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Open Access Publications from the University of California

Optimization of Geometric Multigrid for Emerging Multi-and Manycore Processors


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 Opteron-based Cray XE6, Intel® Xeon® E5-2670 and X5550 processor-based Infiniband clusters, as well as the new Intel® Xeon Phi 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 large-scale multigrid calculations. © 2012 IEEE.

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