Multiprecision computations with Schwarz methods
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918149643829248 |
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| author | Outrata, Michal Szyld, Daniel B. |
| author_facet | Outrata, Michal Szyld, Daniel B. |
| contents | We explore and analyze the use of multiprecision arithmetic for several classes of Schwarz methods and preconditioners, where the approximate solution of the local problems is performed at a lower precision, i.e., with fewer digits of accuracy than in the underlying (double precision) computation. Conditions for the appropriate round-off criteria for the lower precision are presented. It is found experimentally that for the model problems about 5 digits of accuracy are sufficient to achieve the theoretical restrictions, and thus, single precision suffices for the local solves. Several numerical experiments illustrate the obtained results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20937 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiprecision computations with Schwarz methods Outrata, Michal Szyld, Daniel B. Numerical Analysis 65F10, 65F08, 65Y99, 65Y99 We explore and analyze the use of multiprecision arithmetic for several classes of Schwarz methods and preconditioners, where the approximate solution of the local problems is performed at a lower precision, i.e., with fewer digits of accuracy than in the underlying (double precision) computation. Conditions for the appropriate round-off criteria for the lower precision are presented. It is found experimentally that for the model problems about 5 digits of accuracy are sufficient to achieve the theoretical restrictions, and thus, single precision suffices for the local solves. Several numerical experiments illustrate the obtained results. |
| title | Multiprecision computations with Schwarz methods |
| topic | Numerical Analysis 65F10, 65F08, 65Y99, 65Y99 |
| url | https://arxiv.org/abs/2509.20937 |