Numerical integration over 2D NURBS-shaped domains with applications to NURBS-enhanced FEM
This paper focuses on the numerical integration of polynomial functions along non-uniform rational B-splines (NURBS) curves and over 2D NURBS-shaped domains, i.e. domains with NURBS boundaries. The integration of the constant function f=1 is of special interest in computer aided design software and...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/117187 |
| Acceso en línea: | https://hdl.handle.net/2117/117187 https://dx.doi.org/10.1016/j.finel.2011.05.011 |
| Access Level: | acceso abierto |
| Palabra clave: | Numerical analysis Computing Methodologies Numerical integration NURBS NURBS-enhanced finite element method Gauss–Legendre Composite rule Anàlisi numèrica Informàtica Classificació AMS::65 Numerical analysis::65Y Computer aspects of numerical algorithms Classificació AMS::68 Computer science::68U Computing methodologies and applications Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica |
| Sumario: | This paper focuses on the numerical integration of polynomial functions along non-uniform rational B-splines (NURBS) curves and over 2D NURBS-shaped domains, i.e. domains with NURBS boundaries. The integration of the constant function f=1 is of special interest in computer aided design software and the integration of very high-order polynomials is a key aspect in the recently proposed NURBS-enhanced finite element method (NEFEM). Several well-known numerical quadratures are compared for the integration of polynomials along NURBS curves, and two transformations for the definition of numerical quadratures in triangles with one edge defined by a trimmed NURBS are proposed, analyzed and compared. When exact integration is feasible, explicit formulas for the selection of the number of integration points are deduced. Numerical examples show the influence of the number of integration points in NEFEM computations. |
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