{"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-hybrid-lagrangian-eulerian-method-for","title":"Lagrangian-Eulerian Multi-Density Topology Optimization with the Material Point Method","arxiv_id":"2003.01215","date":"2020-03-02","proceeding":null,"authors":["Yue Li","Xuan Li","Minchen Li","Yixin Zhu","Bo Zhu","Chenfanfu Jiang"],"abstract":"In this paper, a hybrid Lagrangian-Eulerian topology optimization (LETO) method is proposed to solve the elastic force equilibrium with the Material Point Method (MPM). LETO transfers density information from freely movable Lagrangian carrier particles to a fixed set of Eulerian quadrature points. This transfer is based on a smooth radial kernel involved in the compliance objective to avoid the artificial checkerboard pattern. The quadrature points act as MPM particles embedded in a lower-resolution grid and enable a sub-cell multi-density resolution of intricate structures with a reduced computational cost. A quadrature-level connectivity graph-based method is adopted to avoid the artificial checkerboard issues commonly existing in multi-resolution topology optimization methods. Numerical experiments are provided to demonstrate the efficacy of the proposed approach.","url_abs":"https://arxiv.org/abs/2003.01215v4","url_pdf":"https://arxiv.org/pdf/2003.01215v4.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-hybrid-lagrangian-eulerian-method-for","repo_url":"https://github.com/penn-graphics-research/LETO","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"a-hybrid-lagrangian-eulerian-method-for","repo_url":"https://github.com/xuan-li/LETO","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}