FETI-DP domain decomposition methods for elasticity with structural changes: P-elasticity
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 3, p. 563-602

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.

DOI : https://doi.org/10.1051/m2an/2010067
Classification:  65F10,  65N30,  65N55
Keywords: FETU-DP, plasticity, eigenstresses, inhomogeneity, extended elasticity, structural changes, micromorphic model
@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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {3},
     year = {2011},
     pages = {563-602},
     doi = {10.1051/m2an/2010067},
     zbl = {1268.74037},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 3, pp. 563-602. doi : 10.1051/m2an/2010067. http://www.numdam.org/item/M2AN_2011__45_3_563_0/

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