Weighted quadrature for hierarchical B-splines

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 t...

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Bibliographic Details
Published in:arXiv.org 2021-09
Main Authors: Giannelli, Carlotta, Kanduc, Tadej, Martinelli, Massimiliano, Sangalli, Giancarlo, Tani, Mattia
Format: Article
Language:English
Subjects:
Algorithms
Galerkin method
Mathematical analysis
Quadratures
Tensors
Online Access:Get full text
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Summary: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 spline degree. To illustrate the performance of the method and confirm the theoretical estimates, a selection of 2D and 3D numerical tests is provided.
ISSN:2331-8422
DOI:10.48550/arxiv.2109.12632