Performance tuning of the Helmholtz matrix-vector product kernel in the computational fluid dynamics solver Nek5000/RS for the A64FX processor
Authors: 
Miwako Tsuji, Misun Min, Stefan Kerkemeier, Paul Fischer, Elia Merzari, Mitsuhisa SatoAuthors Info & Claims
Miwako Tsuji, Misun Min, Stefan Kerkemeier, Paul Fischer, Elia Merzari, Mitsuhisa SatoAuthors Info & ClaimsPages 49 - 59
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.
References
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Paul Fischer, Stefan Kerkemeier, Misun Min, Yu-Hsiang Lan, Malachi Phillips, Thilina Rathnayake, Elia Merzari, Ananias Tomboulides, Ali Karakus, Noel Chalmers, and Tim Warburton. 2021. NekRS, a GPU-Accelerated Spectral Element Navier-Stokes Solver. arXiv:arXiv:2104.05829
[2]
Paul Fischer, Misun Min, Thilina Rathnayake, Som Dutta, Tzanio Kolev, Veselin Dobrev, Jean-Sylvain Camier, Martin Kronbichler, Tim Warburton, Kasia Swirydowicz, and Jed Brown. 2020. Scalability of high-performance PDE solvers. Int. J. HPC App. 34, 5 (2020), 562–586.
[3]
Fujitsu Limited. 2021. A64FX Microarchtecture Manual. https://github.com/ fujitsu/A64FX/blob/master/doc/A64FX_Microarchitecture_Manual_en_1.6.pdf.
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Arm Limited. 2021. Arm A64 Instruction Set Architecture (version 2021-06). https://developer.arm.com/documentation/ddi0596/2021-06.
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David S Medina, Amik St-Cyr, and Timothy Warburton. 2014. OCCA: A unified approach to multi-threading languages. arXiv:arXiv:1403.0968
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NekBench. [n. d.]. A benchmark suite of Nek5000/RS. https://github.com/ Nek5000/nekBench.
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NekBench. [n. d.]. readme.md. https://github.com/Nek5000/nekBench/blob/master /axhelm/readme.md.
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Ryohei Okazaki, Takekazu Tabata, Sota Sakashita, Kenichi Kitamura, Noriko Takagi, Hideki Sakata, Takeshi Ishibashi, Takeo Nakamura, and Yuichiro Ajima. 2020. Supercomputer Fugaku CPU A64FX Realizing High Performance, High-Density Packaging, and Low Power Consumption. Technical Report Fujitsu technical review.
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Mitsuhisa Sato, Yutaka Ishikawa, Hirofumi Tomita, Yuetsu Kodama, Tetsuya Odajima, Miwako Tsuji, Hisashi Yashiro, Masaki Aoki, Naoyuki Shida, Ikuo Miyoshi, Kouichi Hirai, Atsushi Furuya, Akira Asato, Kuniki Morita, and Toshiyuki Shimizu. 2020. Co-Design for A64FX Manycore Processor and Fugaku. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (SC20). Article 47, 15 pages.
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- 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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Published In
January 2022
83 pages
ISBN:9781450395649
DOI:10.1145/3503470
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© 2022 Association for Computing Machinery. ACM acknowledges that this contribution was authored or co-authored by an employee, contractor or affiliate of the United States government. As such, the United States Government retains a nonexclusive, royalty-free right to publish or reproduce this article, or to allow others to do so, for Government purposes only.
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Association for Computing Machinery
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Published: 13 January 2022
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- U.S. Department of Energy, Office of Science
- Exascale Computing Project
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HPCAsia 2022 Workshop
HPCAsia 2022 Workshop: International Conference on High Performance Computing in Asia-Pacific Region Workshops
January 11 - 14, 2022
Virtual Event, Japan
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Overall Acceptance Rate 69 of 143 submissions, 48%
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