Discretization of non-uniform rational B-spline (NURBS) models for meshless isogeometric analysis

Duh, Urban (author), Shankar, Varun (author), Kosec, Gregor (author)

We present an algorithm for fast generation of quasi-uniform and variable-spacing nodes on domains whose boundaries are represented as computer-aided design (CAD) models, more specifically non-uniform rational B-splines (NURBS). This new algorithm enables the solution of partial differential equations within the volumes enclosed by these CAD models using (collocation-based) meshless numerical discretizations. Our hierarchical algorithm first generates quasi-uniform node sets directly on the NURBS surfaces representing the domain boundary, then uses the NURBS representation in conjunction with the surface nodes to generate nodes within the volume enclosed by the NURBS surface. We provide evidence for the quality of these node sets by analyzing them in terms of local regularity and separation distances. Finally, we demonstrate that these node sets are well-suited (both in terms of accuracy and numerical stability) for meshless radial basis function generated finite differences discretizations of the Poisson, Navier-Cauchy, and heat equations. Our algorithm constitutes an important step in bridging the field of node generation for meshless discretizations with isogeometric analysis.

• Language: English
• Keywords: meshless, advancing front algorithms, NURBS, B-splines, CAD, RBF-FD
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 22 str.
• Numbering: Vol. 100, iss. 2, art. 51
• PID: 20.500.12556/RUL-159395
• UDC: 51
• ISSN on article: 1573-7691
• DOI: 10.1007/s10915-024-02597-z
• COBISS.SI-ID: 201006595
• Publication date in RUL: 09.07.2024

Record is a part of a journal

• Title: Journal of scientific computing
• Shortened title: J. sci. comput.
• Publisher: Springer Nature
• ISSN: 1573-7691
• COBISS.SI-ID: 2707220

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: računalniško načrtovanje, računalniški algoritmi, parcialne diferencialne enačbe