@Article{cmes.2020.08697,
AUTHOR = {Zijun Wu, Shuting Wang, Wenjun Shao, Lianqing Yu},
TITLE = {Reusing the Evaluations of Basis Functions in the Integration for Isogeometric Analysis},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {122},
YEAR = {2020},
NUMBER = {2},
PAGES = {459--485},
URL = {http://www.techscience.com/CMES/v122n2/38309},
ISSN = {1526-1506},
ABSTRACT = {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.},
DOI = {10.32604/cmes.2020.08697}
}