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FETI-DP domain decomposition methods for elasticitywith structural changes: P-elasticity

Published online by Cambridge University Press:  30 November 2010

Axel Klawonn ,
Patrizio Neff ,
Oliver Rheinbach  and
Stefanie Vanis
Axel Klawonn
Affiliation:
Fakultät für Mathematik, Universität Duisburg-Essen, Campus Essen, Universitätsstraße 3, 45117 Essen, Germany. axel.klawonn@uni-duisburg-essen.de; patrizio.neff@uni-duisburg-essen.de; oliver.rheinbach@uni-duisburg-essen.de; stefanie.vanis@uni-duisburg-essen.de
Patrizio Neff
Affiliation:
Fakultät für Mathematik, Universität Duisburg-Essen, Campus Essen, Universitätsstraße 3, 45117 Essen, Germany. axel.klawonn@uni-duisburg-essen.de; patrizio.neff@uni-duisburg-essen.de; oliver.rheinbach@uni-duisburg-essen.de; stefanie.vanis@uni-duisburg-essen.de
Oliver Rheinbach
Affiliation:
Fakultät für Mathematik, Universität Duisburg-Essen, Campus Essen, Universitätsstraße 3, 45117 Essen, Germany. axel.klawonn@uni-duisburg-essen.de; patrizio.neff@uni-duisburg-essen.de; oliver.rheinbach@uni-duisburg-essen.de; stefanie.vanis@uni-duisburg-essen.de
Stefanie Vanis
Affiliation:
Fakultät für Mathematik, Universität Duisburg-Essen, Campus Essen, Universitätsstraße 3, 45117 Essen, Germany. axel.klawonn@uni-duisburg-essen.de; patrizio.neff@uni-duisburg-essen.de; oliver.rheinbach@uni-duisburg-essen.de; stefanie.vanis@uni-duisburg-essen.de
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Abstract

We consider linear elliptic systems which arisein coupled elastic continuum mechanical models. In these systems, the straintensor ε P := sym (P -1∇u) is redefined to include amatrix valued inhomogeneity P(x) which cannot be described by a spacedependent fourth order elasticity tensor. Such systems arise naturally ingeometrically exact plasticity or in problems with eigenstresses.The tensor field P induces a structural change of the elasticity equations. Forsuch a model the FETI-DP method is formulated and a convergence estimateis provided for the special case that P -T = ∇ψ is a gradient.It is shown that the condition number depends only quadratic-logarithmicallyon the number of unknowns of each subdomain. Thedependence of the constants of the bound on P is highlighted. Numericalexamples confirm our theoretical findings. Promising results are also obtainedfor settings which are not covered by our theoretical estimates.

Keywords

FETI-DPplasticityeigenstressesinhomogeneityextended elasticitystructural changesmicromorphic model

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Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 3 , May 2011 , pp. 563 - 602
Copyright
© EDP Sciences, SMAI, 2010

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