Numerical Aspects of Isogeometric Boundary Element Methods: (Nearly) Singular Quadrature, Trimmed NURBS and Surface Crack Modeling

Efficient quadrature for NURBS-based isogeometric analysis

We initiate the study of efficient quadrature rules for NURBS-based isogeometric analysis. A rule of thumb emerges, the “half-point rule”, indicating that optimal rules involve a number of points roughly equal to half the number of degrees-of-freedom, or equivalently half the number of basis functions of the space under consideration. The half-point rule is independent of the polynomial order o...

A Simple Algorithm for Obtaining Nearly Optimal Quadrature Rules for NURBS-based Isogeometric Analysis

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 boun...

Boundary Element Analysis with trimmed NURBS and a generalized IGA approach

Gernot Beer, Benjamin Marussig, Jürgen Zechner , Christian Dünser and Thomas-Peter Fries 1 Emeritus professor , TU Graz, Lessingstrasse 25, Graz, Austria and conjoint professor Centre for Geotechnical and Materials Modeling, University of Newcastle, Callaghan, Australia, [email protected] 2 PhD Student, TU Graz , Lessingstrasse 25, Graz, Austria [email protected] 3 Postdoc, TU Graz , Lessi...

Efficient Trimmed NURBS Tessellation

Interactive rendering of trimmed NURBS models is of great importance for CAD systems. For this the model needs to be transformed into a polygonal representation. This transformation can be either performed in a preprocessing step, at the cost of losing the capability to edit the surfaces, or on the fly during rendering. Since the number of frames per second is usually critical, efficient on the...

The Trimmed Nurbs Age