Contact on multiprocessor environment : from multicontact problems to multiscale approaches
Résumé
This course is devoted to the recent developments in the numerical treatment of large multicontact problems requiring multiprocessor computers to get admissible computer time simulations. Contact conditions lead to non smooth mathematical formulations of steady-state and dynamical problems arising from structural and granular mechanics. Specific solvers, as the Non Linear Gauss Seidel algorithm and the Conjugate Projected Gradient method, have been developed and may be adapted to a parallel treatment. The domain decomposition methods allow to deal with large-scale mechanical problems and take advantage of the multiprocessor architecture of powerful computers. Their efficiency is proved for linear problems. Two different strategy for inserting the contact treatment are detailled and compared: the Newton-Schur approach and the FETI-C method. A multiscale description is finally coupled with a substructuring technique to tackle multicontact problems with diffuse non smoothness.