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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.
@article{M2AN_2011__45_3_563_0,
author = {Klawonn, Axel and Neff, Patrizio and Rheinbach, Oliver and Vanis, Stefanie},
title = {FETI-DP domain decomposition methods for elasticity with structural changes: $P$-elasticity},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {563--602},
publisher = {EDP-Sciences},
volume = {45},
number = {3},
year = {2011},
doi = {10.1051/m2an/2010067},
zbl = {1268.74037},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010067/}
}
TY - JOUR AU - Klawonn, Axel AU - Neff, Patrizio AU - Rheinbach, Oliver AU - Vanis, Stefanie TI - FETI-DP domain decomposition methods for elasticity with structural changes: $P$-elasticity JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2011 SP - 563 EP - 602 VL - 45 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010067/ DO - 10.1051/m2an/2010067 LA - en ID - M2AN_2011__45_3_563_0 ER -
%0 Journal Article %A Klawonn, Axel %A Neff, Patrizio %A Rheinbach, Oliver %A Vanis, Stefanie %T FETI-DP domain decomposition methods for elasticity with structural changes: $P$-elasticity %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2011 %P 563-602 %V 45 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010067/ %R 10.1051/m2an/2010067 %G en %F M2AN_2011__45_3_563_0
Klawonn, Axel; Neff, Patrizio; Rheinbach, Oliver; Vanis, Stefanie. FETI-DP domain decomposition methods for elasticity with structural changes: $P$-elasticity. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 3, pp. 563-602. doi: 10.1051/m2an/2010067
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