{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-high-order-fully-lagrangian-particle-level","title":"A high-order fully Lagrangian particle level-set method for dynamic surfaces","arxiv_id":"2306.07986","date":"2023-06-09","proceeding":null,"authors":["Lennart J. Schulze","Sachin K. T. Veettill","Ivo F. Sbalzarini"],"abstract":"We present a fully Lagrangian particle level-set method based on high-order polynomial regression. This enables closest-point redistancing without requiring a regular Cartesian mesh, relaxing the need for particle-mesh interpolation. Instead, we perform level-set redistancing directly on irregularly distributed particles by polynomial regression in a Newton-Lagrange basis on a set of unisolvent nodes. We demonstrate that the resulting particle closest-point (PCP) redistancing achieves high-order accuracy for 2D and 3D geometries discretized on highly irregular particle distributions and has better robustness against particle distortion than regression in a monomial basis. Further, we show convergence in a classic level-set benchmark case involving ill-conditioned particle distributions, and we present an application to an oscillating droplet simulation in multi-phase flow.","url_abs":"https://arxiv.org/abs/2306.07986v1","url_pdf":"https://arxiv.org/pdf/2306.07986v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-high-order-fully-lagrangian-particle-level","repo_url":"https://github.com/mosaic-group/openfpm_numerics","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}