Block-Relaxation Methods for 3D Constant-Coefficient Stencils on GPUs and Multicore CPUs

Manuel Rodriguez Rodriguez, Bobby Philip, Zhen Wang, Mark Berrill
Oak Ridge Leadership Computing Facility, Oak Ridge National Laboratory, Oak Ridge, TN, 37831
arXiv:1208.1975v1 [cs.DC] (9 Aug 2012)


   author={Rodriguez, Manuel Rodriguez and Philip, Bobby and Wang, Zhen and Berrill, Mark},

   title={"{Block-Relaxation Methods for 3D Constant-Coefficient Stencils on GPUs and Multicore CPUs}"},

   journal={ArXiv e-prints},




   keywords={Distributed, Parallel, and Cluster Computing},




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Block iterative methods are extremely important as smoothers for multigrid methods, as preconditioners for Krylov methods, and as solvers for diagonally dominant linear systems. Developing robust and efficient algorithms suitable for current and evolving GPU and multicore CPU systems is a significant challenge. We address this issue in the case of constant-coefficient stencils arising in the solution of elliptic partial differential equations on structured 3D uniform and adaptively refined grids. Robust, highly parallel implementations of block Jacobi and chaotic block Gauss-Seidel algorithms with exact inversion of the blocks are developed using different parallelization techniques. Experimental results for NVIDIA Fermi GPUs and AMD multicore systems are presented.
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