Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: Geometric design and isogeometric analysis …

D Toshniwal, H Speleers, TJR Hughes - Computer Methods in Applied …, 2017‏ - Elsevier
We present a framework for geometric design and isogeometric analysis on unstructured
quadrilateral meshes. Acknowledging the differing requirements posed by design (eg, the …

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 …

Splines for meshes with irregularities

J Peters - The SMAI Journal of computational …, 2019‏ - smai-jcm.centre-mersenne.org
Splines form an elegant bridge between the continuous real world and the discrete
computational world. Their tensor-product form lifts many univariate properties effortlessly to …

Construction of analysis-suitable G1 planar multi-patch parameterizations

M Kapl, G Sangalli, T Takacs - Computer-Aided Design, 2018‏ - Elsevier
The construction of smooth surfaces of complex shapes is at the heart of computer-aided
design (CAD). Many different approaches generating C 1-smooth surfaces are available and …

Blended B-spline construction on unstructured quadrilateral and hexahedral meshes with optimal convergence rates in isogeometric analysis

X Wei, YJ Zhang, D Toshniwal, H Speleers, X Li… - Computer Methods in …, 2018‏ - Elsevier
We present a novel blended B-spline method to construct bicubic/tricubic splines over
unstructured quadrilateral and hexahedral meshes for isogeometric analysis. C 1 and …

Isogeometric analysis with C1-smooth functions over multi-patch surfaces

A Farahat, B Jüttler, M Kapl, T Takacs - Computer Methods in Applied …, 2023‏ - Elsevier
We present a framework for the construction of a globally C 1-smooth isogeometric spline
space over a particular class of G 1-smooth multi-patch surfaces called analysis-suitable G 1 …

A family of C1 quadrilateral finite elements

M Kapl, G Sangalli, T Takacs - Advances in Computational Mathematics, 2021‏ - Springer
We present a novel family of C 1 quadrilateral finite elements, which define global C 1
spaces over a general quadrilateral mesh with vertices of arbitrary valency. The elements …

Construction of Cubic Splines on Arbitrary Triangulations

T Lyche, C Manni, H Speleers - Foundations of Computational …, 2022‏ - Springer
In this paper, we address the problem of constructing C 2 cubic spline functions on a given
arbitrary triangulation T. To this end, we endow every triangle of T with a Wang–Shi macro …

Mathematics of isogeometric analysis: a conspectus

TJR Hughes, G Sangalli - Encyclopedia of Computational …, 2018‏ - Wiley Online Library
Isogeometric analysis (IGA) is a successful generalization of finite element analysis. The use
of smooth splines simplifies the interaction with geometric design, but also opens new …

[HTML][HTML] Construction of approximate C1 bases for isogeometric analysis on two-patch domains

P Weinmüller, T Takacs - Computer Methods in Applied Mechanics and …, 2021‏ - Elsevier
In this paper, we develop and study approximately smooth basis constructions for
isogeometric analysis over two-patch domains. One key element of isogeometric analysis is …