Automatic Data Partitioning Applied to Multigrid PDE Solvers

This paper studies the impact of using automatic data-layout techniques on the process of coding the well-known multigrid MG NAS parallel benchmark. We describe the sequential problem in detail, and discuss the parallel version and its optimizations. Then, we implement the parallel algorithm using Hit map, a highly-efficient modular library for hierarchical tiling and mapping of arrays. We describe how to use the library plug-in system to add a new data-layout module that encapsulates a generalization of the data-alignment policy of the MG benchmark. The module system applies this policy to automatically adapt the data distribution and communication code to any grain level. The impact of using these techniques is qualitatively and quantitatively described in terms of development effort and performance. Our results show that it is possible to introduce flexible automatic data-layout techniques in current parallel compiler technology, without sacrificing performance.