AN AUGMENTED LAGRANGIAN QUASI-NEWTON SOLVER FOR CONSTRAINED NONLINEARFINITE-ELEMENT APPLICATIONS

A solution scheme is presented for constrained non-linear equations of evolution that result, for example, from the finite element discretiz ation of mechanical contact problems. The algorithm discussed utilizes a quasi-Newton non-linear equation solving strategy, with constraints enforced by an augmented Lagrangian iteration procedure. Through pres entation of a simple model problem and its generalization, it is shown that the iterations associated with both the quasi-Newton algorithm a nd the augmentation procedure can be interwoven to produce a highly ef ficient and robust solution strategy.