Study of computational efficiency of numerical quadrature schemes in the isogeometric analysis

Abstract eng:
Isogeometric analysis 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 which 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 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.

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