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    Optimal spectral approximation of 2n-order differential operators by mixed isogeometric analysis

    73580.pdf (1.856Mb)
    Access Status
    Open access
    Authors
    Deng, Quanling
    Puzyrev, Vladimir
    Calo, Victor
    Date
    2019
    Type
    Journal Article
    
    Metadata
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    Citation
    Deng, Q. and Puzyrev, V. and Calo, V. 2019. Optimal spectral approximation of 2n-order differential operators by mixed isogeometric analysis. Computer Methods in Applied Mechanics and Engineering. 343: pp. 297-313.
    Source Title
    Computer Methods in Applied Mechanics and Engineering
    DOI
    10.1016/j.cma.2018.08.042
    ISSN
    0045-7825
    School
    School of Earth and Planetary Sciences (EPS)
    Remarks

    https://creativecommons.org/licenses/by/4.0/

    URI
    http://hdl.handle.net/20.500.11937/73337
    Collection
    • Curtin Research Publications
    Abstract

    © 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.

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