Optimal spectral approximation of 2n-order differential operators by mixed isogeometric analysis
© 2018 Elsevier B.V. We approximate the spectra of a class of 2n-order differential operators using isogeometric analysis in mixed formulations. This class includes a wide range of differential operators such as those arising in elliptic, biharmonic, Cahn–Hilliard, Swift–Hohenberg, and phase-field c...
| Main Authors: | , , |
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| Format: | Journal Article |
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Elsevier BV
2019
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| Online Access: | http://hdl.handle.net/20.500.11937/73337 |
| _version_ | 1848762987645501440 |
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| author | Deng, Quanling Puzyrev, Vladimir Calo, Victor |
| author_facet | Deng, Quanling Puzyrev, Vladimir Calo, Victor |
| author_sort | Deng, Quanling |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2018 Elsevier B.V. We approximate the spectra of a class of 2n-order differential operators using isogeometric analysis in mixed formulations. This class includes a wide range of differential operators such as those arising in elliptic, biharmonic, Cahn–Hilliard, Swift–Hohenberg, and phase-field crystal equations. The spectra of the differential operators are approximated by solving differential eigenvalue problems in mixed formulations, which require auxiliary parameters. The mixed isogeometric formulation when applying classical quadrature rules leads to an eigenvalue error convergence of order 2p where p is the order of the underlying B-spline space. We improve this order to be 2p+2 by applying optimally-blended quadrature rules developed in Puzyrev et al. (2017), Caloet al. (0000) and this order is an optimum in the view of dispersion error. We also compare these results with the mixed finite elements and show numerically that the mixed isogeometric analysis leads to significantly better spectral approximations. |
| first_indexed | 2025-11-14T10:56:18Z |
| format | Journal Article |
| id | curtin-20.500.11937-73337 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:56:18Z |
| publishDate | 2019 |
| publisher | Elsevier BV |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-733372020-09-18T01:29:37Z Optimal spectral approximation of 2n-order differential operators by mixed isogeometric analysis Deng, Quanling Puzyrev, Vladimir Calo, Victor © 2018 Elsevier B.V. We approximate the spectra of a class of 2n-order differential operators using isogeometric analysis in mixed formulations. This class includes a wide range of differential operators such as those arising in elliptic, biharmonic, Cahn–Hilliard, Swift–Hohenberg, and phase-field crystal equations. The spectra of the differential operators are approximated by solving differential eigenvalue problems in mixed formulations, which require auxiliary parameters. The mixed isogeometric formulation when applying classical quadrature rules leads to an eigenvalue error convergence of order 2p where p is the order of the underlying B-spline space. We improve this order to be 2p+2 by applying optimally-blended quadrature rules developed in Puzyrev et al. (2017), Caloet al. (0000) and this order is an optimum in the view of dispersion error. We also compare these results with the mixed finite elements and show numerically that the mixed isogeometric analysis leads to significantly better spectral approximations. 2019 Journal Article http://hdl.handle.net/20.500.11937/73337 10.1016/j.cma.2018.08.042 Elsevier BV fulltext |
| spellingShingle | Deng, Quanling Puzyrev, Vladimir Calo, Victor Optimal spectral approximation of 2n-order differential operators by mixed isogeometric analysis |
| title | Optimal spectral approximation of 2n-order differential operators by mixed isogeometric analysis |
| title_full | Optimal spectral approximation of 2n-order differential operators by mixed isogeometric analysis |
| title_fullStr | Optimal spectral approximation of 2n-order differential operators by mixed isogeometric analysis |
| title_full_unstemmed | Optimal spectral approximation of 2n-order differential operators by mixed isogeometric analysis |
| title_short | Optimal spectral approximation of 2n-order differential operators by mixed isogeometric analysis |
| title_sort | optimal spectral approximation of 2n-order differential operators by mixed isogeometric analysis |
| url | http://hdl.handle.net/20.500.11937/73337 |