Simulation of reaction-diffusion processes in three dimensions using CUDA

Chemometrics and Intelligent Laboratory Systems

Volumn 108, Issue 1, 2011, Pages 76-85

  Molnár, Ferenc ^a   Izsák, Ferenc ^a,b   Mészáros, Róbert ^a   Lagzi, István ^a  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^b UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

CUDA; Parallel computing; Pattern formation; Reaction diffusion; Video card

Indexed keywords

AIR POLLUTION; ARTICLE; ATMOSPHERIC DISPERSION; COMPUTER MEMORY; COMPUTER PROGRAM; DIFFUSION; GRAPHICS PROCESSING UNIT; INFORMATION PROCESSING; KERNEL METHOD; MATHEMATICAL ANALYSIS; PERFORMANCE MEASUREMENT SYSTEM; PHASE SEPARATION; PRIORITY JOURNAL; PROBLEM SOLVING; REACTION DIFFUSION EQUATION; SIMULATION; THREE DIMENSIONAL IMAGING;

EID: 79960137932     PISSN: 01697439     EISSN: 18733239     Source Type: Journal    
DOI: 10.1016/j.chemolab.2011.03.009     Document Type: Article

References (61)

1. Cross M.C., Hohenberg P.C. Pattern formation outside of equilibrium. Rev. Mod. Phys. 1993, 65:851-1112.
2. Horváth D., Petrov V., Scott S.K., Showalter K. Instabilities in propagating reaction-diffusion fronts. J. Chem. Phys. 1993, 98:6332-6343.
3. Epstein I.R., Showalter K. Nonlinear chemical dynamics: oscillations, patterns, and chaos. J. Phys. Chem. 1996, 100:13132-13147.
4. Castets V., Dulos E., Boissonade J., De Kepper P. Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern. Phys. Rev. Lett. 1990, 64:2953-2956.
5. Horváth J., Szalai I., De Kepper P. An experimental design method leading to chemical Turing patterns. Science 2009, 324:772-775.
6. Fowler D.R., Meinhardt H., Prusinkiewicz P. Modeling seashells. Comp. Grap. 1992, 26:379-387.
7. Lagzi I., Ueyama D. Pattern transition between periodic Liesegang pattern and crystal growth regime in reaction-diffusion systems. Chem. Phys. Lett. 2009, 468:188-192.
8. Anderson A.G., Goddard W.A., Schröder P. Quantum Monte Carlo on graphical processing units. Comput. Phys. Commun. 2007, 177:298-306.
9. Liu W., Schmidt B., Voss G., Müller-Wittig W. Molecular dynamics simulations on commodity GPUs with CUDA. Lect. Notes Comput. Sci. 2007, 4873:185-196.
10. Stone J.E., Phillips J.C., Freddolino P.L., Hardy D.J., Trabuco L.G., Schulten K. Accelerating molecular modeling applications with graphics processors. J. Comput. Chem. 2007, 28:2618-2640.
11. Preis T., Virnau P., Paul W., Schneider J.J. GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model. J. Comput. Phys. 2009, 228:4468-4477.
12. Liu W., Schmidt B., Voss G., Müller-Wittig W. Accelerating molecular dynamics simulations using Graphics Processing Units with CUDA. Comput. Phys. Commun. 2008, 179:634-641.
13. Gutiérrez E., Romero S., Trenas M.A., Zapata E.L. Quantum computer simulation using the CUDA programming model. Comput. Phys. Commun. 2010, 181:283-300.
14. Sanna N., Baccarelli I., Morelli G. The VOLSCAT package for electron and positron scattering of molecular targets: a new high throughput approach to cross-section and resonances computation. Comput. Phys. Commun. 2009, 180:2550-2562.
15. Sanna N., Baccarelli I., Morelli G. SCELib3.0: the new revision of SCELib, the parallel computational library of molecular properties in the Single Center Approach. Comput. Phys. Commun. 2009, 180:2544-2549.
16. Li S., Livshitz B., Lomakin V. Fast evaluation of Helmholtz potential on graphics processing units (GPUs). J. Comput. Phys. 2010, 229:8463-8483.
17. Block B., Virnau P., Preis T. Multi-GPU accelerated multi-spin Monte Carlo simulations of the 2D Ising model. Comput. Phys. Commun. 2010, 181:1549-1556.
18. Belleman R.G., Bédorf J., Portegies Zwart S.F. High performance direct gravitational N-body simulations on graphics processing units II: an implementation in CUDA 2008, 13:103-112. New Astron.
19. Ford E.B. Parallel algorithm for solving Kepler's equation on graphics processing units: application to analysis of Doppler exoplanet searches. New Astron. 2009, 14:406-412.
20. Sainio J. CUDAEASY - a GPU accelerated cosmological lattice program. Comput. Phys. Commun. 2010, 181:906-912.
21. Stone S.S., Haldar J.P., Tsao S.C., Hwua W.-M.W., Sutton B.P., Liang Z.-P. Accelerating advanced MRI reconstructions on GPUs. J. Parallel Distrib. Comput. 2008, 68:1307-1318.
22. Castano-Diez D., Moser D., Schoenegger A., Pruggnaller S., Frangakis A.S. Performance evaluation of image processing algorithms on the GPU. J. Struct. Biol. 2008, 164:153-160.
23. Melchionna S., Bernaschi M., Succi S., Kaxiras E., Rybicki F.J., Mitsouras D., Coskun A.U., Feldman C.L. Hydrokinetic approach to large-scale cardiovascular blood flow. Comput. Phys. Commun. 2010, 181:462-472.
24. Komatitsch D., Michea D., Erlebacher G. Porting a high-order finite-element earthquake modeling application to NVIDIA graphics cards using CUDA. J. Parallel Distrib. Comput. 2009, 69:451-460.
25. Walsh S.D.C., Saar M.O., Bailey P., Lilja D.J. Accelerating geoscience and engineering system simulations on graphics hardware. Comput. Geosci. 2009, 35:2353-2364.
26. Komatitsch D., Erlebacher G., Goddeke D., Michea D. High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster. J. Comput. Phys. 2010, 229:7692-7714.
27. Molnár F., Szakály T., Mészáros R., Lagzi I. Air pollution modelling using a Graphics Processing Unit with CUDA. Comput. Phys. Commun. 2010, 181:105-112.
28. Senocak I., Thibault J., Caylor M. Rapid-response urban CFD simulations using a GPU computing paradigm on desktop supercomputers. Eighth Symposium on the Urban Environment, Phoenix Arizona 2009, J19.2.
29. Simek V., Dvorak R., Zboril F., Kunovsky J. Towards accelerated computation of atmospheric equations using CUDA. Proceedings of the UKSim 2009: 11th International Conference on Computer Modelling and Simulation 2009, 449-454.
30. Huang B., Mielikainen J., Oh H., Huang H.-L.A. Development of a GPU-based High-Performance Radiative Transfer Model for the Infrared Atmospheric Sounding Interferometer (IASI). J. Comput. Phys. 2011, 230:2207-2221.
31. Januszewski M., Kostur M. Accelerating numerical solution of stochastic differential equations with CUDA. Comput. Phys. Commun. 2010, 181:183-188.
32. Buluc A., Gilbert J.R., Budak C. Solving path problems on the GPU. Parallel Comput. 2010, 36:241-253.
33. Owens J.D., Houston M., Luebke D., Green S., Stone J.E., Phillips J.C. GPU computing. Proc. IEEE 2008, 96:879-899.
34. Che S., Boyer M., Meng J., Tarjan D., Sheaffer J.W., Skadron K. A performance study of general purpose applications on graphics processors using CUDA. J. Parallel Distrib. Comput. 2008, 68:1370-1380.
35. Garland M., Le Grand S., Nickolls J., Anderson J., Hardwick J., Morton S., Phillips E., Zhang Y., Volkov V. Parallel computing experiences with CUDA. Micro IEEE 2008, 28:13-27.
36. http://www.nvidia.com/object/cuda_get.html.
37. D.P. Playne, K.A. Hawick, Data parallel three-dimensional Cahn-Hilliard field equation simulation on GPUs with CUDA, Technical Report CSTN-073 (2009).
38. P. Micikevicius, 3D finite difference computation on GPUs using CUDA, Technical Report NVIDIA (2009).
39. Sanderson A.R., Meyer M.D., Kirby R.M., Johnson C.R. A framework for exploring numerical solutions of advection-reaction-diffusion equations using a GPU-based approach. Comput. Vis. Sci. 2009, 12:155-170.
40. NVIDIA Corporation NVIDIA CUDA Programming guide http://developer.download.nvidia.com/compute/cuda/2_1/toolkit/docs/NVIDIA_CUDA_Programming_Guide_2.1.pdf.
41. Micikevicius P. 3D finite difference computation on GPUs using CUDA. ACM Int. Conf. Proc. Ser. 2009, 383:79-84.
42. Lengyel I., Epstein I.R. Modeling of Turing structures in the chlorite-iodide-malonic acid-starch reaction system. Science 1991, 251:650-652.
43. Shoji H., Yamada K. Most stable patterns among three-dimensional Turing patterns. Jpn. J. Ind. Appl. Math. 2007, 24:67-77.
44. Shoji H., Yamada K., Ueyama D., Ohta T. Turing patterns in three dimensions. Phys. Rev. E 2007, 75:046212.
45. Horváth J., Szalai I., De Kepper P. Pattern formation in the thiourea-iodate-sulfite system: spatial bistability, waves, and stationary patterns. Phys. D 2010, 239:776-784.
46. Nakamasu A., Takahashi G., Kanbe A., Kondo S. Interactions between zebrafish pigment cells responsible for the generation of Turing patterns. Proc. Natl Acad. Sci. 2009, 106:8429-8434.
47. Volford A., Lagzi I., Molnár F., Rácz Z. Coarsening of precipitation patterns in a moving reaction-diffusion front. Phys. Rev. E. 2009, 80:055102(R).
48. Sultan R.F. Propagating fronts in periodic precipitation systems with redissolution. Phys. Chem. Chem. Phys. 2002, 4:1253-1261.
49. Rácz Z. Formation of Liesegang patterns. Phys. A 1999, 274:50-59.
50. Volford A., Izsák F., Ripszám M., Lagzi I. Pattern formation and self-organization in a simple precipitation system. Langmuir 2007, 23:961-964.
51. Costello B.P.J.D. Control of complex travelling waves in simple inorganic systems - the potential for computing. Int. J. Unconv. Comput. 2008, 4:297-314.
52. Pápai P., Lagzi I., Rácz Z. Complex motion of precipitation bands. Chem. Phys. Lett. 2007, 433:286-291.
53. Lagzi I., Mészáros R., Horváth L., Tomlin A.S., Weidinger T., Turányi T., Ács F., Haszpra L. Modelling ozone fluxes over Hungary. Atmos. Environ. 2004, 38:6211-6222.
54. Lagzi I., Tomlin A.S., Turányi T., Haszpra L. Modelling photochemical air pollutant formation in Hungary using an adaptive grid technique. Int. J. Environ. Pollut. 2009, 36:44-58.
55. Lagzi I., Kármán D., Turányi T., Tomlin A.S., Haszpra L. Simulation of the dispersion of nuclear contamination using an adaptive Eulerian grid model. J. Environ. Radioactiv. 2004, 75:59-82.
56. Dabdub D., Seinfeld J.H. Parallel computation in atmospheric chemical modeling. Parallel Comput. 1996, 22:111-130.
57. Schmidt M., Schafer R.P. An integrated simulation system for traffic induced air pollution. Environ. Modell. Softw. 1998, 13:295-303.
58. Martin M., Oberson O., Chopard B., Mueller F., Clappier A. Atmospheric pollution transport: the parallelization of a transport & chemistry code. Atmos. Environ. 1999, 33:1853-1860.
59. Alexandrov V.N., Owczarz W., Thomson P.G., Zlatev Z. Parallel runs of a large air pollution model on a grid of Sun computers. Math. Comput. Simul. 2004, 65:557-577.
60. Lovas R., Kacsuk P., Lagzi I., Turányi T. Unified development solution for cluster and Grid computing and its application in chemistry. Lect. Notes Comput. Sci. 2004, 3044:226-235.
61. http://nimbus.elte.hu/~cuda/RD/cuda.html.