Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.17830 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918067451199488 |
|---|---|
| author | Bachari, Amina El Rannou, Johann Yastrebov, Vladislav A. Kerfriden, Pierre Claus, Susanne |
| author_facet | Bachari, Amina El Rannou, Johann Yastrebov, Vladislav A. Kerfriden, Pierre Claus, Susanne |
| contents | In this article, we introduce a finite element method designed for the robust computation of approximate signed distance functions to arbitrary boundaries in two and three dimensions. Our method employs a novel prediction-correction approach, involving first the solution of a linear diffusion-based prediction problem, followed by a nonlinear minimization-based correction problem associated with the Eikonal equation. The prediction step efficiently generates a suitable initial guess, significantly facilitating convergence of the nonlinear correction step. A key strength of our approach is its ability to handle complex interfaces and initial level set functions with arbitrary steep or flat regions, a notable challenge for existing techniques. Through several representative examples, including classical geometries and more complex shapes such as star domains and three-dimensional tori, we demonstrate the accuracy, efficiency, and robustness of the method, validating its broad applicability for reinitializing diverse level set functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17830 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A predictor-corrector scheme for approximating signed distances using finite element methods Bachari, Amina El Rannou, Johann Yastrebov, Vladislav A. Kerfriden, Pierre Claus, Susanne Computational Engineering, Finance, and Science In this article, we introduce a finite element method designed for the robust computation of approximate signed distance functions to arbitrary boundaries in two and three dimensions. Our method employs a novel prediction-correction approach, involving first the solution of a linear diffusion-based prediction problem, followed by a nonlinear minimization-based correction problem associated with the Eikonal equation. The prediction step efficiently generates a suitable initial guess, significantly facilitating convergence of the nonlinear correction step. A key strength of our approach is its ability to handle complex interfaces and initial level set functions with arbitrary steep or flat regions, a notable challenge for existing techniques. Through several representative examples, including classical geometries and more complex shapes such as star domains and three-dimensional tori, we demonstrate the accuracy, efficiency, and robustness of the method, validating its broad applicability for reinitializing diverse level set functions. |
| title | A predictor-corrector scheme for approximating signed distances using finite element methods |
| topic | Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2506.17830 |