GPU-based LU Factorization and Solve on Batches of Matrices with Band Structure

Ahmad Abdelfattah; Stanimire Tomov; Piotr Luszczek; Hartwig Anzt; Jack Dongarra

doi:10.1145/3624062.3624247

GPU-based LU Factorization and Solve on Batches of Matrices with Band Structure

Ahmad Abdelfattah
, Stanimire Tomov
, Piotr Luszczek
, Hartwig Anzt
, Jack Dongarra

Computer Science and Mathematics Div

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

This paper presents a portable and performance-efficient approach to solve a batch of linear systems of equations using Graphics Processing Units (GPUs). Each system is represented using a special type of matrices with a band structure above and/or below the diagonal. Each matrix is factorized using an LU factorization with partial pivoting for numerical stability. Subsequently, the factors are used to find the solution for as many right hand sides as needed. The width of the band is often small enough that performing a fully dense LU factorization results in poor performance. We follow the standard LAPACK specifications for addressing this type of problems and develop a dedicated solver that runs efficiently on GPUs. No similar solver is currently available in the vendor's software stack, so performance results are shown on both NVIDIA and AMD GPUs relative to a parallel CPU solution utilizing OpenMP for thread-level parallelization.

Original language	English
Title of host publication	Proceedings of 2023 SC Workshops of the International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023
Publisher	Association for Computing Machinery
Pages	1672-1679
Number of pages	8
ISBN (Electronic)	9798400707858
DOIs	https://doi.org/10.1145/3624062.3624247
State	Published - Nov 12 2023
Event	2023 International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023 - Denver, United States Duration: Nov 12 2023 → Nov 17 2023

Publication series

Name	ACM International Conference Proceeding Series

Conference

Conference	2023 International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023
Country/Territory	United States
City	Denver
Period	11/12/23 → 11/17/23

Funding

This research is supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration.

Keywords

Band matrix
GPU computing
LU factorization
batch solvers
performance portability

Access to Document

10.1145/3624062.3624247

Cite this

Abdelfattah, A., Tomov, S., Luszczek, P., Anzt, H., & Dongarra, J. (2023). GPU-based LU Factorization and Solve on Batches of Matrices with Band Structure. In Proceedings of 2023 SC Workshops of the International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023 (pp. 1672-1679). (ACM International Conference Proceeding Series). Association for Computing Machinery. https://doi.org/10.1145/3624062.3624247

Abdelfattah, Ahmad ; Tomov, Stanimire ; Luszczek, Piotr et al. / GPU-based LU Factorization and Solve on Batches of Matrices with Band Structure. Proceedings of 2023 SC Workshops of the International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023. Association for Computing Machinery, 2023. pp. 1672-1679 (ACM International Conference Proceeding Series).

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title = "GPU-based LU Factorization and Solve on Batches of Matrices with Band Structure",

abstract = "This paper presents a portable and performance-efficient approach to solve a batch of linear systems of equations using Graphics Processing Units (GPUs). Each system is represented using a special type of matrices with a band structure above and/or below the diagonal. Each matrix is factorized using an LU factorization with partial pivoting for numerical stability. Subsequently, the factors are used to find the solution for as many right hand sides as needed. The width of the band is often small enough that performing a fully dense LU factorization results in poor performance. We follow the standard LAPACK specifications for addressing this type of problems and develop a dedicated solver that runs efficiently on GPUs. No similar solver is currently available in the vendor's software stack, so performance results are shown on both NVIDIA and AMD GPUs relative to a parallel CPU solution utilizing OpenMP for thread-level parallelization.",

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Abdelfattah, A, Tomov, S, Luszczek, P, Anzt, H & Dongarra, J 2023, GPU-based LU Factorization and Solve on Batches of Matrices with Band Structure. in Proceedings of 2023 SC Workshops of the International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023. ACM International Conference Proceeding Series, Association for Computing Machinery, pp. 1672-1679, 2023 International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023, Denver, United States, 11/12/23. https://doi.org/10.1145/3624062.3624247

GPU-based LU Factorization and Solve on Batches of Matrices with Band Structure. / Abdelfattah, Ahmad; Tomov, Stanimire; Luszczek, Piotr et al.
Proceedings of 2023 SC Workshops of the International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023. Association for Computing Machinery, 2023. p. 1672-1679 (ACM International Conference Proceeding Series).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - This paper presents a portable and performance-efficient approach to solve a batch of linear systems of equations using Graphics Processing Units (GPUs). Each system is represented using a special type of matrices with a band structure above and/or below the diagonal. Each matrix is factorized using an LU factorization with partial pivoting for numerical stability. Subsequently, the factors are used to find the solution for as many right hand sides as needed. The width of the band is often small enough that performing a fully dense LU factorization results in poor performance. We follow the standard LAPACK specifications for addressing this type of problems and develop a dedicated solver that runs efficiently on GPUs. No similar solver is currently available in the vendor's software stack, so performance results are shown on both NVIDIA and AMD GPUs relative to a parallel CPU solution utilizing OpenMP for thread-level parallelization.

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Abdelfattah A, Tomov S, Luszczek P, Anzt H, Dongarra J. GPU-based LU Factorization and Solve on Batches of Matrices with Band Structure. In Proceedings of 2023 SC Workshops of the International Conference on High Performance Computing, Network, Storage, and Analysis, SC Workshops 2023. Association for Computing Machinery. 2023. p. 1672-1679. (ACM International Conference Proceeding Series). doi: 10.1145/3624062.3624247

GPU-based LU Factorization and Solve on Batches of Matrices with Band Structure

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