Premium
An augmented Lagrangian quasi‐Newton solver for constrained nonlinear finite element applications
Author(s) -
Laursen T. A.,
Maker B. N.
Publication year - 1995
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/nme.1620382103
Subject(s) - augmented lagrangian method , finite element method , discretization , solver , newton's method , mathematics , nonlinear system , generalization , simple (philosophy) , mathematical optimization , lagrangian , computer science , mathematical analysis , physics , philosophy , epistemology , quantum mechanics , thermodynamics
A solution scheme is presented for constrained non‐linear equations of evolution that result, for example, from the finite element discretization 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 presentation of a simple model problem and its generalization, it is shown that the iterations associated with both the quasi‐Newton algorithm and the augmentation procedure can be interwoven to produce a highly efficient and robust solution strategy.