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. (c) 2022 Elsevier B.V. All rights reserved.

Weighted quadrature for hierarchical B-splines

Giancarlo Sangalli;Mattia Tani
2022-01-01

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. (c) 2022 Elsevier B.V. All rights reserved.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/1466902
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