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...

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Bibliographic Details
Published in:Finite elements in analysis and design Vol. 47; no. 10; pp. 1209 - 1220
Main Authors: Sevilla, Ruben, Fernández-Méndez, Sonia
Format: Journal Article Publication
Language:English
Published: Amsterdam Elsevier B.V 01.10.2011
Elsevier
Subjects:
65 Numerical analysis
65Y Computer aspects of numerical algorithms
68 Computer science
68U Computing methodologies and applications
Anàlisi numèrica
Boundaries
Classificació AMS
Composite rule
Computing Methodologies
Exact sciences and technology
Finite element method
Gauss–Legendre
Informàtica
Matemàtica aplicada a les ciències
Matemàtiques i estadística
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Numerical integration
NURBS
NURBS-enhanced finite element method
Quadratures
Sciences and techniques of general use
Transformations
Two dimensional
Àrees temàtiques de la UPC
NURBS-enhanced finite element method
Numerical integration
Gauss–Legendre
Composite rule
NURBS
B spline
Polynomial
Spectral method
Modeling
Spline approximation
Polynomial function
Finite element method
Quadrature
Non uniform rational B spline
Gauss-Legendre
Computer aided design
ISSN:0168-874X, 1872-6925
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0168-874X
1872-6925
DOI:10.1016/j.finel.2011.05.011