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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.09939 |
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| _version_ | 1866914256133292032 |
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| author | He, Jinjin Zhang, Taiyuan Li, Zhiqi Zhou, Junwei Chen, Duowen Zhu, Bo |
| author_facet | He, Jinjin Zhang, Taiyuan Li, Zhiqi Zhou, Junwei Chen, Duowen Zhu, Bo |
| contents | This paper introduces a Particle Flow Map Level Set (PFM-LS) method for high-fidelity interface tracking. We store level-set values, gradients, and Hessians on particles concentrated in a narrow band around the interface, advecting them via bidirectional flow maps while using a conventional grid-based representation elsewhere. By interpreting the level set value as a 3-form and its gradient as a 1-form, PFM-LS achieves exceptional geometric fidelity during complex deformations and preserves sub-grid features that traditional methods cannot capture. Our dual-timescale approach utilizes long-range maps for values and gradients, with frequent reinitialization of short-range maps for the distortion-sensitive Hessian, alongside adaptive particle control that maintains sufficient density within the narrow band. We also develop a hybrid particle-grid quasi-Newton redistancing scheme that preserves fine-scale features while enforcing the signed-distance property. Benchmark comparisons in 2D and 3D demonstrate that PFM-LS achieves state-of-the-art volume preservation and shape fidelity against a broad range of existing level-set methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09939 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Level Set Method on Particle Flow Maps He, Jinjin Zhang, Taiyuan Li, Zhiqi Zhou, Junwei Chen, Duowen Zhu, Bo Computational Physics Numerical Analysis This paper introduces a Particle Flow Map Level Set (PFM-LS) method for high-fidelity interface tracking. We store level-set values, gradients, and Hessians on particles concentrated in a narrow band around the interface, advecting them via bidirectional flow maps while using a conventional grid-based representation elsewhere. By interpreting the level set value as a 3-form and its gradient as a 1-form, PFM-LS achieves exceptional geometric fidelity during complex deformations and preserves sub-grid features that traditional methods cannot capture. Our dual-timescale approach utilizes long-range maps for values and gradients, with frequent reinitialization of short-range maps for the distortion-sensitive Hessian, alongside adaptive particle control that maintains sufficient density within the narrow band. We also develop a hybrid particle-grid quasi-Newton redistancing scheme that preserves fine-scale features while enforcing the signed-distance property. Benchmark comparisons in 2D and 3D demonstrate that PFM-LS achieves state-of-the-art volume preservation and shape fidelity against a broad range of existing level-set methods. |
| title | A Level Set Method on Particle Flow Maps |
| topic | Computational Physics Numerical Analysis |
| url | https://arxiv.org/abs/2601.09939 |