESSING SYSTEMS; PROGRAM PROCESSORS; SUPERCOMPUTERS; VISUALIZATION;

COMPUTE UNIFIED DEVICE ARCHITECTURE(CUDA); CUDA; DOUBLE PRECISION COMPUTATION; GPUS; HIGH-RESOLUTION METHODS; MAGNETOHYDRODYNAMIC SIMULATIONS; MHD SIMULATION; PERFORMANCE MEASUREMENTS;

GRAPHICS PROCESSING UNIT;

EID: 79960053483     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2011.05.011     Document Type: Article

References (59)

1. D.S. Balsara, and D.S. Spicer A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations J. Comput. Phys. 149 1999 270 292
2. R.G. Belleman, J. Bédorf, and S.F. Portegies Zwart High performance direct gravitational N-body simulations on graphics processing units II: an implementation in CUDA New Astronomy 13 2008 103 112
3. M. Brio, and C.C. Wu An upwind differencing scheme for the equations of ideal magnetohydrodynamics J. Comput. Phys. 75 1988 400 422
4. S. Che, M. Boyer, J. Meng, D. Tarjan, J.W. Sheaffer, and K. Skadron A performance study of general-purpose applications on graphics processors using CUDA J. Parallel Distrib. Comput. 68 2008 1370 1380
5. A. Ciardi, S. Lebedev, A. Frank, E. Blackman, D. Ampleford, C. Jennings, J. Chittenden, T. Lery, S. Bland, S. Bott, G. Hall, J. Rapley, F. Vidal, and A. Marocchino 3D MHD simulations of laboratory plasma jets Astrophysics and Space Science 307 2007 17 22
6. W. Dai, and P.R. Woodward An approximate Riemann solver for ideal magnetohydrodynamics J. Comput. Phys. 111 1994 354 372 (Pubitemid 124013404)
7. P. Daum VisAn MHD: a toolbox in Matlab for MHD computer model data visualization and analysis Ann. Geophys. 25 2007 779 784 (Pubitemid 46514961)
8. M. Dryer Multi-dimensional MHD simulation of solar-generated disturbances: space weather forecasting of geomagnetic storms AIAA J. 36 1998 365 370 (Pubitemid 128556203)
9. M. Dryer Space weather simulations in 3D MHD from the Sun to Earth and beyond to 100 AU: a modelers perspective of the present state of the art (Invited Review) Asia J. of Physics 16 2007 97 121
10. C.R. Evans, and J.F. Hawley Simulation of magnetohydrodynamic flow: a constrained transport method Astrophys. J. 332 1988 659 677
11. X. Feng, Y. Zhou, and S.T. Wu A novel numerical implementation for solar wind modeling by the modified conservation element/solution element method Astrophys. J. 655 2007 1110 1126
12. T.A. Gardiner, and J.M. Stone An unsplit Godunov method for ideal MHD via constrained transport J. Comput. Phys. 205 2005 509 539 (Pubitemid 40518385)
13. E. Gaburov, S. Harfst, and S.P. Zwart SAPPORO: a way to turn your graphics cards into a GRAPE-6 New Astronomy 14 2009 630 637
14. J.P. Goedbloed, and S. Poedts Principles of Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas 2004 Cambridge University Press
15. M. Hadwiger, J.M. Kniss, C. Rezk-Salama, D. Weiskopf, and K. Engel Real-Time Volume Graphics 2006 A K Peters
16. J.C. Hayes, M.L. Norman, R.A. Fiedler, J.O. Bordner, P.S. Li, S.E. Clark, A. Ud-Doula, and M.-M.M. Low Simulating radiating and magnetized flows in multiple dimensions with ZEUS-MP Astrophys. J. Supp. 165 2006 188 228 (Pubitemid 44366577)
17. Z. Huang, C. Wang, Y. Hu, and X. Guo Parallel implementation of 3D global MHD simulations for Earths magnetosphere Comput. Math. Appl. 55 2008 419 425
18. S. Jin, and Z. Xin The relaxation schemes for systems of conservation laws in arbitrary space dimensions Commun. Pure Appl. Math. 48 1995 235 276
19. R. Käppeli, S.C. Whitehouse, S. Scheidegger, U.-L. Pen, and M. Liebendörfer FISH: a 3D parallel MHD code for astrophysical applications arXiv:0910.2854v1 2009
20. D.B. Kirk, and W.W. Hwu Programming Massively Parallel Processors 2010 Addison-Wesley
21. A.G. Kulikovskii, N.V. Pogorelov, and A.Yu. Semenov Mathematical Aspects of Numerical Solution of Hyperbolic Systems 2001 CRC Press
22. D. Lee, and A.E. Deane A parallel unsplit staggered mesh algorithm for magnetohydrodynamics A. Deane, Parallel Computational Fluid Dynamics - Theory and Applications 2006 Elsevier 243 250
23. D. Lee, and A.E. Deane An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics J. Comput. Phys. 228 2009 952 975
24. R.J. LeVeque Numerical Methods for Conservation Laws second edition 1992 Birkhauser
25. R.J. LeVeque Finite Volume Methods for Hyperbolic Problems 2002 Cambridge University Press
26. S. Li, and H. Li A novel approach of divergence-free reconstruction for adaptive mesh refinement J. Comput. Phys. 199 2004 1 15 (Pubitemid 39150732)
27. E. Lindholm, J. Nickolls, S. Oberman, and J. Montrym NVIDIA Tesla: a unified graphics and computing architecture IEEE Micro 28 2008 39 55 (Pubitemid 351796170)
28. W.R. Mark, R.S. Glanville, K. Akeley, and M.J. Kilgard Cg: a system for programming graphics hardware in a C-like language ACM Trans. Graph. 22 2003 896 907
29. P.M. Meijer, S. Poedts, and J.P. Goedbloed Parallel magnetohydrodynamics on the Cray T3D Future Generation Computer Systems 12 1996 307 323 (Pubitemid 126686554)
30. NVIDIA Corporation, NVIDIA CUDA compute unified device architecture programming Guide 3.2, Oct. 2010, http://www.nvidia.com/object/cuda-develop. html.
31. NVIDIA Corporation, CUDA C programming best practices guides 3.2, August 2010, http://www.nvidia.com/object/cuda-develop.html.
32. NVIDIA Corporation, NVIDIAs next generation CUDA compute architecture: Fermi, Whitepaper, 2009, http://www.nvidia.com/object/cuda-develop.html.
33. A. Orszag, and C.M. Tang Small-scale structure of two-dimensional magneto-hydrodynamics turbulence J. Fluid Mech. 90 1979 129 143
34. B. Pang, U.-L. Pen, and E.T. Vishniac Fast magnetic reconnection in three-dimensional magnetohydrodynamics simulations Physics of Plasmas 17 2010 102302
35. U.-L. Pen, P. Arras, and S. Wong A free, fast, simple and efficient TVD MHD code Astrophys. J. Supp. 149 2003 447 455
36. U.-L. Pen, C.D. Matzner, and S. Wong The fate of nonradiative magnetized accretion flows: Magnetically frustrated convection Astrophys. J. 596 2003 L207 L210
37. U.-L. Pen MHD code: http://www.cita.utoronto.ca/~pen/MHD/
38. D. Ryu, and T.W. Jones Numerical magnetohydrodynamics in astrophysics: algorithm and tests for one-dimensional flow Astrophys. J. 442 1995 228 258
39. J. Sainio CUDAEASY - a GPU accelerated cosmological lattice program Comput. Phys. Commun. 181 2010 906 912
40. J. Sanders, and E. Kandrot CUDA by Example 2011 Addison-Wesley
41. O. Schenk, M. Christen, and H. Burkhart Algorithmic performance studies on graphics processing units J. Parallel Distrib. Comput. 68 2008 1360 1369
42. H.-Y. Schive, C.-H. Chien, S.-K. Wong, Y.-C. Tsai, and T. Chiueh Graphic-card cluster for astrophysics (GraCCA) - performance tests New Astronomy 13 2008 418 435
43. L. Seiler, D. Carmean, E. Sprangle, T. Forsyth, M. Abrash, P. Dubey, S. Junkins, A. Lake, J. Sugerman, R. Cavin, R. Espasa, E. Grochowski, T. Juan, and P. Hanrahan Larrabee: a many-core x86 architecture for visual computing ACM Trans. Graph. 27 2008 Article 18
44. G. Sod A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws J. Comput. Phys. 27 1978 1 31
45. Spherical blast wave test page of Athena3D test suite: http://www.astro.virginia.edu/VITA/ATHENA/blast.html.
46. G. Stantchev, W. Dorland, and N. Gumerov Fast parallel particle-to-grid interpolation for plasma PIC simulations J. Parallel Distrib. Comput. 68 2008 1339 1349
47. G. Stantchev, D. Juba, W. Dorland, and A. Varshney Using graphics processors for high-performance computation and visualization of plasma turbulence Computing in Science and Engineering 11 2009 52 59
48. J. Stone, and T.A. Gardiner Recent progress in astrophysical MHD Comput. Phys. Commun. 177 2007 257 259 (Pubitemid 46935621)
49. J. Stone, T.A. Gardiner, P. Teuben, J.F. Hawley, and J.B. Simon Athena a new code for astrophysical MHD Astrophys. J. Supp. 178 2008 137 177
50. J. Stone, and T. Gardiner A simple unsplit Godunov method for multidimensional MHD New Astronomy 14 2009 139 148
51. G. Strang On the construction and comparison of difference schemes SIAM J. Numer. Anal. 5 1968 506 517
52. G. Tóth, and D. Odstrčil Comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magnetohydrodynamic problems J. Comput. Phys. 128 1996 82 100 (Pubitemid 126165828)
53. G. Tóth The ∇ · B = 0 constraint in shock-capturing magnetohydrodynamics codes J. Comput. Phys. 161 2000 605 656
54. H. Trac, and U.-L. Pen A primer on Eulerian computational fluid dynamics for astrophysics Publications of the Astronomical Society of the Pacific 115 2003 303 321
55. B. van Leer Towards the ultimate conservative difference scheme II. Monotonicity and conservation combined in a second order scheme J. Comput. Phys. 14 1974 361 370
56. B. van Leer Towards the ultimate conservative difference scheme V. A second-order sequel to Godunovs method J. Comput. Phys. 32 1979 101 136
57. R.S. Wright Jr., B. Lipchak, and N. Haemel OpenGL Superbible: Comprehensive Tutorial and Reference fourth edition 2007 Addison-Wesley
58. A. Zachary, A. Malagoli, and P. Colella A higher-order Godunov method for multidimensional ideal magnetohydrodynamics SIAM J. Sci. Comput. 15 1994 263 284
59. U. Ziegler The NIRVANA code: parallel computational MHD with adaptive mesh refinement Comput. Phys. Commun. 179 2008 227 244