44 citations · 255 across the 25 of their papers we have counts for
25 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}…
Quadrature rules for splines of high smoothness on uniformly refined triangles
Salah Eddargani, Carla Manni, Hendrik Speleers
In this paper, we identify families of quadrature rules that are exact for sufficiently smooth spline spaces on uniformly refined triangles in . Given any symmetric q…
Using Geometric Symmetries to Achieve Super-Smoothness for Cubic Powell-Sabin Splines
Jan Grošelj, Hendrik Speleers
In this paper, we investigate super-smoothness of the full cubic spline space on a Powell-Sabin refined triangulation, for which a B-spline basis can be constructed. Bl…
Extraction and application of super-smooth cubic B-splines over triangulations
Jan Grošelj, Hendrik Speleers
The space of cubic Clough-Tocher splines is a classical finite element approximation space over triangulations for solving partial differential equations. However, for such a…
Tchebycheffian B-splines in isogeometric Galerkin methods
Krunal Raval, Carla Manni, Hendrik Speleers
Tchebycheffian splines are smooth piecewise functions whose pieces are drawn from (possibly different) Tchebycheff spaces, a natural generalization of algebraic polynomial spaces.…
ExSpliNet: An interpretable and expressive spline-based neural network
Daniele Fakhoury, Emanuele Fakhoury, Hendrik Speleers
In this paper we present ExSpliNet, an interpretable and expressive neural network model. The model combines ideas of Kolmogorov neural networks, ensembles of probabilistic trees,…
Construction of cubic splines on arbitrary triangulations
Tom Lyche, Carla Manni, Hendrik Speleers
In this paper, we address the problem of constructing cubic spline functions on a given arbitrary triangulation . To this end, we endow every triangle of $\mathc…
On the matrices in B-spline collocation methods for Riesz fractional equations and their spectral properties
Mariarosa Mazza, Marco Donatelli, Carla Manni +1
In this work, we focus on a fractional differential equation in Riesz form discretized by a polynomial B-spline collocation method. For an arbitrary polynomial degree , we show…
Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations
Carla Manni, Espen Sande, Hendrik Speleers
We show that isogeometric Galerkin discretizations of eigenvalue problems related to the Laplace operator subject to any standard type of homogeneous boundary conditions have no ou…
Ritz-type projectors with boundary interpolation properties and explicit spline error estimates
Espen Sande, Carla Manni, Hendrik Speleers
In this paper we construct Ritz-type projectors with boundary interpolation properties in finite dimensional subspaces of the usual Sobolev space and we provide a priori error esti…
Computation of multi-degree Tchebycheffian B-splines
Hendrik Speleers
Multi-degree Tchebycheffian splines are splines with pieces drawn from extended (complete) Tchebycheff spaces, which may differ from interval to interval, and possibly of different…
A general class of smooth rational splines: Application to construction of exact ellipses and ellipsoids
Hendrik Speleers, Deepesh Toshniwal
In this paper, we describe a general class of smooth rational splines that enables, in particular, exact descriptions of ellipses and ellipsoids - some of the most important…
Best low-rank approximations and Kolmogorov n-widths
Michael S. Floater, Carla Manni, Espen Sande +1
We relate the problem of best low-rank approximation in the spectral norm for a matrix to Kolmogorov -widths and corresponding optimal spaces. We characterize all the optima…
Adaptive refinement with locally linearly independent LR B-splines: Theory and applications
Francesco Patrizi, Carla Manni, Francesca Pelosi +1
In this paper we describe an adaptive refinement strategy for LR B-splines. The presented strategy ensures, at each iteration, local linear independence of the obtained set of LR B…
A Tchebycheffian extension of multi-degree B-splines: Algorithmic computation and properties
Rene R. Hiemstra, Thomas J. R. Hughes, Carla Manni +2
In this paper we present an efficient and robust approach to compute a normalized B-spline-like basis for spline spaces with pieces drawn from extended Tchebycheff spaces. The exte…
Explicit error estimates for spline approximation of arbitrary smoothness in isogeometric analysis
Espen Sande, Carla Manni, Hendrik Speleers
In this paper we provide a priori error estimates with explicit constants for both the -projection and the Ritz projection onto spline spaces of arbitrary smoothness defined o…
Sharp error estimates for spline approximation: explicit constants, -widths, and eigenfunction convergence
Espen Sande, Carla Manni, Hendrik Speleers
In this paper we provide a priori error estimates in standard Sobolev (semi-)norms for approximation in spline spaces of maximal smoothness on arbitrary grids. The error estimates…
Computation of multi-degree B-splines
Hendrik Speleers
Multi-degree splines are smooth piecewise-polynomial functions where the pieces can have different degrees. We describe a simple algorithmic construction of a set of basis function…
Isogeometric analysis for 2D and 3D curl-div problems: Spectral symbols and fast iterative solvers
Mariarosa Mazza, Carla Manni, Ahmed Ratnani +2
Alfvén-like operators are of interest in magnetohydrodynamics, which is used in plasma physics to study the macroscopic behavior of plasma. Motivated by this important and complex…