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

Block iterative methods are extremely important as smoothers for multi-grid methods, as pre-conditioners 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. The authors 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.