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    Generalization of the Pythagorean Eigenvalue Error Theorem and Its Application to Isogeometric Analysis

    Access Status
    Fulltext not available
    Authors
    Barton, M.
    Calo, Victor
    Deng, Quanling
    Puzyrev, Vladimir
    Date
    2018
    Type
    Book Chapter
    
    Metadata
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    Citation
    Barton, M. and Calo, V. and Deng, Q. and Puzyrev, V. 2018. Generalization of the Pythagorean Eigenvalue Error Theorem and Its Application to Isogeometric Analysis. In SEMA SIMAI Springer Series, 147-170.
    Source Title
    SEMA SIMAI Springer Series
    DOI
    10.1007/978-3-319-94676-4_6
    School
    School of Earth and Planetary Sciences (EPS)
    URI
    http://hdl.handle.net/20.500.11937/70784
    Collection
    • Curtin Research Publications
    Abstract

    © 2018, Springer Nature Switzerland AG. This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagation and structural vibration problems. The dispersion error of the isogeometric elements is minimized by optimally blending two standard Gauss-type quadrature rules. These blending rules approximate the inner products and increase the convergence rate by two extra orders when compared to those with fully-integrated inner products. To quantify the approximation errors, we generalize the Pythagorean eigenvalue error theorem of Strang and Fix. To reduce the computational cost, we further propose a two-point rule for C1 quadratic isogeometric elements which produces equivalent inner products on uniform meshes and yet requires fewer quadrature points than the optimally-blended rules.

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