NDLI: Field-Split Preconditioned Inexact Newton Algorithms

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Keyes, David E. Liu, Lulu
Copyright Year	2015
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.
Starting Page	A1388
Ending Page	A1409
Page Count	22
File Format	PDF
ISSN	10648275
DOI	10.1137/140970379
e-ISSN	10957197
Issue Number	3
Volume Number	37
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2015-06-02
Access Restriction	Subscribed
Subject Keyword	nonlinear equations field splitting Systems of equations Solution of discretized equations nonlinear preconditioning Navier--Stokes equations Multigrid methods; domain decomposition Newton method Global methods, including homotopy approaches
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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