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    On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers

    Access Status
    Fulltext not available
    Authors
    Collier, N.
    Dalcin, L.
    Calo, Victor
    Date
    2014
    Type
    Journal Article
    
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    Citation
    Collier, N. and Dalcin, L. and Calo, V. 2014. On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers. International Journal for Numerical Methods in Engineering. 100 (8): pp. 620-632.
    Source Title
    International Journal for Numerical Methods in Engineering
    DOI
    10.1002/nme.4769
    ISSN
    0029-5981
    School
    Department of Applied Geology
    URI
    http://hdl.handle.net/20.500.11937/51430
    Collection
    • Curtin Research Publications
    Abstract

    © 2014 John Wiley & Sons, Ltd.SUMMARY: We compare the computational efficiency of isogeometric Galerkin and collocation methods for partial differential equations in the asymptotic regime. We define a metric to identify when numerical experiments have reached this regime. We then apply these ideas to analyze the performance of different isogeometric discretizations, which encompass C0 finite element spaces and higher-continuous spaces. We derive convergence and cost estimates in terms of the total number of degrees of freedom and then perform an asymptotic numerical comparison of the efficiency of these methods applied to an elliptic problem. These estimates are derived assuming that the underlying solution is smooth, the full Gauss quadrature is used in each non-zero knot span and the numerical solution of the discrete system is found using a direct multi-frontal solver. We conclude that under the assumptions detailed in this paper, higher-continuous basis functions provide marginal benefits.

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