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    Quasi-optimal elimination trees for 2D grids with singularities

    250781.pdf (3.347Mb)
    Access Status
    Open access
    Authors
    Paszynska, A.
    Paszynski, M.
    Jopek, K.
    Wofniak, M.
    Goik, D.
    Gurgul, P.
    Aboueisha, H.
    Moshkov, M.
    Calo, Victor
    Lenharth, A.
    Nguyen, D.
    Pingali, K.
    Date
    2015
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Paszynska, A. and Paszynski, M. and Jopek, K. and Wofniak, M. and Goik, D. and Gurgul, P. and Aboueisha, H. et al. 2015. Quasi-optimal elimination trees for 2D grids with singularities. Scientific Programming. 2015: Article ID 303024.
    Source Title
    Scientific Programming
    DOI
    10.1155/2015/303024
    ISSN
    1058-9244
    School
    Department of Applied Geology
    URI
    http://hdl.handle.net/20.500.11937/48957
    Collection
    • Curtin Research Publications
    Abstract

    We construct quasi-optimal elimination trees for 2D finite element meshes with singularities.These trees minimize the complexity of the solution of the discrete system. The computational cost estimates of the elimination process model the execution of the multifrontal algorithms in serial and in parallel shared-memory executions. Since the meshes considered are a subspace of all possible mesh partitions, we call these minimizers quasi-optimal.We minimize the cost functionals using dynamic programming. Finding these minimizers is more computationally expensive than solving the original algebraic system. Nevertheless, from the insights provided by the analysis of the dynamic programming minima, we propose a heuristic construction of the elimination trees that has cost O(log(Ne log(Ne)), where N e is the number of elements in the mesh.We show that this heuristic ordering has similar computational cost to the quasi-optimal elimination trees found with dynamic programming and outperforms state-of-the-art alternatives in our numerical experiments.

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