Geodesic
Numerical integration of Poisson's equation using a graphics processing unit with CUDA-technology
Numerical methods and programming, Tome 10 (2009) no. 2, pp. 268-274

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A parallel implementation of the cyclic multigrid method for solving a boundary value problem for Poisson's equation in $R^3$ is discussed for a graphics processor unit using NVIDIA CUDA technology. The results obtained by the graphics processing unit is compared with the analytical solution for the Dirichlet problem and with the numerical CPU-solution for the Dirichlet-Neumann problem. The acceleration of the parallel NVIDIA GeForce 8800 GTX code compared to the AMD Athlon 64X2 4800+ serial code is found to be about 200 times for 1 000 000 discrete elements. Moreover, a 8-core workstation based on two Intel(R) Xeon(R) 2.33HHz CPUs is found to be slower by 40 times than that of the GPU code.
Keywords: Poisson's equation; cyclic multigrid method; parallel computing; graphics processing unit; CUDA technology. 
@article{VMP_2009_10_2_a9,
     author = {N. M. Evstigneev},
     title = {Numerical integration of {Poisson's} equation using a graphics processing unit with {CUDA-technology}},
     journal = {Numerical methods and programming},
     pages = {268--274},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2009_10_2_a9/}
}
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N. M. Evstigneev. Numerical integration of Poisson's equation using a graphics processing unit with CUDA-technology. Numerical methods and programming, Tome 10 (2009) no. 2, pp. 268-274. http://geodesic.mathdoc.fr/item/VMP_2009_10_2_a9/