Assessment of Computational Efficiency of Numerical Quadrature Schemes
in the Isogeometric Analysis
Daniel Rypl, Bořek Patzák
Department of Mechanics
Faculty of Civil Engineering
Czech Technical University in Prague
Thákurova 7, 166 29 Prague, Czech Republic
Abstract:
Isogeometric analysis (IGA) has been recently introduced as a viable alternative to the
standard, polynomial-based finite element analysis. One of the fundamental performance
issues of the isogeometric analysis is the quadrature of individual components
of the discretized governing differential equation. The capability of the isogeometric
analysis to easily adopt basis functions of high degree together with the (generally)
rational form of those basis functions implies that high order numerical quadrature
schemes must be employed. This may become computationally prohibitive because
the evaluation of the high degree basis functions and/or their derivatives at individual
integration points is quite demanding. The situation tends to be critical in
three-dimensional space where the total number of integration points can increase
dramatically. The aim of this paper is to compare computational efficiency of several
numerical quadrature concepts which are nowadays available in the isogeometric
analysis. Their performance is assessed on the assembly of stiffness matrix of B-spline
based problems with special geometrical arrangement allowing to determine minimum
number of integration points leading to exact results.