Convergence of a semi-explicit scheme for a one dimensional periodic nonlocal eikonal equation modeling dislocation dynamics
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915378671648768 |
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| author | Zareef, Diana Al Hajj, Ahmad El Ibrahim, Hassan Zurek, Antoine |
| author_facet | Zareef, Diana Al Hajj, Ahmad El Ibrahim, Hassan Zurek, Antoine |
| contents | In this paper, we derive a periodic model from a one dimensional nonlocal eikonal equation set on the full space modeling dislocation dynamics. Thanks to a gradient entropy estimate, we show that this periodic model converges toward the initial one when the period goes to infinity. Moreover, we design a semi-explicit numerical scheme for the periodic model that we introduce. We show the well-posedness of the scheme and a discrete gradient entropy inequality. We also prove the convergence of the scheme and we present some numerical experiments. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_18428 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence of a semi-explicit scheme for a one dimensional periodic nonlocal eikonal equation modeling dislocation dynamics Zareef, Diana Al Hajj, Ahmad El Ibrahim, Hassan Zurek, Antoine Numerical Analysis 35F20, 35F21, 70H20, 65M12, 65M06 In this paper, we derive a periodic model from a one dimensional nonlocal eikonal equation set on the full space modeling dislocation dynamics. Thanks to a gradient entropy estimate, we show that this periodic model converges toward the initial one when the period goes to infinity. Moreover, we design a semi-explicit numerical scheme for the periodic model that we introduce. We show the well-posedness of the scheme and a discrete gradient entropy inequality. We also prove the convergence of the scheme and we present some numerical experiments. |
| title | Convergence of a semi-explicit scheme for a one dimensional periodic nonlocal eikonal equation modeling dislocation dynamics |
| topic | Numerical Analysis 35F20, 35F21, 70H20, 65M12, 65M06 |
| url | https://arxiv.org/abs/2501.18428 |