Low-Order Finite Element Solver with Small Matrix-Matrix Multiplication Accelerated by AI-Specific Hardware for Crustal Deformation Computation

Takuma Yamaguchi; Kohei Fujita; Tsuyoshi Ichimura; Akira Naruse; Jack C. Wells; Christopher J. Zimmer; Tjerk P. Straatsma; Muneo Hori; Lalith Maddegedara; Naonori Ueda

doi:10.1145/3394277.3401860

Low-Order Finite Element Solver with Small Matrix-Matrix Multiplication Accelerated by AI-Specific Hardware for Crustal Deformation Computation

Takuma Yamaguchi, Kohei Fujita, Tsuyoshi Ichimura, Akira Naruse, Jack C. Wells, Christopher J. Zimmer, Tjerk P. Straatsma, Muneo Hori, Lalith Maddegedara, Naonori Ueda

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

5 Scopus citations

Abstract

This study proposes a fast low-order finite element solver for crustal deformation computations by applying Tensor Core, AI-specific hardware on a Volta GPU. Tensor Core can compute large matrix-matrix multiplications rapidly in half precision. We redesign a state-of-the-art solver algorithm so that lower-precision data types can be used and memory access costs can be reduced even when we use small matrices. With the proposed solver, we solved 13 billion degrees-of-freedom two-layered problems that mimicked the Earth's crust and mantle using 36 compute nodes of Summit. In the matrix-vector kernel, we obtained a 4.1-fold speedup over a standard kernel in a single-precision format. Our proposed solver increased the FLOP count of the entire solver; however, we reduced the time-to-solution by 1.7-fold since the Tensor Core provided a high effective performance.

Original language	English
Title of host publication	Proceedings of the Platform for Advanced Scientific Computing Conference, PASC 2020
Publisher	Association for Computing Machinery
ISBN (Electronic)	9781450379939
DOIs	https://doi.org/10.1145/3394277.3401860
State	Published - Jun 29 2020
Event	7th Annual Platform for Advanced Scientific Computing Conference, PASC 2020 - Geneva, Switzerland Duration: Jun 29 2020 → Jul 1 2020

Publication series

Name	Proceedings of the Platform for Advanced Scientific Computing Conference, PASC 2020

Conference

Conference	7th Annual Platform for Advanced Scientific Computing Conference, PASC 2020
Country/Territory	Switzerland
City	Geneva
Period	06/29/20 → 07/1/20

Funding

Our results were obtained using the Summit at Oak Ridge Leadership Computing Facility, a US Department of Energy, Office of Science User Facility at Oak Ridge National Laboratory (ORNL). We thank Yukihiko Hirano (NVIDIA) for coordination of the collaborative research project. We thank Christopher B. Fuson, Don E. Maxwell, Oscar Hernandez, Scott Atchley, Veronica Melesse-Vergara (ORNL), Jeff Larkin, Stephen Abbott (NVIDIA), Lixiang Luo (IBM), Richard Graham (Mellanox Technologies) for generous support concerning use of Summit. We thank Noda Tomoyuki and Hikaru Inoue (Fujitsu Limited) for support in program development. We acknowledge support from Japan Society for the Promotion of Science (18H05239 and 18K18873).

Keywords

Conjugate gradient method
Finite element analysis
GPU computation
Transprecision computing

Access to Document

10.1145/3394277.3401860

Cite this

Yamaguchi, T., Fujita, K., Ichimura, T., Naruse, A., Wells, J. C., Zimmer, C. J., Straatsma, T. P., Hori, M., Maddegedara, L., & Ueda, N. (2020). Low-Order Finite Element Solver with Small Matrix-Matrix Multiplication Accelerated by AI-Specific Hardware for Crustal Deformation Computation. In Proceedings of the Platform for Advanced Scientific Computing Conference, PASC 2020 (Proceedings of the Platform for Advanced Scientific Computing Conference, PASC 2020). Association for Computing Machinery. https://doi.org/10.1145/3394277.3401860

Yamaguchi, Takuma ; Fujita, Kohei ; Ichimura, Tsuyoshi et al. / Low-Order Finite Element Solver with Small Matrix-Matrix Multiplication Accelerated by AI-Specific Hardware for Crustal Deformation Computation. Proceedings of the Platform for Advanced Scientific Computing Conference, PASC 2020. Association for Computing Machinery, 2020. (Proceedings of the Platform for Advanced Scientific Computing Conference, PASC 2020).

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abstract = "This study proposes a fast low-order finite element solver for crustal deformation computations by applying Tensor Core, AI-specific hardware on a Volta GPU. Tensor Core can compute large matrix-matrix multiplications rapidly in half precision. We redesign a state-of-the-art solver algorithm so that lower-precision data types can be used and memory access costs can be reduced even when we use small matrices. With the proposed solver, we solved 13 billion degrees-of-freedom two-layered problems that mimicked the Earth's crust and mantle using 36 compute nodes of Summit. In the matrix-vector kernel, we obtained a 4.1-fold speedup over a standard kernel in a single-precision format. Our proposed solver increased the FLOP count of the entire solver; however, we reduced the time-to-solution by 1.7-fold since the Tensor Core provided a high effective performance.",

keywords = "Conjugate gradient method, Finite element analysis, GPU computation, Transprecision computing",

author = "Takuma Yamaguchi and Kohei Fujita and Tsuyoshi Ichimura and Akira Naruse and Wells, {Jack C.} and Zimmer, {Christopher J.} and Straatsma, {Tjerk P.} and Muneo Hori and Lalith Maddegedara and Naonori Ueda",

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Yamaguchi, T, Fujita, K, Ichimura, T, Naruse, A, Wells, JC, Zimmer, CJ , Straatsma, TP, Hori, M, Maddegedara, L & Ueda, N 2020, Low-Order Finite Element Solver with Small Matrix-Matrix Multiplication Accelerated by AI-Specific Hardware for Crustal Deformation Computation. in Proceedings of the Platform for Advanced Scientific Computing Conference, PASC 2020. Proceedings of the Platform for Advanced Scientific Computing Conference, PASC 2020, Association for Computing Machinery, 7th Annual Platform for Advanced Scientific Computing Conference, PASC 2020, Geneva, Switzerland, 06/29/20. https://doi.org/10.1145/3394277.3401860

Low-Order Finite Element Solver with Small Matrix-Matrix Multiplication Accelerated by AI-Specific Hardware for Crustal Deformation Computation. / Yamaguchi, Takuma; Fujita, Kohei; Ichimura, Tsuyoshi et al.
Proceedings of the Platform for Advanced Scientific Computing Conference, PASC 2020. Association for Computing Machinery, 2020. (Proceedings of the Platform for Advanced Scientific Computing Conference, PASC 2020).

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

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AU - Naruse, Akira

AU - Wells, Jack C.

AU - Zimmer, Christopher J.

AU - Straatsma, Tjerk P.

AU - Hori, Muneo

AU - Maddegedara, Lalith

AU - Ueda, Naonori

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AB - This study proposes a fast low-order finite element solver for crustal deformation computations by applying Tensor Core, AI-specific hardware on a Volta GPU. Tensor Core can compute large matrix-matrix multiplications rapidly in half precision. We redesign a state-of-the-art solver algorithm so that lower-precision data types can be used and memory access costs can be reduced even when we use small matrices. With the proposed solver, we solved 13 billion degrees-of-freedom two-layered problems that mimicked the Earth's crust and mantle using 36 compute nodes of Summit. In the matrix-vector kernel, we obtained a 4.1-fold speedup over a standard kernel in a single-precision format. Our proposed solver increased the FLOP count of the entire solver; however, we reduced the time-to-solution by 1.7-fold since the Tensor Core provided a high effective performance.

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Yamaguchi T, Fujita K, Ichimura T, Naruse A, Wells JC, Zimmer CJ et al. Low-Order Finite Element Solver with Small Matrix-Matrix Multiplication Accelerated by AI-Specific Hardware for Crustal Deformation Computation. In Proceedings of the Platform for Advanced Scientific Computing Conference, PASC 2020. Association for Computing Machinery. 2020. (Proceedings of the Platform for Advanced Scientific Computing Conference, PASC 2020). doi: 10.1145/3394277.3401860

Low-Order Finite Element Solver with Small Matrix-Matrix Multiplication Accelerated by AI-Specific Hardware for Crustal Deformation Computation

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