A multi-grid enhanced GMRES algorithm for elasto-plastic problems

A combination of both GMRES and multi-grid (MG) methods is presented in this paper for solving large- scale two- and three-dimensional elasto-plastic problems, in which each MG iteration cycle serves as the preconditioning step for the GMRES procedure. A particular multi-grid approach, termed the Galerkin multi- grid scheme, is considered and the main e ort is devoted to the implementation aspects of the proposed algorithm. Numerical examples, characterised by large-scale (up to 82145 DOF), strong non-linearity (nearly plastic limit state, necking and localization) and severe ill-conditioned states (presence of loading limit points), and also involving symmetric and unsymmetric as well as SPD and inde nite system matrices, are provided. The numerical results illustrate that the proposed method exhibits a remarkable performance in terms of e ciency and robustness in all circumstances.