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    Composing Scalable Nonlinear Algebraic Solvers

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    Brune_2015_SIAM.pdf (1.328Mb)
    Issue Date
    2015-11-05
    Author
    Brune, Peter R.
    Knepley, Matthew G.
    Smith, Barry F.
    Tu, Xuemin
    Publisher
    Society for Industrial and Applied Mathematics (SIAM)
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Rights
    Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
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    Abstract
    Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for nonlinear algebraic systems, where nonlinear composition of different nonlinear solvers may significantly improve the time to solution. We describe the basic concepts of nonlinear composition and preconditioning and present a number of solvers applicable to nonlinear partial differential equations. We have developed a software framework in order to easily explore the possible combinations of solvers. We show that the performance gains from using composed solvers can be substantial compared with gains from standard Newton–Krylov methods.
    URI
    http://hdl.handle.net/1808/22270
    DOI
    https://doi.org/10.1137/130936725
    Collections
    • Mathematics Scholarly Works [273]
    Citation
    Brune, P. R., Knepley, M. G., Smith, B. F., & Tu, X. (2015). Composing Scalable Nonlinear Algebraic Solvers. SIAM Review, 57(4), 535-565. doi:10.1137/130936725

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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