  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.
