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    Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients

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    Type
    Article
    Authors
    Chavez Chavez, Gustavo Ivan cc
    Turkiyyah, George
    Zampini, Stefano cc
    Keyes, David E. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Computer Science Program
    Extreme Computing Research Center
    Applied Mathematics and Computational Science Program
    Date
    2017-12-07
    Online Publication Date
    2017-12-07
    Print Publication Date
    2018-12
    Permanent link to this record
    http://hdl.handle.net/10754/626377
    
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    Abstract
    We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank approximations and the cyclic reduction method. The setup and application phases of the preconditioner achieve log-linear complexity in memory footprint and number of operations, and numerical experiments exhibit good weak and strong scalability at large processor counts in a distributed memory environment. Numerical experiments with linear systems that feature symmetry and nonsymmetry, definiteness and indefiniteness, constant and variable coefficients demonstrate the preconditioner applicability and robustness. Furthermore, it is possible to control the number of iterations via the accuracy threshold of the hierarchical matrix approximations and their arithmetic operations, and the tuning of the admissibility condition parameter. Together, these parameters allow for optimization of the memory requirements and performance of the preconditioner.
    Citation
    Chávez G, Turkiyyah G, Zampini S, Keyes D (2017) Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients. Journal of Computational and Applied Mathematics. Available: http://dx.doi.org/10.1016/j.cam.2017.11.035.
    Sponsors
    We thank the editors and the reviewers for their time and comments during the review process of this work. Support from the KAUST Supercomputing Laboratory and access to Shaheen Cray XC40 is gratefully acknowledged.
    Publisher
    Elsevier BV
    Journal
    Journal of Computational and Applied Mathematics
    DOI
    10.1016/j.cam.2017.11.035
    arXiv
    1712.08872
    Additional Links
    http://www.sciencedirect.com/science/article/pii/S0377042717305952
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.cam.2017.11.035
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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