Approximation and application of minimizing movements for surface PDE
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929487272214528 |
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| author | Ginder, Elliott Svadlenka, Karel Muramatsu, Takuma |
| author_facet | Ginder, Elliott Svadlenka, Karel Muramatsu, Takuma |
| contents | By employing the closest point method, we extend the applicability of minimizing movements to the surface PDE setting. The corresponding approximation methods are created, and their convergence is observed. The numerical methods are then used to develop threshold dynamics algorithms for surface-constrained interfacial motions. In particular, show how the minimizing movements enable one to approximate multiphase, volume-preserving, curvature flows on surfaces via generalized MBO and HMBO algorithms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_03139 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation and application of minimizing movements for surface PDE Ginder, Elliott Svadlenka, Karel Muramatsu, Takuma Numerical Analysis By employing the closest point method, we extend the applicability of minimizing movements to the surface PDE setting. The corresponding approximation methods are created, and their convergence is observed. The numerical methods are then used to develop threshold dynamics algorithms for surface-constrained interfacial motions. In particular, show how the minimizing movements enable one to approximate multiphase, volume-preserving, curvature flows on surfaces via generalized MBO and HMBO algorithms. |
| title | Approximation and application of minimizing movements for surface PDE |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2409.03139 |