Skip to main content
eScholarship
Open Access Publications from the University of California

Optimization of geometric multigrid for emerging multi- and manycore processors

  • Author(s): Williams, S
  • Kalamkar, DD
  • Singh, A
  • Deshpande, AM
  • Van Straalen, B
  • Smelyanskiy, M
  • Almgren, A
  • Dubey, P
  • Shalf, J
  • Oliker, L
  • et al.
Abstract

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.

Main Content
Current View