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Simulation of reaction-diffusion processes in three dimensions using CUDA

Ferenc Molnar Jr., Ferenc Izsak, Robert Meszaros, Istvan Lagzi
Department of Theoretical Physics, Eotvos Lorand University, Budapest, Hungary
arXiv:1004.0480 [physics.comp-ph] (4 Apr 2010)

@article{molnar2010simulation,

   title={Simulation of reaction-diffusion processes in three dimensions using CUDA},

   author={Molnar Jr, F. and Izsak, F. and Meszaros, R. and Lagzi, I. and Lin, L. and Morrone, J. and Car, R. and Parrinello, M. and Zeman, J. and Vond{v{r}}ejc, J. and others},

   journal={Arxiv preprint arXiv:1004.0480},

   year={2010}

}

Numerical solution of reaction-diffusion equations in three dimensions is one of the most challenging applied mathematical problems. Since these simulations are very time consuming, any ideas and strategies aiming at the reduction of CPU time are important topics of research. A general and robust idea is the parallelization of source codes/programs. Recently, the technological development of graphics hardware created a possibility to use desktop video cards to solve numerically intensive problems. We present a powerful parallel computing framework to solve reaction-diffusion equations numerically using the Graphics Processing Units (GPUs) with CUDA. Four different reaction-diffusion problems, (i) diffusion of chemically inert compound, (ii) Turing pattern formation, (iii) phase separation in the wake of a moving diffusion front and (iv) air pollution dispersion were solved, and additionally both the Shared method and the Moving Tiles method were tested. Our results show that parallel implementation achieves typical acceleration values in the order of 5-40 times compared to CPU using a single-threaded implementation on a 2.8 GHz desktop computer.
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