Foundations of spline theory: B-splines, spline approximation, and hierarchical refinement

A Kunoth, T Lyche, G Sangalli… - Splines and PDEs: From …, 2018‏ - Springer
This chapter presents an overview of polynomial spline theory, with special emphasis on the
B-spline representation, spline approximation properties, and hierarchical spline refinement …

Analysis-suitable G1 multi-patch parametrizations for C1 isogeometric spaces

A Collin, G Sangalli, T Takacs - Computer Aided Geometric Design, 2016‏ - Elsevier
One key feature of isogeometric analysis is that it allows smooth shape functions. Indeed,
when isogeometric spaces are constructed from p-degree splines (and extensions, such as …

Isogeometric preconditioners based on fast solvers for the Sylvester equation

G Sangalli, M Tani - SIAM Journal on Scientific Computing, 2016‏ - SIAM
We consider large linear systems arising from the isogeometric discretization of the Poisson
problem on a single-patch domain. The numerical solution of such systems is considered a …

Removal of spurious outlier frequencies and modes from isogeometric discretizations of second-and fourth-order problems in one, two, and three dimensions

RR Hiemstra, TJR Hughes, A Reali… - Computer Methods in …, 2021‏ - Elsevier
A key advantage of isogeometric discretizations is their accurate and well-behaved
eigenfrequencies and eigenmodes. For degree two and higher, however, a few spurious …

Explicit error estimates for spline approximation of arbitrary smoothness in isogeometric analysis

E Sande, C Manni, H Speleers - Numerische Mathematik, 2020‏ - Springer
In this paper we provide a priori error estimates with explicit constants for both the L^ 2 L 2-
projection and the Ritz projection onto spline spaces of arbitrary smoothness defined on …

Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations

C Manni, E Sande, H Speleers - Computer Methods in Applied Mechanics …, 2022‏ - Elsevier
We show that isogeometric Galerkin discretizations of eigenvalue problems related to the
Laplace operator subject to any standard type of homogeneous boundary conditions have …

Robust multigrid for isogeometric analysis based on stable splittings of spline spaces

C Hofreither, S Takacs - SIAM Journal on Numerical Analysis, 2017‏ - SIAM
We present a robust and efficient multigrid method for single-patch isogeometric
discretizations using tensor product B-splines of maximum smoothness. Our method is …

Approximation in FEM, DG and IGA: a theoretical comparison

A Bressan, E Sande - Numerische Mathematik, 2019‏ - Springer
In this paper we compare the approximation properties of degree p spline spaces with
different numbers of continuous derivatives. We prove that, for a given space dimension, C …

Smooth multi-patch discretizations in isogeometric analysis

TJR Hughes, G Sangalli, T Takacs… - Handbook of Numerical …, 2021‏ - Elsevier
With the aim of a seamless integration with Computer-Aided Design, Isogeometric Analysis
has been proposed by Hughes et al.(2005) as a numerical technique for the solution of …

Sharp error estimates for spline approximation: Explicit constants, -widths, and eigenfunction convergence

E Sande, C Manni, H Speleers - Mathematical Models and Methods …, 2019‏ - World Scientific
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 …