The Closest Point Method for Surface PDEs with General Boundary Conditions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915632550772736 |
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| author | Wong, Tony Macdonald, Colin B. Lee, Byungjoon |
| author_facet | Wong, Tony Macdonald, Colin B. Lee, Byungjoon |
| contents | We generalize the closest point method (CPM) to solve surface partial differential equations with general boundary conditions. The proposed extrapolation method provides a unified framework for treating a broad class of inhomogeneous Neumann and Robin boundary conditions within the framework of CPM. The accuracy and robustness of the method are demonstrated through numerical convergence studies of an elliptic problem, Steklov eigenvalue problems, and a nonlinear reaction-diffusion system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17820 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Closest Point Method for Surface PDEs with General Boundary Conditions Wong, Tony Macdonald, Colin B. Lee, Byungjoon Numerical Analysis 58J05, 65M06, 65M20, 65N06, 65N40, 65D18 We generalize the closest point method (CPM) to solve surface partial differential equations with general boundary conditions. The proposed extrapolation method provides a unified framework for treating a broad class of inhomogeneous Neumann and Robin boundary conditions within the framework of CPM. The accuracy and robustness of the method are demonstrated through numerical convergence studies of an elliptic problem, Steklov eigenvalue problems, and a nonlinear reaction-diffusion system. |
| title | The Closest Point Method for Surface PDEs with General Boundary Conditions |
| topic | Numerical Analysis 58J05, 65M06, 65M20, 65N06, 65N40, 65D18 |
| url | https://arxiv.org/abs/2511.17820 |