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    The value of continuity: Refined isogeometric analysis and fast direct solvers

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    Access Status
    Open access
    Authors
    Garcia, D.
    Pardo, D.
    Dalcin, L.
    Paszynski, M.
    Collier, N.
    Calo, Victor
    Date
    2016
    Type
    Journal Article
    
    Metadata
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    Citation
    Garcia, D. and Pardo, D. and Dalcin, L. and Paszynski, M. and Collier, N. and Calo, V. 2016. The value of continuity: Refined isogeometric analysis and fast direct solvers. Computer Methods in Applied Mechanics and Engineering. 316: pp. 586-605.
    Source Title
    Computer Methods in Applied Mechanics and Engineering
    DOI
    10.1016/j.cma.2016.08.017
    ISSN
    0045-7825
    School
    Department of Applied Geology
    URI
    http://hdl.handle.net/20.500.11937/50863
    Collection
    • Curtin Research Publications
    Abstract

    We propose the use of highly continuous finite element spaces interconnected with low continuity hyperplanes to maximize the performance of direct solvers. Starting from a highly continuous Isogeometric Analysis (IGA) discretization, we introduce . C0-separators to reduce the interconnection between degrees of freedom in the mesh. By doing so, both the solution time and best approximation errors are simultaneously improved. We call the resulting method "refined Isogeometric Analysis (rIGA)". To illustrate the impact of the continuity reduction, we analyze the number of Floating Point Operations (FLOPs), computational times, and memory required to solve the linear system obtained by discretizing the Laplace problem with structured meshes and uniform polynomial orders. Theoretical estimates demonstrate that an optimal continuity reduction may decrease the total computational time by a factor between . p2 and . p3, with . p being the polynomial order of the discretization. Numerical results indicate that our proposed refined isogeometric analysis delivers a speed-up factor proportional to . p2. In a . 2D mesh with four million elements and . p=5, the linear system resulting from rIGA is solved 22 times faster than the one from highly continuous IGA. In a . 3D mesh with one million elements and . p=3, the linear system is solved 15 times faster for the refined than the maximum continuity isogeometric analysis.

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