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    Field-Split Preconditioned Inexact Newton Algorithms

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    Type
    Article
    Authors
    Liu, Lulu cc
    Keyes, David E. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Extreme Computing Research Center
    Date
    2015-06-02
    Online Publication Date
    2015-06-02
    Print Publication Date
    2015-01
    Permanent link to this record
    http://hdl.handle.net/10754/577006
    
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    Abstract
    The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm is presented as a complement to additive Schwarz preconditioned inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. We consider both types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Numerical experiments show that MSPIN can be significantly more robust than Newton methods based on global linearizations, and that MSPIN can be more robust than ASPIN and maintain fast convergence even for challenging problems, such as high Reynolds number Navier--Stokes equations.
    Citation
    Field-Split Preconditioned Inexact Newton Algorithms 2015, 37 (3):A1388 SIAM Journal on Scientific Computing
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Journal on Scientific Computing
    DOI
    10.1137/140970379
    Additional Links
    http://epubs.siam.org/doi/10.1137/140970379
    ae974a485f413a2113503eed53cd6c53
    10.1137/140970379
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center

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