Performance evaluation of mixed-precision Runge-Kutta methods for the solution of partial differential equations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915075084779520 |
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| author | Dravins, Ivo Koch, Marcel Griehl, Victoria Kormann, Katharina |
| author_facet | Dravins, Ivo Koch, Marcel Griehl, Victoria Kormann, Katharina |
| contents | This work focuses on the numerical study of a recently published class of Runge-Kutta methods designed for mixed-precision arithmetic. We employ the methods in solving partial differential equations on modern hardware. In particular we investigate what speedups are achievable by the use of mixed precision and the dependence of the methods algorithmic compatibility with the computational hardware. We use state-of-the-art software, utilizing the Ginkgo library, which is designed to incorporate mixed precision arithmetic, and perform numerical tests of 3D problems on both GPU and CPU architectures. We show that significant speedups can be achieved but that performance depends on solver parameters and performance of software kernels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16638 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Performance evaluation of mixed-precision Runge-Kutta methods for the solution of partial differential equations Dravins, Ivo Koch, Marcel Griehl, Victoria Kormann, Katharina Numerical Analysis Performance 65F10, 65L06, 65M12, 65M06 This work focuses on the numerical study of a recently published class of Runge-Kutta methods designed for mixed-precision arithmetic. We employ the methods in solving partial differential equations on modern hardware. In particular we investigate what speedups are achievable by the use of mixed precision and the dependence of the methods algorithmic compatibility with the computational hardware. We use state-of-the-art software, utilizing the Ginkgo library, which is designed to incorporate mixed precision arithmetic, and perform numerical tests of 3D problems on both GPU and CPU architectures. We show that significant speedups can be achieved but that performance depends on solver parameters and performance of software kernels. |
| title | Performance evaluation of mixed-precision Runge-Kutta methods for the solution of partial differential equations |
| topic | Numerical Analysis Performance 65F10, 65L06, 65M12, 65M06 |
| url | https://arxiv.org/abs/2412.16638 |