Unstructured spline spaces for isogeometric analysis based on spline manifolds

@article{Sangalli2016UnstructuredSS,
  title={Unstructured spline spaces for isogeometric analysis based on spline manifolds},
  author={Giancarlo Sangalli and Thomas Takacs and Rafael V{\'a}zquez Hern{\'a}ndez},
  journal={Comput. Aided Geom. Des.},
  year={2016},
  volume={47},
  pages={61-82}
}
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22 Citations
Background Citations
9
Methods Citations
2

22 Citations

Manifold-based B-splines on unstructured meshes
TLDR
New manifold-based splines that are able to exactly reproduce B-splines on unstructured surface meshes are introduced that study and compare analytically and numerically the finite element convergence of several univariate constructions.
Manifold-based isogeometric analysis basis functions with prescribed sharp features
Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: Geometric design and isogeometric analysis considerations
Construction of approximate C1 bases for isogeometric analysis on two-patch domains
Adaptive Refinement for Unstructured T-Splines with Linear Complexity
Template Mapping Using Adaptive Splines and Optimal Parameterization
TLDR
The construction of a spline map that transforms a template, which is given in the domain, into a target shape based on least-squares fitting is considered, which should be useful when performing isogeometric segmentation and parameterization for a large class of computational domains possessing similar shapes.
Splines for Meshes with Irregularities
  • J. Peters
  • Computer Science
    The SMAI journal of computational mathematics
  • 2019
TLDR
This paper reviews and categorizes techniques for splines on meshes with irregularities, of particular interest are quad-dominant meshes that can have n 6= 4 valent interior points and T-junctions where quad-strips end.
Blended B-spline construction on unstructured quadrilateral and hexahedral meshes with optimal convergence rates in isogeometric analysis
A super-smooth C1 spline space over planar mixed triangle and quadrilateral meshes
Globally Structured Three-Dimensional Analysis-Suitable T-Splines: Definition, Linear Independence and m-graded local refinement
TLDR
An abstract definition of analysis-suitability is given and it is proved that it is equivalent to dual-compatibility, which guarantees linear independence of the T-spline blending functions.
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References

SHOWING 1-10 OF 52 REFERENCES
Adaptively refined multi-patch B-splines with enhanced smoothness
Isogeometric spline forests
C1 finite elements on non-tensor-product 2d and 3d manifolds
Isogeometric analysis with geometrically continuous functions on two-patch geometries
Polynomial splines over locally refined box-partitions
ANALYSIS-SUITABLE T-SPLINES OF ARBITRARY DEGREE: DEFINITION, LINEAR INDEPENDENCE AND APPROXIMATION PROPERTIES
TLDR
This paper defines analysis-suitable T-splines of arbitrary degree and proves fundamental properties: Linear independence of the blending functions and optimal approximation properties of the associated T- Spline space.
Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications
Recursively generated B-spline surfaces on arbitrary topological meshes
Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement
Mathematical analysis of variational isogeometric methods*
This review paper collects several results that form part of the theoretical foundation of isogeometric methods. We analyse variational techniques for the numerical resolution of PDEs based on…
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