Efficient Parallel Multigrid Methods on Manycore Clusters with Double/Single Precision Computing

Abstract

The parallel multigrid method is expected to play an important role in scientific computing on exa-scale supercomputer systems for solving large-scale linear equations with sparse coefficient matrices. Because solving sparse linear systems is a very memory-bound process, efficient method for storage of coefficient matrices is a crucial issue. In the previous works, authors implemented sliced ELL method to parallel conjugate gradient solvers with multigrid preconditioning (MGCG) for the application on 3D groundwater flow through heterogeneous porous media (pGW3D-LVM), and excellent performance has been obtained on large-scale multicore/manycore clusters. In the present work, authors introduced SELL-C-σ with double/single precision computing to the MGCG solver, and evaluated the performance of the solver with OpenMP/MPI hybrid parallel programing models on the Oakforest-PACS (OLP) system at JCAHPC using up to 2,048 nodes of Intel Xeon Phi. Because SELL-C-σ is suitable for wide-SIMD architecture, such as Xeon Phi, improvement of the performance over the sliced ELL was more than 35% for double precision and more than 45% for single precision on OFP. Finally, accuracy verification was conducted based on the method proposed by authors for solving linear equations with sparse coefficient matrices with M-property.