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Stencils are finite-difference algorithms for solving large-scale and high-dimension partial differential equations. Due to the data dependences among the iterative statements in Stencils, traditional Stencil computations are be executed serially, rather than in parallel. It’s challenging to design an effective and scalable Stencil parallelized method. To address the issue of 3D data space computing, we present a serial execution model based on multilayers symmetric Stencil method and time skewing techniques. Within this model, the iteration space is divided to multiple tiles based on time skewing, where the executive process is ordered by the sequence of tiles, and the nodes in each individual tile can be swept repeatedly to improve the data locality. In addition, we propose a novel 3D iterative space alternate tiling Stencil parallel method, which subdivides the iteration space along high dimension, and changes the execution sequence of tiles to reduce the data dependency and communication cost, where the partial order of tiles is still guaranteed. Experimental results demonstrate our proposed alternative tiling parallel method achieves better parallel efficiency and scalability compared with the domain-decomposition methods.

An Iterative Space Alternative Tiling Parallel Algorithm for 3D Finite Difference Stencil Computations