A local relaxation method for solving PDEs on mesh-connected arrays
SIAM Journal on Scientific and Statistical Computing
Analysis of the SOR iteration for the 9-point Laplacian
SIAM Journal on Numerical Analysis
Scalable parallel programming with CUDA
ACM SIGGRAPH 2008 classes
Programming Massively Parallel Processors: A Hands-on Approach
Programming Massively Parallel Processors: A Hands-on Approach
Accelerating the red/black SOR method using GPUs with CUDA
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
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In this paper we study a parallel form of the SOR method for the numerical solution of the Convection Diffusion equation suitable for GPUs using CUDA. To exploit the parallelism offered by GPUs we consider the fine grain parallelism model. This is achieved by considering the local relaxation version of SOR. More specifically, we use SOR with red black ordering with two sets of parameters ωij and $\omega_{ij}^{'}$. The parameter ωij is associated with each red (i+j even) grid point (ij), whereas the parameter $\omega_{ij}^{'}$ is associated with each black (i+j odd) grid point (ij). The use of a parameter for each grid point avoids the global communication required in the adaptive determination of the best value of ω and also increases the convergence rate of the SOR method [3]. We present our strategy and the results of our effort to exploit the computational capabilities of GPUs under the CUDA environment. Additionally, a program for the CPU was developed as a performance reference. Significant performance improvement was achieved with the three developed GPU kernel variations which proved to have different pros and cons.