Corpus ID: 237941129

Weighted quadrature for hierarchical B-splines

@article{Giannelli2021WeightedQF,
  title={Weighted quadrature for hierarchical B-splines},
  author={Carlotta Giannelli and Tadej Kanduc and Massimiliano Martinelli and Giancarlo Sangalli and Mattia Tani},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.12632}
}
We present weighted quadrature for hierarchical B-splines to address the fast formation of system matrices arising from adaptive isogeometric Galerkin methods with suitably graded hierarchical meshes. By exploiting a local tensor-product structure, we extend the construction of weighted rules from the tensor-product to the hierarchical spline setting. The proposed algorithm has a computational cost proportional to the number of degrees of freedom and advantageous properties with increasing… Expand

References

SHOWING 1-10 OF 32 REFERENCES
Refinement Algorithms for Adaptive Isogeometric Methods with Hierarchical Splines
TLDR
This work investigates the design and implementation of refinement algorithms for hierarchical B-spline spaces that enable the construction of locally graded meshes that guarantees a bounded number of nonvanishing (truncated) hierarchicalB-splines on any mesh element. Expand
Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines
We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations in arbitrary spaceExpand
THB-splines: The truncated basis for hierarchical splines
TLDR
It is shown that the construction of classical hierarchical B-splines can be suitably modified in order to define locally supported basis functions that form a partition of unity by reducing the support of basis functions defined on coarse grids, according to finer levels in the hierarchy of splines. Expand
THB-splines: An effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis
Local refinement with hierarchical B-spline structures is an active topic of research in the context of geometric modeling and isogeometric analysis. By exploiting a multilevel control structure, weExpand
Reduced Bézier element quadrature rules for quadratic and cubic splines in isogeometric analysis
Abstract We explore the use of various element-based reduced quadrature strategies for bivariate and trivariate quadratic and cubic spline elements used in isogeometric analysis. The rules studiedExpand
Efficient matrix assembly in isogeometric analysis with hierarchical B-splines
TLDR
This work proposes an efficient matrix assembly approach for bivariate hierarchical B-splines based on the previous work and shows that the complexity has the order O(N p 3) under a mild assumption about mesh admissibility. Expand
Optimal and reduced quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis
Abstract We continue the study initiated in Hughes et al. (2010) in search of optimal quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis. These rules areExpand
Matrix-free weighted quadrature for a computationally efficient isogeometric k-method
Abstract The k -method is the isogeometric method based on splines (or NURBS, etc.) with maximum regularity. When implemented following the paradigms of classical finite element methods, theExpand
Adaptive isogeometric methods with hierarchical splines: error estimator and convergence
The problem of developing an adaptive isogeometric method (AIGM) for solving elliptic second-order partial differential equations with truncated hierarchical B-splines of arbitrary degree andExpand
Sum factorization techniques in Isogeometric Analysis
Abstract The fast assembling of stiffness and mass matrices is a key issue in Isogeometric Analysis, particularly if the spline degree is increased. We present two algorithms based on the idea of sumExpand
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