2025/09/09 by Gengchen Li, Hongwei Lin, Li, Gengchen +1
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2509.08192
openalex publication_date 2025/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we conduct a systematic numerical analysis of the spectral properties of the collocation and mass matrices in the isogeometric least-squares collocation method (IGA-L), for the approximation of the Poisson problem with homogeneous Dirichlet boundary conditions. This study primarily focuses on the spectral properties of the IGA-L collocation and mass matrices in relation to the isogeometric discretization parameters, such as the mesh size, degree, regularity, spatial dimension, and the number and distribution of the collocation points. Through a comprehensive numerical investigation, we provide estimations for the condition number, as well as the maximum and minimum singular values, in relation to the mesh size, degree and regularity. Moreover, in this paper we also study the effect of the number and distribution of the collocation points on the spectral properties of the collocation matrix, providing insights into the optimization of the collocation points for achieving better-conditioned linear systems.