Dispersion-optimized quadrature rules for isogeometric analysis: Modified inner products, their dispersion properties, and optimally blended schemes
This paper introduces optimally-blended quadrature rules for isogeometric analysis and analyzes the numerical dispersion of the resulting discretizations. To quantify the approximation errors when we modify the inner products, we generalize the Pythagorean eigenvalue theorem of Strang and Fix. The p...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/53707 |
| _version_ | 1848759208498954240 |
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| author | Puzyrev, Vladimir Deng, Quanling Calo, Victor |
| author_facet | Puzyrev, Vladimir Deng, Quanling Calo, Victor |
| author_sort | Puzyrev, Vladimir |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper introduces optimally-blended quadrature rules for isogeometric analysis and analyzes the numerical dispersion of the resulting discretizations. To quantify the approximation errors when we modify the inner products, we generalize the Pythagorean eigenvalue theorem of Strang and Fix. The proposed blended quadrature rules have advantages over alternative integration rules for isogeometric analysis on uniform and non-uniform meshes as well as for different polynomial orders and continuity of the basis. The optimally-blended schemes improve the convergence rate of the method by two orders with respect to the fully-integrated Galerkin method. The proposed technique increases the accuracy and robustness of isogeometric analysis for wave propagation problems. |
| first_indexed | 2025-11-14T09:56:14Z |
| format | Journal Article |
| id | curtin-20.500.11937-53707 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:56:14Z |
| publishDate | 2017 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-537072019-04-02T04:57:12Z Dispersion-optimized quadrature rules for isogeometric analysis: Modified inner products, their dispersion properties, and optimally blended schemes Puzyrev, Vladimir Deng, Quanling Calo, Victor This paper introduces optimally-blended quadrature rules for isogeometric analysis and analyzes the numerical dispersion of the resulting discretizations. To quantify the approximation errors when we modify the inner products, we generalize the Pythagorean eigenvalue theorem of Strang and Fix. The proposed blended quadrature rules have advantages over alternative integration rules for isogeometric analysis on uniform and non-uniform meshes as well as for different polynomial orders and continuity of the basis. The optimally-blended schemes improve the convergence rate of the method by two orders with respect to the fully-integrated Galerkin method. The proposed technique increases the accuracy and robustness of isogeometric analysis for wave propagation problems. 2017 Journal Article http://hdl.handle.net/20.500.11937/53707 10.1016/j.cma.2017.03.029 fulltext |
| spellingShingle | Puzyrev, Vladimir Deng, Quanling Calo, Victor Dispersion-optimized quadrature rules for isogeometric analysis: Modified inner products, their dispersion properties, and optimally blended schemes |
| title | Dispersion-optimized quadrature rules for isogeometric analysis: Modified inner products, their dispersion properties, and optimally blended schemes |
| title_full | Dispersion-optimized quadrature rules for isogeometric analysis: Modified inner products, their dispersion properties, and optimally blended schemes |
| title_fullStr | Dispersion-optimized quadrature rules for isogeometric analysis: Modified inner products, their dispersion properties, and optimally blended schemes |
| title_full_unstemmed | Dispersion-optimized quadrature rules for isogeometric analysis: Modified inner products, their dispersion properties, and optimally blended schemes |
| title_short | Dispersion-optimized quadrature rules for isogeometric analysis: Modified inner products, their dispersion properties, and optimally blended schemes |
| title_sort | dispersion-optimized quadrature rules for isogeometric analysis: modified inner products, their dispersion properties, and optimally blended schemes |
| url | http://hdl.handle.net/20.500.11937/53707 |