Numerical integration of Poisson's equation using a graphics processing unit with CUDA-technology

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.