Newton-Krylov-Schur Method with a Nonlinear Localization: Parallel Implementation for Post-Buckling Analysis of Large Structures
Résumé
The study was focused on the primal and mixed domain decomposition methods, showing that the mixed method is the best choice, because it can reduced the number of global iterations increasing the load step size, and as a consequence of these, reducing also the number of total local iterations.
Another important point is the capability, when choosing the appropriate Robin parameter, of passing critical points much more easily than for the primal version. Different options are presented for choosing the Robin parameter, in this work the Schur complement of the neighbouring substructures was used. An analysis of the influence of this parameter was carried out. In order to describe the complete behaviour of the structure an "arc-length" method was implemented at the global level.
The method was tested over a wing-box type structure made of triangular plate elements, the final configuration shows some parts of the structure buckling.
Finally the method is parallelized; a BDDC method was implemented, solved by a GMRES algorithm, because of the non-symmetry of the operator as a result of the corotationnal formulation used.