Spectral analysis of matrices in collocation methods based on generalized B-splines with high smoothness
This work provides a theoretical analysis of spectral properties for a specific numerical method, which is incremental for researchers in isogeometric analysis.
The paper analyzes the spectral properties of matrices from isogeometric collocation methods using GB-splines for elliptic PDEs with variable coefficients and generic geometry, providing insights into their behavior.
Although Galerkin discretizations have been intensively employed in the IgA context, an efficient implementation requires special numerical quadrature rules when constructing the system of equations. To avoid this issue, isogeometric collocation methods have been recently introduced, giving origin to a topic of study which is proceeding almost parallel to the Galerkin evolution. In this paper we analyze the spectral properties of the matrices arising from isogeometric collocation methods based on GB-splines to approximate an elliptic PDE with variable coefficients and a generic geometry map.