A non-invasive implementation of mixed transmission conditions for a domain decomposition method - application to contact problems
Résumé
In the last years, domain decompositions methods (DDM) have been adapted to tackle large nonlinear problems, but efficiency and robustness still remains a challenge. For nonlinearity " in the volume " relocalization approaches have proved their ability to cast the global problem into small independent nonlinear problems on the subdomains. For surface nonlinearity, frictional contact has also been inserted in the FETI framework and the Latin method which can also deal with cohesive interfaces. The Latin DDM can be viewed as a fixed point for which an iteration is decomposed into (i) a problem verifying only the relations of the interfaces and (ii) the subdomains' equilibrium. Each step is linked to the other one through mixed transmission conditions. A non-invasive Latin DDM (i.e. without altering a FEM commercial software) has been proposed by the authors. Here, the mixed conditions were related to the stiffness of a new layer of elements patched on the subdomains' boundaries. The optimal Robin parameters for the fastest convergence depends on global data which is too expensive in a parallel implementation. This work aims at proposing an automated choice of the Robin conditions for friction contact problems in the non-invasive framework. The idea is to approach the subdomains' stiffness to adapt the one of the patched elements.