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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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    Authors
    AbouEisha, H.
    Calo, Victor
    Jopek, K.
    Moshkov, M.
    Paszynska, A.
    Paszynski, M.
    Date
    2018
    Type
    Conference Paper
    
    Metadata
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    Citation
    AbouEisha, H. and Calo, V. and Jopek, K. and Moshkov, M. and Paszynska, A. and Paszynski, M. 2018. Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive Grids, in Shi Y. et al. (eds), Computational Science – ICCS 2018, Lecture Notes in Computer Science, vol 10861, pp. 760-772. Cham: Springer.
    Source Title
    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    DOI
    10.1007/978-3-319-93701-4_60
    ISBN
    9783319937007
    School
    School of Earth and Planetary Sciences (EPS)
    URI
    http://hdl.handle.net/20.500.11937/69673
    Collection
    • Curtin Research Publications
    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.

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