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.
Weighted quadrature for hierarchical B-splines / Carlotta Giannelli; Tadej Kanduč; Massimiliano Martinelli; Giancarlo Sangalli; Mattia Tani. - In: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING. - ISSN 0045-7825. - STAMPA. - 400:(2022), pp. 115465.1-115465.24. [10.1016/j.cma.2022.115465]
Weighted quadrature for hierarchical B-splines
Carlotta Giannelli;
2022
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.
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