Isogeometric Least-squares Collocation Method with Consistency and Convergence Analysis
Abstract
In this paper, we present the isogeometric least-squares collocation (IGA-L) method, which determines the numerical solution by making the approximate differential operator fit the real differential operator in a least-squares sense. The number of collocation points employed in IGA-L can be larger than that of the unknowns. Theoretical analysis and numerical examples presented in this paper show the superiority of IGA-L over state-of-the-art collocation methods. First, a small increase in the number of collocation points in IGA-L leads to a large improvement in the accuracy of its numerical solution. Second, IGA-L method is more flexible and more stable, because the number of collocation points in IGA-L is variable. Third, IGA-L is convergent in some cases of singular parameterization. Moreover, the consistency and convergence analysis are also developed in this paper.
Cite
@article{arxiv.1601.07244,
title = {Isogeometric Least-squares Collocation Method with Consistency and Convergence Analysis},
author = {Hongwei Lin and Yunyang Xiong and Xiao Wang and Qianqian Hu},
journal= {arXiv preprint arXiv:1601.07244},
year = {2018}
}