High-order stencil computations on multicore clusters

Stencil computation (SC) is of critical importance for broad scientific and engineering applications. However, it is a challenge to optimize complex, high-order SC on emerging clusters of multicore processors. We have developed a hierarchical SC parallelization framework that combines: (1) spatial decomposition based on message passing; (2) multithreading using critical section-free, dual representation; and (3) single-instruction multiple-data (SIMD) parallelism based on various code transformations. Our SIMD transformations include translocated statement fusion, vector composition via shuffle, and vectorized data layout reordering (e.g. matrix transpose), which are combined with traditional optimization techniques such as loop unrolling. We have thereby implemented two SCs of different characteristics-diagonally dominant, lattice Boltzmann method (LBM) for fluid flow simulation and highly off-diagonal (6-th order) finite-difference time-domain (FDTD) code for seismic wave propagation-on a Cell Broadband Engine (Cell BE) based system (a cluster of PlayStation3 consoles), a dual Intel quadcore platform, and IBM BlueGene/L and P. We have achieved high inter-node and intra-node (multithreading and SIMD) scalability for the diagonally dominant LBM: Weak-scaling parallel efficiency 0.978 on 131,072 BlueGene/P processors; strong-scaling multithreading efficiency 0.882 on 6 cores of Cell BE; and strong-scaling SIMD efficiency 0.780 using 4-element vector registers of Cell BE. Implementation of the high-order SC, on the contrary, is less efficient due to long-stride memory access and the limited size of the vector register file, which points out the need for further optimizations.