NUMA Aware Iterative Stencil Computations on Many-Core Systems

Temporal blocking in iterative stencil computations allows to surpass the performance of peak system bandwidth that holds for a single stencil computation. However, the effectiveness of temporal blocking depends strongly on the tiling scheme, which must account for the contradicting goals of spatio-temporal data locality, regular memory access patterns, parallelization into many independent tasks, and datato-core affinity for NUMA-aware data distribution. Despite the prevalence of cache coherent non-uniform memory access (ccNUMA) in todays many-core systems, this latter aspect has been largely ignored in the development of temporal blocking algorithms. Building upon previous cache-aware 1 and cacheoblivious 2 schemes, this paper develops their NUMA-aware variants, explaining why the incorporation of data-to-core affinity as an equally important goal necessitates also new tiling and parallelization strategies. Results are presented on an 8 socket dual-core and a 4 socket oct-core systems and compared against an optimized naive scheme, various peak performance characteristics, and related schemes from literature.