Generalized Gaussian quadrature rules on arbitrary polygons

In this paper, we present a numerical algorithm based on group theory and numerical optimization to compute efficient quadrature rules for integration of bivariate polynomials over arbitrary polygons. These quadratures have desirable properties such as positivity of weights and interiority of nodes...

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Veröffentlicht in:	International journal for numerical methods in engineering 2010-04, Vol.82 (1), p.99-113
Hauptverfasser:	Mousavi, S. E., Xiao, H., Sukumar, N.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithms Computer programs convex and concave polygons Exact sciences and technology Gaussian quadrature Gram-Schmidt orthogonalization Mathematics Newton's method Numerical analysis Numerical analysis. Scientific computation Numerical approximation numerical integration polygonal finite elements Polygons Quadratures Sciences and techniques of general use Shape functions Software Stiffness matrix
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