8 papers
Isogeometric discretizations for the spectrum of the Laplace operator: outlier-free spline bases
Damiano Ricci, Carla Manni, Hendrik Speleers
Optimal spline subspaces are an elegant and efficient tool to remove spurious outliers in isogeometric Galerkin discretizations for the approximation of the spectrum of the Laplace…
On the completeness of generalized hierarchical spline spaces
Ahmed Oufqir, Carla Manni, Hendrik Speleers
We introduce a general theoretical approach to hierarchical spline spaces that replaces the classical constructive definition - based on basis selection - with a descriptive formul…
Isogeometric analysis with cubic Powell-Sabin splines
Jan Grošelj, Ada Šadl Praprotnik, Hendrik Speleers
In this paper, we consider cubic Powell-Sabin splines for the numerical solution of boundary value problems on planar and spatial surface domains. We first review the constru…
On the normalization of trigonometric and hyperbolic B-splines
Hendrik Speleers
Trigonometric and hyperbolic B-splines can be computed via recurrence relations analogous to the classical polynomial B-splines. However, in their original formulation, these two t…
Outlier-free isogeometric discretizations for Laplace eigenvalue problems: closed-form eigenvalue and eigenvector expressions
Noureddine Lamsahel, Carla Manni, Ahmed Ratnani +2
We derive explicit closed-form expressions for the eigenvalues and eigenvectors of the matrices resulting from isogeometric Galerkin discretizations based on outlier-free spline su…
A parsimonious approach to cubic splines on arbitrary triangulations: Reduced macro-elements on the cubic Wang-Shi split
Tom Lyche, Carla Manni, Hendrik Speleers
We present a general method to obtain interesting subspaces of the cubic spline space defined on the cubic Wang-Shi refinement of a given arbitrary triangulation $\mathcal{T}…