dc.contributor.author Giraldi, Loïc dc.contributor.author Litvinenko, Alexander dc.contributor.author Liu, Dishi dc.contributor.author Matthies, Hermann G. dc.contributor.author Nouy, Anthony dc.date.accessioned 2015-05-25T08:32:51Z dc.date.available 2015-05-25T08:32:51Z dc.date.issued 2014-01 dc.identifier.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 dc.identifier.issn 1064-8275 dc.identifier.issn 1095-7197 dc.identifier.doi 10.1137/130942802 dc.identifier.uri http://hdl.handle.net/10754/555669 dc.description.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). dc.publisher Society for Industrial & Applied Mathematics (SIAM) dc.relation.url http://epubs.siam.org/doi/abs/10.1137/130942802 dc.relation.url http://arxiv.org/abs/1309.1617 dc.rights Archived with thanks to SIAM Journal on Scientific Computing dc.subject parametric problems dc.subject stochastic equation dc.subject uncertainty quantification dc.subject Galerkin approximation dc.subject coupled system dc.subject nonintrusive computation dc.title To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case dc.type Article dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.identifier.journal SIAM Journal on Scientific Computing dc.eprint.version Publisher's Version/PDF dc.contributor.institution École centrale de Nantes, GeM, UMR CNRS 6183, LUNAM Université, 44321 Nantes, France dc.contributor.institution Institute of Aerodynamics and Flow Control, German Aerospace Center (DLR), 38108 Braunschweig, Germany dc.contributor.institution Institute of Scientific Computing, Department of Computer Science, TU Braunschweig, 38092 Braunschweig, Germany dc.identifier.arxivid arXiv:1309.1617 kaust.person Litvinenko, Alexander dc.version v1 refterms.dateFOA 2018-06-14T07:55:24Z dc.date.posted 2013-09-06
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