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    Preconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficients

    250772.pdf (780.9Kb)
    Access Status
    Open access
    Authors
    Gao, L.
    Calo, Victor
    Date
    2015
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Gao, L. and Calo, V. 2015. Preconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficients. Journal of Computational and Applied Mathematics. 273: pp. 274-295.
    Source Title
    Journal of Computational and Applied Mathematics
    DOI
    10.1016/j.cam.2014.06.021
    ISSN
    0377-0427
    School
    Department of Applied Geology
    URI
    http://hdl.handle.net/20.500.11937/51470
    Collection
    • Curtin Research Publications
    Abstract

    In this paper, we combine the Alternating Direction Implicit (ADI) algorithm with the concept of preconditioning and apply it to linear systems discretized from the 2D steady-state diffusion equations with orthotropic heterogeneous coefficients by the finite element method assuming tensor product basis functions. Specifically, we adopt the compound iteration idea and use ADI iterations as the preconditioner for the outside Krylov subspace method that is used to solve the preconditioned linear system. An efficient algorithm to perform each ADI iteration is crucial to the efficiency of the overall iterative scheme. We exploit the Kronecker product structure in the matrices, inherited from the tensor product basis functions, to achieve high efficiency in each ADI iteration. Meanwhile, in order to reduce the number of Krylov subspace iterations, we incorporate partially the coefficient information into the preconditioner by exploiting the local support property of the finite element basis functions. Numerical results demonstrated the efficiency and quality of the proposed preconditioner. © 2014 Elsevier B.V. All rights reserved.

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