{"paper_id":"2b4e99ce-2750-4dbd-8df3-81586fa6ae96","body_text":"Weighted Isogeometric Collocation based on Subdivision Surfaces | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Weighted Isogeometric Collocation based on Subdivision Surfaces Xiaomei Li, Hailun Xu, Hongmei Kang, Hongwei Lin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7523622/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract This paper explores the isogeometric collocation method based on subdivision surfaces. Subdivision basis functions offer high-order continuity within elements and smoothness across the entire domain, making them well-suited for isogeo-metric collocation in complex domains. The challenge in isogeometric collocation with subdivision surfaces lies in selecting an appropriate set of collocation points on irregular patches and imposing boundary conditions correctly to ensure consistency in computational accuracy with regular regions. This paper employs the weighted isogeometric collocation method by integrating boundary conditions and interior PDE equations in a weighted manner. Specifically, weights are assigned to each equation corresponding to each collocation point. For regular patches, face centroids are utilized, while each irregular patch is subdivided n times around extraordinary points, with a face centroid positioned within each subpatch. Using the weighted isogeometric collocation method, stable collocation solutions can be achieved. Numerical experiments demonstrate that the proposed isogeometric collocation method with modified Loop subdivision achieves the same convergence order as observed in regular regions, whereas the Loop subdivision fails to achieve it. Isogeometric analysis Isogeometric collocation method Subdivision surface Loop subdivision Modified Loop subdivision Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 24 Oct, 2025 Reviews received at journal 24 Oct, 2025 Reviews received at journal 24 Oct, 2025 Reviewers agreed at journal 25 Sep, 2025 Reviewers agreed at journal 23 Sep, 2025 Reviewers invited by journal 20 Sep, 2025 Editor assigned by journal 03 Sep, 2025 Submission checks completed at journal 03 Sep, 2025 First submitted to journal 03 Sep, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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