Afficher la notice abrégée

hal.structure.identifierSection de mathématiques [Genève]
dc.contributor.authorGANDER, Martin
hal.structure.identifierLaboratoire Analyse, Géométrie et Applications [LAGA]
dc.contributor.authorHALPERN, Laurence
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierModélisation, contrôle et calcul [MC2]
dc.contributor.authorSANTUGINI-REPIQUET, Kévin
dc.date.created2011-05-16
dc.description.abstractEnThe classical convergence result for the additive Schwarz preconditioner with coarse grid is based on a stable decomposition. The result holds for discrete versions of the Schwarz preconditioner, and states that the preconditioned operator has a uniformly bounded condition number that depends only on the number of colors of the domain decomposition, the ratio between the average diameter of the subdomains and the overlap width, and on the shape regularity of the domain decomposition. The classical Schwarz method was however defined at the continuous level, and similarly, the additive Schwarz preconditioner can also be defined at the continuous level. We present in this paper a continuous analysis of the additive Schwarz preconditioned operator with coarse grid in two dimensions. We show that the classical condition number estimate also holds for the continuous formulation, and as in the discrete case, the result is based on a stable decomposition, but now of the Sobolev space H1 . The advantage of such a continuous result is that it is independent of the type of fine grid discretization, and thus does the more natural continuous formulation of the Schwarz method justice. The upper bound we provide for the classical condition number is also explicit, which gives us the quantitative dependance of the upper bound on the shape regularity of the domain decomposition.
dc.language.isoen
dc.title.enContinuous Analysis of the Additive Schwarz Method: a Stable Decomposition in $H^1$ with Explicit Dependence of the Constants on the Shape Regularity of the Decomposition
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
hal.identifierhal-00462006
hal.version1
hal.audienceNon spécifiée
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00462006v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=GANDER,%20Martin&HALPERN,%20Laurence&SANTUGINI-REPIQUET,%20K%C3%A9vin&rft.genre=preprint


Fichier(s) constituant ce document

FichiersTailleFormatVue

Il n'y a pas de fichiers associés à ce document.

Ce document figure dans la(les) collection(s) suivante(s)

Afficher la notice abrégée