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    A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities

    Access Status
    Open access via publisher
    Authors
    Paszynski, M.
    Pardo, D.
    Calo, Victor
    Date
    2013
    Type
    Journal Article
    
    Metadata
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    Citation
    Paszynski, M. and Pardo, D. and Calo, V. 2013. A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities. Computers and Mathematics with Applications. 65 (8): pp. 1140-1151.
    Source Title
    Computers and Mathematics with Applications
    DOI
    10.1016/j.camwa.2013.02.006
    ISSN
    0898-1221
    School
    Department of Applied Geology
    URI
    http://hdl.handle.net/20.500.11937/51330
    Collection
    • Curtin Research Publications
    Abstract

    This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.

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