Volume 45, Number 3, May-June 2011
|Page(s)||563 - 602|
|Published online||30 November 2010|
FETI-DP domain decomposition methods for elasticity with structural changes: P-elasticity
Fakultät für Mathematik, Universität
Duisburg-Essen, Campus Essen, Universitätsstraße 3, 45117 Essen,
Germany. firstname.lastname@example.org; email@example.com; firstname.lastname@example.org; email@example.com
Revised: 22 July 2010
We consider linear elliptic systems which arise in coupled elastic continuum mechanical models. In these systems, the strain tensor εP := sym (P-1∇u) 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.
Mathematics Subject Classification: 65F10 / 65N30 / 65N55
Key words: FETI-DP / plasticity / eigenstresses / inhomogeneity / extended elasticity / structural changes / micromorphic model
© EDP Sciences, SMAI, 2010
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