Séminaire du jeudi 1 mars 2010
Orateur: Christian Rey (LMT)
Titre : Nonlinear mechanics & a posteriori error estimator in a substructured context
Résumé:
Non-overlapping domain decomposition methods (DDM) have been widely
studied in last decade. In the linear case, such approaches have given
rise to robust and efficient iterative linear solvers such as the
well-known BDD and FETI methods. In nonlinear cases various strategies
might be adopted. A first standard one consists in using DDM as linear
solvers in combination with a nonlinear solver (typically Newton). Such
“trivial” association does not take into account the nonlinearities from
the domain decomposition point of view. In particular it does not change
the convergence of the nonlinear solver. We will present domain
decomposition algorithms dedicated to nonlinear structural problems. The
treatment of interface conditions (Dirichlet, Neumann, Robin) leads to a
rich zoology of nonlinear domain decomposition algorithms. Such
algorithms involve the resolution of independent local (per sub-domain)
nonlinear problems and the resolution of global (interface) linear
problems. The key role played by the treatment of interface conditions
will be outlined. Numerical results will be presented on various linear
and nonlinear academic and industrial structural problems (2D and 3D
elasticity, material nonlinearities such as damage or plasticity,
geometric nonlinearities such as buckling).
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CMLA UMR 8536 |
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