Weighted quadrature for hierarchical B-splines
| Autor: | Carlotta Giannelli, Tadej Kanduč, Massimiliano Martinelli, Giancarlo Sangalli, Mattia Tani |
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| Rok vydání: | 2021 |
| Předmět: |
Mechanics of Materials
Mechanical Engineering Computational Mechanics MathematicsofComputing_NUMERICALANALYSIS FOS: Mathematics General Physics and Astronomy Mathematics - Numerical Analysis Numerical Analysis (math.NA) Computer Science Applications ComputingMethodologies_COMPUTERGRAPHICS Mathematics::Numerical Analysis |
| DOI: | 10.48550/arxiv.2109.12632 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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