The need for accuracy and smoothness in numerical simulations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915052117819392 |
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| author | Mikkelsen, Carl Christian Kjelgaard López-Villellas, Lorién |
| author_facet | Mikkelsen, Carl Christian Kjelgaard López-Villellas, Lorién |
| contents | We consider the problem of estimating the error when solving a system of differential algebraic equations. Richardson extrapolation is a classical technique that can be used to judge when computational errors are irrelevant and estimate the discretization error. We have simulated molecular dynamics with constraints using the GROMACS library and found that the output is not always amenable to Richardson extrapolation. We derive and illustrate Richardson extrapolation using a variety of numerical experiments. We identify two necessary conditions that are not always satisfied by the GROMACS library. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08257 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The need for accuracy and smoothness in numerical simulations Mikkelsen, Carl Christian Kjelgaard López-Villellas, Lorién Numerical Analysis 65L70, 65L80, 65G99 We consider the problem of estimating the error when solving a system of differential algebraic equations. Richardson extrapolation is a classical technique that can be used to judge when computational errors are irrelevant and estimate the discretization error. We have simulated molecular dynamics with constraints using the GROMACS library and found that the output is not always amenable to Richardson extrapolation. We derive and illustrate Richardson extrapolation using a variety of numerical experiments. We identify two necessary conditions that are not always satisfied by the GROMACS library. |
| title | The need for accuracy and smoothness in numerical simulations |
| topic | Numerical Analysis 65L70, 65L80, 65G99 |
| url | https://arxiv.org/abs/2406.08257 |