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

Axel Klawonn; Patrizio Neff; Oliver Rheinbach; Stefanie Vanis

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

- Volume: 45, Issue: 3, page 563-602
- ISSN: 0764-583X

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topKlawonn, Axel, et al. "FETI-DP domain decomposition methods for elasticity with structural changes: P-elasticity." ESAIM: Mathematical Modelling and Numerical Analysis 45.3 (2011): 563-602. <http://eudml.org/doc/197565>.

@article{Klawonn2011,

abstract = {
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.
},

author = {Klawonn, Axel, Neff, Patrizio, Rheinbach, Oliver, Vanis, Stefanie},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {FETI-DP; plasticity; eigenstresses; inhomogeneity; extended elasticity; structural changes; micromorphic model},

language = {eng},

month = {1},

number = {3},

pages = {563-602},

publisher = {EDP Sciences},

title = {FETI-DP domain decomposition methods for elasticity with structural changes: P-elasticity},

url = {http://eudml.org/doc/197565},

volume = {45},

year = {2011},

}

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

DA - 2011/1//

PB - EDP Sciences

VL - 45

IS - 3

SP - 563

EP - 602

AB -
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.

LA - eng

KW - FETI-DP; plasticity; eigenstresses; inhomogeneity; extended elasticity; structural changes; micromorphic model

UR - http://eudml.org/doc/197565

ER -

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