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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23 Citations
Background Citations
12
Methods Citations
2

23 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

Isogeometric analysis with C1 hierarchical functions on planar two-patch geometries

TLDR
This paper shows how the adaptive isogeometric approaches can be combined with the hierarchical construction to obtain global $C^1$ continuous hierarchical splines on two-patch domains.

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.

Template Mapping Using Adaptive Splines and Optimization of the 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.

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

References

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