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    Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive Grids

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    Type
    Conference Paper
    Authors
    AbouEisha, Hassan M. cc
    Calo, V. M.
    Jopek, K.
    Moshkov, Mikhail cc
    Paszyńska, A.
    Paszyński, M.
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Computer Science Program
    Applied Mathematics and Computational Science Program
    Date
    2018-06-12
    Online Publication Date
    2018-06-12
    Print Publication Date
    2018
    Permanent link to this record
    http://hdl.handle.net/10754/630484
    
    Metadata
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    Abstract
    The hp-adaptive Finite Element Method (hp-FEM) generates a sequence of adaptive grids with different polynomial orders of approximation and element sizes. The hp-FEM delivers exponential convergence of the numerical error with respect to the mesh size. In this paper, we propose a heuristic algorithm to construct element partition trees. The trees can be transformed directly into the orderings, which control the execution of the multi-frontal direct solvers during the hp refined finite element method. In particular, the orderings determine the number of floating point operations performed by the solver. Thus, the quality of the orderings obtained from the element partition trees is important for good performance of the solver. Our heuristic algorithm has been implemented in 3D and tested on a sequence of hp-refined meshes. We compare the quality of the orderings found by the heuristic algorithm to those generated by alternative state-of-the-art algorithms. We show 50% reduction in flops number and execution time.
    Citation
    AbouEisha H, Calo VM, Jopek K, Moshkov M, Paszyńska A, et al. (2018) Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive Grids. Computational Science – ICCS 2018: 760–772. Available: http://dx.doi.org/10.1007/978-3-319-93701-4_60.
    Publisher
    Springer Nature
    Journal
    Computational Science – ICCS 2018
    Conference/Event name
    18th International Conference on Computational Science, ICCS 2018
    DOI
    10.1007/978-3-319-93701-4_60
    Additional Links
    https://link.springer.com/chapter/10.1007%2F978-3-319-93701-4_60
    ae974a485f413a2113503eed53cd6c53
    10.1007/978-3-319-93701-4_60
    Scopus Count
    Collections
    Conference Papers; Applied Mathematics and Computational Science Program; Computer Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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