Weighted quadrature for hierarchical B-splines
Numerical Analysis
2022-09-07 v1 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2109.12632,
title = {Weighted quadrature for hierarchical B-splines},
author = {Carlotta Giannelli and Tadej Kanduc and Massimiliano Martinelli and Giancarlo Sangalli and Mattia Tani},
journal= {arXiv preprint arXiv:2109.12632},
year = {2022}
}