Hierarchical parallelization and optimization of high-order stencil computations on multicore clusters

We present a scalable parallelization scheme for high-order stencil computations that also optimizes memory behavior on multicore clusters. Our multilevel approach combines: (i)?inter-node parallelization via spatial decomposition; (ii)?inter-core parallelization via multithreading and explicit non-uniform memory access (NUMA) control; (iii)?data locality optimizations through auto-tuned tiling for efficient use of hierarchical memory; and (iv)?register blocking and data parallelism via single-instruction multiple-data techniques to utilize registers and exploit data locality. The scheme is applied to a sixth-order stencil based finite-difference time-domain code. Weak-scaling parallel efficiency is over 98?% on 32,768 BlueGene/P processors. Multithreading with explicit NUMA control attains 9.9-fold speedup on a dual 12-core AMD Opteron system. Data locality optimizations achieve 7.7-fold reduction of the last level cache miss rate of Intel Nehalem, whereas register blocking increases data parallelism and thereby achieves 5.9 Gflops performance on a single core. Register blocking?+ multithreading optimizations achieve 5.8-fold speedup on a single quadcore Nehalem.