Performance tuning of the Helmholtz matrix-vector product kernel in the computational fluid dynamics solver Nek5000/RS for the A64FX processor

Miwako Tsuji; Misun Min; Stefan Kerkemeier; Paul Fischer; Elia Merzari; Mitsuhisa Sato

doi:10.1145/3503470.3503476

Performance tuning of the Helmholtz matrix-vector product kernel in the computational fluid dynamics solver Nek5000/RS for the A64FX processor

Miwako Tsuji, Misun Min, Stefan Kerkemeier, Paul Fischer, Elia Merzari, Mitsuhisa Sato

Ken and Mary Alice Lindquist Department of Nuclear Engineering

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

1 Scopus citations

Abstract

Nek5000/RS is an open source computational fluid dynamics solver based on the spectral element method. One of the important kernel of the Nek5000/RS is called "axhelm", which computes the Helmholtz matrix-vector product. In this paper, we have evaluated the axhelm kernel on the A64FX processor for the simplest case of polynomial degree N = 7. We have optimized the kernel for the A64FX processor by using well known optimization techniques such as SIMDization, software pipelining, continuous access enhancing, and software prefetch. We also provide the performance analysis data to investigate the effects of the optimization techniques to help understanding the A64FX processor and the Fujitsu compiler.

Original language	English (US)
Title of host publication	Proceedings of International Conference on High Performance Computing in Asia-Pacific Region Workshops, HPCAsia 2022
Publisher	Association for Computing Machinery
Pages	49-59
Number of pages	11
ISBN (Electronic)	9781450395649
DOIs	https://doi.org/10.1145/3503470.3503476
State	Published - Jan 11 2022
Event	2022 International Conference on High Performance Computing in Asia-Pacific Region Workshops, HPCAsia 2022 - Virtual, Online, Japan Duration: Jan 11 2022 → Jan 14 2022

Publication series

Name	ACM International Conference Proceeding Series

Conference

Conference	2022 International Conference on High Performance Computing in Asia-Pacific Region Workshops, HPCAsia 2022
Country/Territory	Japan
City	Virtual, Online
Period	1/11/22 → 1/14/22

All Science Journal Classification (ASJC) codes

Software
Human-Computer Interaction
Computer Vision and Pattern Recognition
Computer Networks and Communications

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10.1145/3503470.3503476

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Tsuji, M., Min, M., Kerkemeier, S., Fischer, P., Merzari, E., & Sato, M. (2022). Performance tuning of the Helmholtz matrix-vector product kernel in the computational fluid dynamics solver Nek5000/RS for the A64FX processor. In Proceedings of International Conference on High Performance Computing in Asia-Pacific Region Workshops, HPCAsia 2022 (pp. 49-59). (ACM International Conference Proceeding Series). Association for Computing Machinery. https://doi.org/10.1145/3503470.3503476

Tsuji, Miwako ; Min, Misun ; Kerkemeier, Stefan et al. / Performance tuning of the Helmholtz matrix-vector product kernel in the computational fluid dynamics solver Nek5000/RS for the A64FX processor. Proceedings of International Conference on High Performance Computing in Asia-Pacific Region Workshops, HPCAsia 2022. Association for Computing Machinery, 2022. pp. 49-59 (ACM International Conference Proceeding Series).

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title = "Performance tuning of the Helmholtz matrix-vector product kernel in the computational fluid dynamics solver Nek5000/RS for the A64FX processor",

abstract = "Nek5000/RS is an open source computational fluid dynamics solver based on the spectral element method. One of the important kernel of the Nek5000/RS is called {"}axhelm{"}, which computes the Helmholtz matrix-vector product. In this paper, we have evaluated the axhelm kernel on the A64FX processor for the simplest case of polynomial degree N = 7. We have optimized the kernel for the A64FX processor by using well known optimization techniques such as SIMDization, software pipelining, continuous access enhancing, and software prefetch. We also provide the performance analysis data to investigate the effects of the optimization techniques to help understanding the A64FX processor and the Fujitsu compiler.",

author = "Miwako Tsuji and Misun Min and Stefan Kerkemeier and Paul Fischer and Elia Merzari and Mitsuhisa Sato",

note = "Funding Information: This research used computational resources of the supercomputer Fugaku provided by the RIKEN Center for Computational Science. This research is partially supported by the U.S. Department of Energy, Office of Science, under contract DE-AC02-06CH11357 and by the Exascale Computing Project (17-SC-20-SC). Publisher Copyright: {\textcopyright} 2022 ACM.; 2022 International Conference on High Performance Computing in Asia-Pacific Region Workshops, HPCAsia 2022 ; Conference date: 11-01-2022 Through 14-01-2022",

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doi = "10.1145/3503470.3503476",

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Tsuji, M, Min, M, Kerkemeier, S, Fischer, P, Merzari, E & Sato, M 2022, Performance tuning of the Helmholtz matrix-vector product kernel in the computational fluid dynamics solver Nek5000/RS for the A64FX processor. in Proceedings of International Conference on High Performance Computing in Asia-Pacific Region Workshops, HPCAsia 2022. ACM International Conference Proceeding Series, Association for Computing Machinery, pp. 49-59, 2022 International Conference on High Performance Computing in Asia-Pacific Region Workshops, HPCAsia 2022, Virtual, Online, Japan, 1/11/22. https://doi.org/10.1145/3503470.3503476

Performance tuning of the Helmholtz matrix-vector product kernel in the computational fluid dynamics solver Nek5000/RS for the A64FX processor. / Tsuji, Miwako; Min, Misun; Kerkemeier, Stefan et al.
Proceedings of International Conference on High Performance Computing in Asia-Pacific Region Workshops, HPCAsia 2022. Association for Computing Machinery, 2022. p. 49-59 (ACM International Conference Proceeding Series).

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

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AU - Merzari, Elia

AU - Sato, Mitsuhisa

N1 - Funding Information: This research used computational resources of the supercomputer Fugaku provided by the RIKEN Center for Computational Science. This research is partially supported by the U.S. Department of Energy, Office of Science, under contract DE-AC02-06CH11357 and by the Exascale Computing Project (17-SC-20-SC). Publisher Copyright: © 2022 ACM.

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AB - Nek5000/RS is an open source computational fluid dynamics solver based on the spectral element method. One of the important kernel of the Nek5000/RS is called "axhelm", which computes the Helmholtz matrix-vector product. In this paper, we have evaluated the axhelm kernel on the A64FX processor for the simplest case of polynomial degree N = 7. We have optimized the kernel for the A64FX processor by using well known optimization techniques such as SIMDization, software pipelining, continuous access enhancing, and software prefetch. We also provide the performance analysis data to investigate the effects of the optimization techniques to help understanding the A64FX processor and the Fujitsu compiler.

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Tsuji M, Min M, Kerkemeier S, Fischer P, Merzari E, Sato M. Performance tuning of the Helmholtz matrix-vector product kernel in the computational fluid dynamics solver Nek5000/RS for the A64FX processor. In Proceedings of International Conference on High Performance Computing in Asia-Pacific Region Workshops, HPCAsia 2022. Association for Computing Machinery. 2022. p. 49-59. (ACM International Conference Proceeding Series). doi: 10.1145/3503470.3503476

Performance tuning of the Helmholtz matrix-vector product kernel in the computational fluid dynamics solver Nek5000/RS for the A64FX processor

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