Reusing the Evaluations of Basis Functions in the Integration for Isogeometric Analysis

We propose a new approach to reuse the basis function evaluations in the numerical integration of isogeometric analysis.The concept of reusability of the basis functions is introduced according to their symmetrical,translational and proportional features on both the coarse and refined levels.Based on these features and the parametric domain regularity of each basis,we classify the bases on the original level and then reuse them on the refined level,which can reduce the time for basis calculations at integration nodes.By using the sum factorization method and the mean value theorem for the integrals,a new integration method with high integral efficiency is proposed.We validate the proposed method by some structural analysis problems in domains with different dimensionality.Comparing the numerical result accuracy and the time cost of the proposed integration method with the full Gauss integration quadrature,it turns out to be very promising.