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Application of a parallel algebraic multigrid method for the solution of elastoplastic shell problems
Author(s) -
Meynen S.,
Boersma A.,
Wriggers P.
Publication year - 1997
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/(sici)1099-1506(199705/06)4:3<223::aid-nla111>3.0.co;2-2
Subject(s) - multigrid method , domain decomposition methods , mimd , preconditioner , finite element method , conjugate gradient method , solver , mathematics , linear system , computer science , algorithm , parallel computing , partial differential equation , mathematical analysis , mathematical optimization , structural engineering , engineering
The algebraic multigrid method (AMG) can be applied as a preconditioner for the conjugate gradient method. Since no special hierarchical mesh structure has to be specified, this method is very well suited for the implementation into a standard finite element program. A general concept for the parallelization of a finite element code to a parallel machine with distributed memory of the MIMD class is presented. Here, a non‐overlapping domain decomposition is employed. A non‐linear shell theory involving elastoplastic material behaviour of von Mises type with linear isotropic hardening is briefly introduced and a parallel algebraic multigrid method is derivated. As a numerical example we discuss the pinching of a cylinder undergoing large elastoplastic deformations. The performance of the solver is shown by using speed‐up and scale‐up investigation, as well as the influence of the problem size and the plasticity. © 1997 John Wiley & Sons, Ltd.