Optimal spectral approximation of2n-order differential operators by mixed isogeometric analysis
| Autor: | Victor M. Calo, Quanling Deng, Vladimir Puzyrev |
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| Rok vydání: | 2019 |
| Předmět: |
Mechanical Engineering
Computational Mechanics General Physics and Astronomy 010103 numerical & computational mathematics Isogeometric analysis Differential operator 01 natural sciences Finite element method Computer Science Applications Quadrature (mathematics) 010101 applied mathematics Mechanics of Materials Convergence (routing) Biharmonic equation Applied mathematics 0101 mathematics Eigenvalues and eigenvectors Differential (mathematics) Mathematics |
| Zdroj: | Computer Methods in Applied Mechanics and Engineering. 343:297-313 |
| ISSN: | 0045-7825 |
| DOI: | 10.1016/j.cma.2018.08.042 |
| Popis: | We approximate the spectra of a class of 2 n -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 2 p where p is the order of the underlying B-spline space. We improve this order to be 2 p + 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. |
| Databáze: | OpenAIRE |
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