Curtin University Homepage
  • Library
  • Help
    • Admin

    espace - Curtin’s institutional repository

    JavaScript is disabled for your browser. Some features of this site may not work without it.
    View Item 
    • espace Home
    • espace
    • Curtin Research Publications
    • View Item
    • espace Home
    • espace
    • Curtin Research Publications
    • View Item

    Efficient mass and stiffness matrix assembly via weighted Gaussian quadrature rules for B-splines

    Access Status
    Fulltext not available
    Authors
    Bartoň, M.
    Puzyrev, Vladimir
    Deng, Quanling
    Calo, Victor
    Date
    2017
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Bartoň, M. and Puzyrev, V. and Deng, Q. and Calo, V. 2017. Efficient mass and stiffness matrix assembly via weighted Gaussian quadrature rules for B-splines.
    Source Title
    -
    Additional URLs
    https://arxiv.org/abs/1710.01048
    School
    Department of Applied Geology
    URI
    http://hdl.handle.net/20.500.11937/58067
    Collection
    • Curtin Research Publications
    Abstract

    Calabro et al. (2017) changed the paradigm of the mass and stiffness computation from the traditional element-wise assembly to a row-wise concept, showing that the latter one offers integration that may be orders of magnitude faster. Considering a B-spline basis function as a non-negative measure, each mass matrix row is integrated by its own quadrature rule with respect to that measure. Each rule is easy to compute as it leads to a linear system of equations, however, the quadrature rules are of the Newton-Cotes type, that is, they require a number of quadrature points that is equal to the dimension of the spline space. In this work, we propose weighted quadrature rules of Gaussian type which require the minimum number of quadrature points while guaranteeing exactness of integration with respect to the weight function. The weighted Gaussian rules arise as solutions of non-linear systems of equations. We derive rules for the mass and stiffness matrices for uniform C1 quadratic and C2 cubic isogeometric discretizations. Our rules further reduce the number of quadrature points by a factor of (p+12p+1)d when compared to Calabro et al. (2017), p being the polynomial degree and d the dimension of the problem, and consequently reduce the computational cost of the mass and stiffness matrix assembly by a similar factor.

    Related items

    Showing items related by title, author, creator and subject.

    • Optimal quadrature rules for odd-degree spline spaces and their application to tensor-product-based isogeometric analysis
      Barton, M.; Calo, Victor (2016)
      We introduce optimal quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. Using the homotopy continuation concept (Barton and Calo, 2016) that ...
    • Gauss–Galerkin quadrature rules for quadratic and cubic spline spaces and their application to isogeometric analysis
      Barton, M.; Calo, Victor (2017)
      © 2016 Elsevier LtdWe introduce Gaussian quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. By definition, these spaces are of even degrees. The ...
    • Dispersion-minimized mass for isogeometric analysis
      Deng, Quanling; Calo, Victor (2018)
      We introduce the dispersion-minimized mass for isogeometric analysis to approximate the structural vibration, which we model as a second-order differential eigenvalue problem. The dispersion-minimized mass reduces the ...
    Advanced search

    Browse

    Communities & CollectionsIssue DateAuthorTitleSubjectDocument TypeThis CollectionIssue DateAuthorTitleSubjectDocument Type

    My Account

    Admin

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Follow Curtin

    • 
    • 
    • 
    • 
    • 

    CRICOS Provider Code: 00301JABN: 99 143 842 569TEQSA: PRV12158

    Copyright | Disclaimer | Privacy statement | Accessibility

    Curtin would like to pay respect to the Aboriginal and Torres Strait Islander members of our community by acknowledging the traditional owners of the land on which the Perth campus is located, the Whadjuk people of the Nyungar Nation; and on our Kalgoorlie campus, the Wongutha people of the North-Eastern Goldfields.