Articolo in rivista, 2012, ENG, 10.1016/j.cma.2012.04.014

A simple algorithm for obtaining nearly optimal quadrature rules for NURBS-based isogeometric analysis

F. Auricchio, F. Calabro', T.J.R. Hughes, A. Reali, and G. Sangalli

Dipartimento di Ingegneria Civile ed Architettura, Università degli Studi di Pavia, Italy; Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes del CNR, Pavia, Italy; DIEI, Università degli Studi di Cassino e del Lazio Meridionale, Italy; Institute for Computational Engineering and Sciences, University of Texas at Austin, United States; Dipartimento di Matematica, Università degli Studi di Pavia, Italy

We develop new quadrature rules for isogeometric analysis based on the solution of a local nonlinear problem. A simple and robust algorithm is developed to determine the rules which are exact for important B-spline spaces of uniform and geometrically stretched knot spacings. We consider both periodic and open knot vector configurations and illustrate the efficiency of the rules on selected boundary value problems. We find that the rules are almost optimally efficient, but much easier to obtain than optimal rules, which require the solution of global nonlinear problems that are often ill-posed.

Computer methods in applied mechanics and engineering 249-252 , pp. 15–27

Keywords

B-splines, Isogeometric analysis, Numerical integration, NURBS

CNR authors

Auricchio Ferdinando, Reali Alessandro, Sangalli Giancarlo

CNR institutes

IMATI – Istituto di matematica applicata e tecnologie informatiche "Enrico Magenes"