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

Abstract

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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.

How to cite

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Klawonn, 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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