{"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/scalable-adaptive-pde-solvers-in-arbitrary","title":"Scalable adaptive PDE solvers in arbitrary domains","arxiv_id":"2108.03757","date":"2021-08-08","proceeding":null,"authors":["Kumar Saurabh","Masado Ishii","Milinda Fernando","Boshun Gao","Kendrick Tan","Ming-Chen Hsu","Adarsh Krishnamurthy","Hari Sundar","Baskar Ganapathysubramanian"],"abstract":"Efficiently and accurately simulating partial differential equations (PDEs) in and around arbitrarily defined geometries, especially with high levels of adaptivity, has significant implications for different application domains. A key bottleneck in the above process is the fast construction of a `good' adaptively-refined mesh. In this work, we present an efficient novel octree-based adaptive discretization approach capable of carving out arbitrarily shaped void regions from the parent domain: an essential requirement for fluid simulations around complex objects. Carving out objects produces an $\\textit{incomplete}$ octree. We develop efficient top-down and bottom-up traversal methods to perform finite element computations on $\\textit{incomplete}$ octrees. We validate the framework by (a) showing appropriate convergence analysis and (b) computing the drag coefficient for flow past a sphere for a wide range of Reynolds numbers ($\\mathcal{O}(1-10^6)$) encompassing the drag crisis regime. Finally, we deploy the framework on a realistic geometry on a current project to evaluate COVID-19 transmission risk in classrooms.","url_abs":"https://arxiv.org/abs/2108.03757v1","url_pdf":"https://arxiv.org/pdf/2108.03757v1.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":"scalable-adaptive-pde-solvers-in-arbitrary","repo_url":"https://bitbucket.org/baskargroup/proteus","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}