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

TitleAddressing Irregular Patterns of Matrix Computations on GPUs and Their Impact on Applications Powered by Sparse Direct Solvers
Publication TypeConference Proceedings
Year of Publication2022
AuthorsAbdelfattah, A.., P.. Ghysels, W.. Boukaram, S.. Tomov, X.. Li, and J.. Dongarra
Conference Name2022 SC22: International Conference for High Performance Computing, Networking, Storage and Analysis (SC) (SC)
Pagination354-367
Date Published2022-11
PublisherIEEE Computer Society
Conference LocationLos Alamitos, CA, USA
KeywordsGPU computing, irregular computational workloads, lu factorization, multifrontal solvers, sparse direct solvers
Abstract

Many 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 their application to accelerate sparse direct solvers. We design 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 direct LU solvers using NVIDIA and AMD GPUs. Experimental results are shown for a sparse direct solver based on a 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.

URLhttps://doi.ieeecomputersociety.org/
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