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dc.contributor.authorGiraldi, Loïc
dc.contributor.authorLitvinenko, Alexander
dc.contributor.authorLiu, Dishi
dc.contributor.authorMatthies, Hermann G.
dc.contributor.authorNouy, Anthony
dc.date.accessioned2015-05-25T08:32:51Z
dc.date.available2015-05-25T08:32:51Z
dc.date.issued2014-01
dc.identifier.citationTo Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case 2014, 36 (6):A2720 SIAM Journal on Scientific Computing
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.doi10.1137/130942802
dc.identifier.urihttp://hdl.handle.net/10754/555669
dc.description.abstractIn parametric equations---stochastic equations are a special case---one may want to approximate the solution such that it is easy to evaluate its dependence on the parameters. Interpolation in the parameters is an obvious possibility---in this context often labeled as a collocation method. In the frequent situation where one has a “solver” for a given fixed parameter value, this may be used “nonintrusively” as a black-box component to compute the solution at all the interpolation points independently of each other. By extension, all other methods, and especially simple Galerkin methods, which produce some kind of coupled system, are often classed as “intrusive.” We show how, for such “plain vanilla” Galerkin formulations, one may solve the coupled system in a nonintrusive way, and even the simplest form of block-solver has comparable efficiency. This opens at least two avenues for possible speed-up: first, to benefit from the coupling in the iteration by using more sophisticated block-solvers and, second, the possibility of nonintrusive successive rank-one updates as in the proper generalized decomposition (PGD).
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/130942802
dc.relation.urlhttp://arxiv.org/abs/1309.1617
dc.rightsArchived with thanks to SIAM Journal on Scientific Computing
dc.subjectparametric problems
dc.subjectstochastic equation
dc.subjectuncertainty quantification
dc.subjectGalerkin approximation
dc.subjectcoupled system
dc.subjectnonintrusive computation
dc.titleTo Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalSIAM Journal on Scientific Computing
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionÉcole centrale de Nantes, GeM, UMR CNRS 6183, LUNAM Université, 44321 Nantes, France
dc.contributor.institutionInstitute of Aerodynamics and Flow Control, German Aerospace Center (DLR), 38108 Braunschweig, Germany
dc.contributor.institutionInstitute of Scientific Computing, Department of Computer Science, TU Braunschweig, 38092 Braunschweig, Germany
dc.identifier.arxividarXiv:1309.1617
kaust.personLitvinenko, Alexander
refterms.dateFOA2018-06-14T07:55:24Z
dc.date.posted2013-09-06


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