To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case

Handle URI:
http://hdl.handle.net/10754/555669
Title:
To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case
Authors:
Giraldi, Loïc; Litvinenko, Alexander ( 0000-0001-5427-3598 ) ; Liu, Dishi; Matthies, Hermann G.; Nouy, Anthony
Abstract:
In 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).
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
To 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
Journal:
SIAM Journal on Scientific Computing
Issue Date:
Jan-2014
DOI:
10.1137/130942802
ARXIV:
arXiv:1309.1617
Type:
Article
ISSN:
1064-8275; 1095-7197
Additional Links:
http://epubs.siam.org/doi/abs/10.1137/130942802; http://arxiv.org/abs/1309.1617
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorGiraldi, Loïcen
dc.contributor.authorLitvinenko, Alexanderen
dc.contributor.authorLiu, Dishien
dc.contributor.authorMatthies, Hermann G.en
dc.contributor.authorNouy, Anthonyen
dc.date.accessioned2015-05-25T08:32:51Zen
dc.date.available2015-05-25T08:32:51Zen
dc.date.issued2014-01en
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 Computingen
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/130942802en
dc.identifier.urihttp://hdl.handle.net/10754/555669en
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).en
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/130942802en
dc.relation.urlhttp://arxiv.org/abs/1309.1617en
dc.rightsArchived with thanks to SIAM Journal on Scientific Computingen
dc.subjectparametric problemsen
dc.subjectstochastic equationen
dc.subjectuncertainty quantificationen
dc.subjectGalerkin approximationen
dc.subjectcoupled systemen
dc.subjectnonintrusive computationen
dc.titleTo Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Caseen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionÉcole centrale de Nantes, GeM, UMR CNRS 6183, LUNAM Université, 44321 Nantes, Franceen
dc.contributor.institutionInstitute of Aerodynamics and Flow Control, German Aerospace Center (DLR), 38108 Braunschweig, Germanyen
dc.contributor.institutionInstitute of Scientific Computing, Department of Computer Science, TU Braunschweig, 38092 Braunschweig, Germanyen
dc.identifier.arxividarXiv:1309.1617en
kaust.authorLitvinenko, Alexanderen
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