An efficient solution method for finite element ring-rolling simulation

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.