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

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

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.

• Jezik: Angleški jezik
• Ključne besede: meshless, advancing front algorithms, NURBS, B-splines, CAD, RBF-FD
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2024
• Št. strani: 22 str.
• Številčenje: Vol. 100, iss. 2, art. 51
• PID: 20.500.12556/RUL-159395
• UDK: 51
• ISSN pri članku: 1573-7691
• DOI: 10.1007/s10915-024-02597-z
• COBISS.SI-ID: 201006595
• Datum objave v RUL: 09.07.2024

Gradivo je del revije

• Naslov: Journal of scientific computing
• Skrajšan naslov: J. sci. comput.
• Založnik: Springer Nature
• ISSN: 1573-7691
• COBISS.SI-ID: 2707220

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: računalniško načrtovanje, računalniški algoritmi, parcialne diferencialne enačbe