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An efficient solution method for finite element ring‐rolling simulation
Author(s) -
Davey K.,
Ward M. J.
Publication year - 2000
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(20000430)47:12<1997::aid-nme864>3.0.co;2-7
Subject(s) - finite element method , conjugate gradient method , solver , stability (learning theory) , mathematical optimization , mathematics , flow (mathematics) , linear system , computer science , engineering , mathematical analysis , structural engineering , geometry , machine learning
Finite element ring‐rolling simulation gives rise to poor conditioned non‐linear equations that require repeated solution. The associated computational costs are extreme making analysis impracticable in industry. This paper is concerned with a solution strategy that addresses this problem and involves the combined use of an arbitrary Lagrangian–Eulerian (ALE) formulation and a successive preconditioned conjugate gradient method (SPCGM). This approach, coupled to a finite element flow formulation, is shown to offer considerable computational savings. Through the combined use of the ALE flow formulation and the SPCGM the stability and condition of the non‐linear systems is enhanced. This purely iterative approach takes advantage of the slowly evolving velocity field and the self‐preconditioning offered by the SPCGM. The performance of the solver is compared against well‐known alternatives for varying problem sizes. The approach is shown to be generic but in particular makes ring‐rolling simulation a more practicable proposition. Copyright © 2000 John Wiley & Sons, Ltd.