Field-Split Preconditioned Inexact Newton Algorithms

Handle URI:
http://hdl.handle.net/10754/577006
Title:
Field-Split Preconditioned Inexact Newton Algorithms
Authors:
Liu, Lulu ( 0000-0002-0357-1322 ) ; Keyes, David E. ( 0000-0002-4052-7224 )
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.
KAUST Department:
Applied Mathematics and Computational Science Program; Extreme Computing Research Center
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
Issue Date:
2-Jun-2015
DOI:
10.1137/140970379
Type:
Article
ISSN:
1064-8275; 1095-7197
Additional Links:
http://epubs.siam.org/doi/10.1137/140970379
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center

Full metadata record

DC FieldValue Language
dc.contributor.authorLiu, Luluen
dc.contributor.authorKeyes, David E.en
dc.date.accessioned2015-09-09T13:47:49Zen
dc.date.available2015-09-09T13:47:49Zen
dc.date.issued2015-06-02en
dc.identifier.citationField-Split Preconditioned Inexact Newton Algorithms 2015, 37 (3):A1388 SIAM Journal on Scientific Computingen
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/140970379en
dc.identifier.urihttp://hdl.handle.net/10754/577006en
dc.description.abstractThe 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.en
dc.language.isoenen
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/140970379en
dc.rightsArchived with thanks to SIAM Journal on Scientific Computingen
dc.subjectnonlinear equationsen
dc.subjectnonlinear preconditioningen
dc.subjectfield splittingen
dc.subjectNewton methoden
dc.subjectNavier–Stokes equationsen
dc.titleField-Split Preconditioned Inexact Newton Algorithmsen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorKeyes, David E.en
kaust.authorLiu, Luluen
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