Isogeometric Least-squares Collocation Method with Consistency and Convergence Analysis
For researchers in isogeometric analysis and numerical methods, this work offers a more flexible and accurate collocation approach with theoretical guarantees.
The paper introduces the isogeometric least-squares collocation (IGA-L) method, which improves accuracy and stability over existing collocation methods by allowing more collocation points than unknowns, and demonstrates convergence even with singular parameterization.
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.