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Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: Geometric design and isogeometric analysis …
We present a framework for geometric design and isogeometric analysis on unstructured
quadrilateral meshes. Acknowledging the differing requirements posed by design (eg, the …
quadrilateral meshes. Acknowledging the differing requirements posed by design (eg, the …
Analysis-suitable G1 multi-patch parametrizations for C1 isogeometric spaces
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 …
when isogeometric spaces are constructed from p-degree splines (and extensions, such as …
Splines for meshes with irregularities
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 …
computational world. Their tensor-product form lifts many univariate properties effortlessly to …
Construction of analysis-suitable G1 planar multi-patch parameterizations
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 …
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
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 …
unstructured quadrilateral and hexahedral meshes for isogeometric analysis. C 1 and …
Isogeometric analysis with C1-smooth functions over multi-patch surfaces
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 …
space over a particular class of G 1-smooth multi-patch surfaces called analysis-suitable G 1 …
A family of C1 quadrilateral finite elements
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 …
spaces over a general quadrilateral mesh with vertices of arbitrary valency. The elements …
Construction of Cubic Splines on Arbitrary Triangulations
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 …
arbitrary triangulation T. To this end, we endow every triangle of T with a Wang–Shi macro …
Mathematics of isogeometric analysis: a conspectus
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 …
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
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 …
isogeometric analysis over two-patch domains. One key element of isogeometric analysis is …