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hal.structure.identifierLaboratoire Jacques-Louis Lions [LJLL]
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorAndreev, Roman
dc.date.accessioned2018-02-19T09:43:42Z
dc.date.available2018-02-19T09:43:42Z
dc.date.issued2017
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17413
dc.language.isoenen
dc.subjectB-splinesen
dc.subjectmultigriden
dc.subjectpreconditioningen
dc.subjectdiscretizationen
dc.subjectspace-timeen
dc.subjectaugmented Lagrangianen
dc.subjectALG2en
dc.subjectADMMen
dc.subjectmean field gamesen
dc.subject.ddc621.3en
dc.titlePreconditioning the augmented Lagrangian method for instationary mean field games with diffusionen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe discuss the application of the augmented Lagrangian method to the convex optimization problem of instationary variational mean field games with diffusion. The problem is first discretized with space-time tensor product piecewise polynomial bases. This leads to a sequence of linear problems posed on the space-time cylinder that are second order in the temporal variable and fourth order in the spatial variable. To solve these large linear problems with the preconditioned conjugate gradients method we propose a preconditioner that is based on a temporal transformation coupled with a spatial multigrid. This preconditioner is thus based on standard components and is particularly suitable for parallel computation. It is conditionally parameter-robust in the sense that the condition number of the preconditioned system is low for sufficiently fine temporal discretizations. Numerical examples illustrate the method.en
dc.relation.isversionofjnlnameSIAM Journal on Scientific Computing;1064-8275
dc.relation.isversionofjnlvol39en
dc.relation.isversionofjnlissue6en
dc.relation.isversionofjnlpagesA2763–A2783en
dc.relation.isversionofdoi10.1137/16M1072346en
dc.relation.isversionofjnlpublisherSociety for Industrial and Applied Mathematicsen
dc.subject.ddclabelTraitement du signalen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
hal.author.functionaut


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