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DOI : 10.1137/090756624

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Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 8, 4 (2010) 1102-1127

Hierarchical local model reduction for elliptic problems I: a domain decomposition approach

Simona Perotto 1, Alexandre Ern 2, Alessandro Veneziani 3

(2010)

Some engineering applications, for instance related to fluid dynamics in pipe or channel networks, feature a dominant spatial direction along which the most relevant dynamics develop. Nevertheless, local features of the problem depending on the other directions, that we call \emph{transverse}, can be locally relevant to the whole problem. We propose in the context of elliptic problems such as advection--diffusion--reaction equations, a hierarchical model reduction approach in which a coarse model featuring only the dominant direction dynamics is enriched locally by a fine model that accounts for the transverse variables via an appropriate modal expansion. We introduce a domain decomposition approach allowing us to employ a different number of modal functions in different parts of the domain according to the local complexity of the problem at hand. The methodology is investigated numerically on several test cases.

1 :	Dipartimento di Matematica F. Brioschi (MOX)
	Politecnico di Milano
2 :	Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS)
	Ecole des Ponts ParisTech
3 :	Department of Mathematics and Computer Science [Emory University]
	Emory University, Atlanta GA

Domaine

:

Mathématiques/Analyse numérique

Mots Clés : model reduction – domain decomposition method – modal expansion – finite elements

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Contributeur : Alexandre Ern <>

Soumis le : Mercredi 22 Avril 2009, 10:27:16

Dernière modification le : Vendredi 4 Novembre 2011, 11:30:45