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A multi‐grid enhanced GMRES algorithm for elasto‐plastic problems
Author(s) -
Feng Y. T.,
Perić D.,
Owen D. R. J.
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19980830)42:8<1441::aid-nme428>3.0.co;2-c
Subject(s) - generalized minimal residual method , grid , robustness (evolution) , computer science , algorithm , necking , mathematics , iterative method , mathematical optimization , geometry , materials science , biochemistry , chemistry , metallurgy , gene
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 effort 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 indefinite system matrices, are provided. The numerical results illustrate that the proposed method exhibits a remarkable performance in terms of efficiency and robustness in all circumstances. © 1998 John Wiley & Sons, Ltd.