Comparison of Numerical Quadrature Schemes in Isogeometric Analysis

摘要

Isogeometric analysis has been recently introduced as a viable alternative to the standard,rnpolynomial-based finite element analysis. One of the fundamental performancernissues of the isogeometric analysis is the quadrature of individual components of therndiscretized governing differential equation. The capability of the isogeometric analysisrnto easily adopt basis functions of high degree together with the (generally) rationalrnform of those basis functions implies that high order numerical quadrature schemesrnmust be employed. This may becomes computationally prohibitive because the evaluationrnof the high degree basis functions and/or their derivatives at individual integrationrnpoints is quite demanding. The situation tends to be critical in three-dimensionalrnspace where the total number of integration points can increase dramatically. The aimrnof this paper is to compare computational efficiency of several numerical quadraturernconcepts which are nowadays available in the isogeometric analysis.