Computation of smooth manifolds via rigorous multi-parameter continuation in infinite dimensions

DC FieldValueLanguage
dc.contributor.authorGameiro, Marcio-
dc.contributor.authorLessard, Jean-Philippe-
dc.contributor.authorPugliese, Alessandro-
dc.date.accessioned2016-05-19T14:18:43Z-
dc.date.available2016-06-04T04:00:00Z-
dc.date.issued2015-06-04-
dc.identifier.issn1615-3375fr_CA
dc.identifier.urihttp://hdl.handle.net/20.500.11794/1468-
dc.description.abstractIn this paper, we introduce a constructive rigorous numerical method to compute smooth manifolds implicitly defined by infinite-dimensional nonlinear operators. We compute a simplicial triangulation of the manifold using a multi-parameter continuation method on a finite-dimensional projection. The triangulation is then used to construct local charts and an atlas of the manifold in the infinite-dimensional domain of the operator. The idea behind the construction of the smooth charts is to use the radii polynomial approach to verify the hypotheses of the uniform contraction principle over a simplex. The construction of the manifold is globalized by proving smoothness along the edge of adjacent simplices. We apply the method to compute portions of a two-dimensional manifold of equilibria of the Cahn–Hilliard equation.fr_CA
dc.languageengfr_CA
dc.publisherSpringerfr_CA
dc.subjectContinuationfr_CA
dc.subjectSimplicial approximationfr_CA
dc.subjectTriangulationfr_CA
dc.subjectContraction mappingfr_CA
dc.subjectRigorous numericsfr_CA
dc.titleComputation of smooth manifolds via rigorous multi-parameter continuation in infinite dimensionsfr_CA
dc.typeCOAR1_1::Texte::Périodique::Revue::Contribution à un journal::Article::Article de recherche-
dcterms.bibliographicCitationFoundations of Computational Mathematics, Vol. 16 (2), 531–575 (2016)fr_CA
dc.audienceProfesseurs (Enseignement supérieur)fr_CA
dc.audienceÉtudiantsfr_CA
dc.audienceDoctorantsfr_CA
dc.audienceMathématiciensfr_CA
dc.identifier.doi10.1007/s10208-015-9259-7fr_CA
dc.subject.rvmVariétés (Mathématiques)fr_CA
dc.subject.rvmTriangulationfr_CA
dc.subject.rvmAnalyse numériquefr_CA
dc.subject.rvmProlongement (Mathématiques)fr_CA
rioxxterms.versionVersion of Recordfr_CA
rioxxterms.version_of_recordhttps://doi.org/10.1007/s10208-015-9259-7fr_CA
rioxxterms.project.funder_nameNatural Sciences and Engineering Research Council of Canadafr_CA
bul.rights.periodeEmbargo12 moisfr_CA
Collection:Articles publiés dans des revues avec comité de lecture

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