Selecting tile shape for minimal execution time
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
Sparse Tiling for Stationary Iterative Methods
International Journal of High Performance Computing Applications
A New Block Parallel SOR Method and Its Analysis
SIAM Journal on Scientific Computing
Multigrid and Gauss-Seidel smoothers revisited: parallelization on chip multiprocessors
Proceedings of the 20th annual international conference on Supercomputing
A Cache-Efficient Parallel Gauss-Seidel Solver with Alternating Tiling
ICPADS '09 Proceedings of the 2009 15th International Conference on Parallel and Distributed Systems
Journal of Computational Physics
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SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm is important in the simulation of steady flows. As the traditional 3-D SIMPLE algorithm is time-consuming, we propose a parallel SIMPLE algorithm based on a novel tiling strategy -- alternate tiling, through replacing the original linear system and reordering the iteration space tiles. The novelty of our parallel algorithm lies in the introduction of the sequence of iteration space tiles as the sequence of execution, the time skewing technique to partition the iteration space, update operations of the grids from two directions alternately, and the improvement of the data locality. The effectiveness of the parallel algorithm and serial model of finite difference stencil algorithm are validated. Numerical experiments on distributed clusters show that the cache misses and the cost of communication and synchronization are reduced by reordering the tiles of iteration space, and the parallel SIMPLE algorithm based on alternate tiling has a good data locality and parallel efficiency in the three-dimensional incompressible pipe flow project.