SC22 Proceedings

The International Conference for High Performance Computing, Networking, Storage, and Analysis

Technical Papers Archive

Addressing Irregular Patterns of Matrix Computations on GPUs and Their Impact on Applications Powered by Sparse Direct Solvers

Authors: Ahmad Abdelfattah (University of Tennessee, Innovative Computing Laboratory (ICL)); Pieter Ghysels and Wajih Boukaram (Lawrence Berkeley National Laboratory (LBNL)); Stanimire Tomov (University of Tennessee, Innovative Computing Laboratory (ICL)); Xiaoye Li (Lawrence Berkeley National Laboratory (LBNL)); and Jack Dongarra (University of Tennessee, Innovative Computing Laboratory (ICL))

Abstract: Several scientific applications rely on sparse direct solvers for their numerical robustness. However, performance optimization for these solvers remains a challenging task, especially on GPUs. This is due to workloads of small dense matrices that are different in size. Matrix decompositions on such irregular workloads are rarely addressed on GPUs.

This paper addresses irregular workloads of matrix computations on GPUs and shows their impact on a sparse LU solver. We designed an interface for the basic matrix operations supporting problems of different sizes. The interface enables us to develop irrLU-GPU, an LU decomposition on matrices of different sizes. We demonstrate the impact of irrLU-GPU on sparse LU solvers using NVIDIA and AMD GPUs. Experimental results are shown for a sparse direct solver based on multifrontal sparse LU decomposition applied to linear systems arising from the simulation, using finite element discretization on unstructured meshes, of a high frequency indefinite Maxwell problem.

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