Type
ArticleAuthors
Liu, Lulu
Keyes, David E.

KAUST Department
Applied Mathematics and Computational Science ProgramExtreme Computing Research Center
Date
2015-06-02Online Publication Date
2015-06-02Print Publication Date
2015-01Permanent link to this record
http://hdl.handle.net/10754/577006
Metadata
Show full item recordAbstract
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 ComputingAdditional Links
http://epubs.siam.org/doi/10.1137/140970379ae974a485f413a2113503eed53cd6c53
10.1137/140970379