Multigrid methods are widely used to accelerate the convergence of iterative solvers for linear systems used in a number of different application areas. In this paper, we explore optimization techniques for geometric multigrid on existing and emerging multicore systems including the Opteronbased Cray XE6, Intel R Xeon R E5-2670 and X5550 processorbased Infiniband clusters, as well as the new Intel R Xeon Phi TM coprocessor (Knights Corner). Our work examines a variety of novel techniques including communication-aggregation, threaded wavefront-based DRAM communication-avoiding, dynamic threading decisions, SIMDization, and fusion of operators. We quantify performance through each phase of the V-cycle for both single-node and distributed-memory experiments and provide detailed analysis for each class of optimization. Results show our optimizations yield significant speedups across a variety of subdomain sizes while simultaneously demonstrating the potential of multi-and manycore processors to dramatically accelerate single-node performance. However, our analysis also indicates that improvements in networks and communication will be essential to reap the potential of manycore processors in largescale multigrid calculations.
A variety of optimization techniques, such as communication avoiding, SIMDization, and operator fusion were studied for the MG method on multicore processor systems and the Intel Xeon Phi coprocessor REF .
Optimization of geometric multigrid for emerging multi- and manycore processors
SC '12
Computer Science