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

Published online by Cambridge University Press:  30 November 2010

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 arise in coupled elastic continuum mechanical models. In these systems, the strain tensor εP := sym (P-1u) is redefined to include a matrix valued inhomogeneity P(x) which cannot be described by a space dependent fourth order elasticity tensor. Such systems arise naturally in geometrically exact plasticity or in problems with eigenstresses. The tensor field P induces a structural change of the elasticity equations. For such a model the FETI-DP method is formulated and a convergence estimate is provided for the special case that P-T = ∇ψ is a gradient. It is shown that the condition number depends only quadratic-logarithmically on the number of unknowns of each subdomain. The dependence of the constants of the bound on P is highlighted. Numerical examples confirm our theoretical findings. Promising results are also obtained for settings which are not covered by our theoretical estimates.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2010

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