Reconsidering algorithms for iterative solvers in the multicore era

Efficient solution of computational problems require a match between the algorithm and the underlying architecture. New multicore processors feature low intra-chip communication cost and smaller per-thread caches compared to single-core implementations, indicating that data locality issues are more important than communication overheads. We investigate the impact of these changes on parallel multigrid methods. We present a temporally blocked, naturally ordered, smoother implementation that improves the data locality as much as ten times. compared with the standard red-black algorithm. We present results of the performance of our new algorithm on an SMP system, an UltraSPARC T1 (Niagara) SMT/CMP, and a simulated CMP processor.