dorsal/arxiv
View SchemaA Level Set Method on Particle Flow Maps
| Authors | Jinjin He, Taiyuan Zhang, Zhiqi Li, Junwei Zhou, Duowen Chen, Bo Zhu |
|---|---|
| Categories | |
| ArXiv ID | 2601.09939vv1 |
| URL | https://arxiv.org/abs/2601.09939 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
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.
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"abstract": "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.",
"arxiv_id": "2601.09939",
"authors": [
"Jinjin He",
"Taiyuan Zhang",
"Zhiqi Li",
"Junwei Zhou",
"Duowen Chen",
"Bo Zhu"
],
"categories": [
"physics.comp-ph",
"cs.NA",
"math.NA"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "A Level Set Method on Particle Flow Maps",
"url": "https://arxiv.org/abs/2601.09939",
"version": "v1"
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