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. axel.klawonn@uni-duisburg-essen.de; patrizio.neff@uni-duisburg-essen.de; oliver.rheinbach@uni-duisburg-essen.de; stefanie.vanis@uni-duisburg-essen.de

Received: 21 November 2009
Revised: 22 July 2010

Abstract

We consider linear elliptic systems which arise in coupled elastic continuum mechanical models. In these systems, the strain tensor ε_P := 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.