A Communication-Avoiding 3D LU Factorization Algorithm for Sparse Matrices

Conference · Tue May 01 04:00:00 EDT 2018

DOI:https://doi.org/10.1109/IPDPS.2018.00100· OSTI ID:1544235

Sao, Piyush; Li, Xiaoye Sherry; Vuduc, Richard

We propose a new algorithm to improve the strong scalability of right-looking sparse LU factorization on distributed memory systems. Our 3D sparse LU algorithm uses a three-dimensional MPI process grid, aggressively exploits elimination tree parallelism and trades off increased memory for reduced per-process communication. We also analyze the asymptotic improvements for planar graphs (e.g., from 2D grid or mesh domains) and certain non-planar graphs (specifically for 3D grids and meshes). For planar graphs with n vertices, our algorithm reduces communication volume asymptotically in n by a factor of O{log n} and latency by a factor of O{log n}. For non-planar cases, our algorithm can reduce the per-process communication volume by 3× and latency by O{n^1/3} times. In all cases, the memory needed to achieve these gains is a constant factor. We implemented our algorithm by extending the 2D data structure used in superLU. Our new 3D code achieves speedups up to 27× for planar graphs and up to 3.3× for non-planar graphs over the baseline 2D superLU when run on 24,000 cores of a Cray XC30.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
• Sponsoring Organization: USDOE Office of Science (SC)
• OSTI ID: 1544235
• Country of Publication: United States
• Language: English