Fast Iterative Solvers for Finite Element Analysis in General and Shell Analysis in Particular

Notay, Yvan; Saint-Georges, Pascal; Warzée, Guy; Topping, B. H. V.

doi:10.4203/ccp.39.5.4

Cited by 2 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We have also tested the robust preconditioner by Ajiz and Jennings, 16 which is referred to as corrected IC (CIC) by Saint-Georges et al 17 These authors concluded that CIC performs satisfactorily in thin shell problems. However, our conclusions are more concordant with the observations by Dickinson and Forsyth: 18 this method, although reliable, results in too large modi®cations to the diagonal, thus slowing down the convergence.…”

Section: Numerical Experimentsmentioning

confidence: 99%

An assessment of some preconditioning techniques in shell problems

Benzi

Kouhia²,

Tůma

1998

Commun. Numer. Meth. Engng.

View full text Add to dashboard Cite

Preconditioned Krylov subspace methods have proved to be ecient in solving large, sparse linear systems in many areas of scienti®c computing. The success of these methods in many cases is due to the existence of good preconditioning techniques. In problems of structural mechanics, like the analysis of heat transfer and deformation of solid bodies, iterative solution of the linear equation system can result in a signi®cant reduction of computing time. Also many preconditioning techniques can be applied to these problems, thus facilitating the choice of an optimal preconditioning on the particular computer architecture available. However, in the analysis of thin shells the situation is not so transparent. It is well known that the stiness matrices generated by the FE discretization of thin shells are very ill-conditioned. Thus, many preconditioning techniques fail to converge or they converge too slowly to be competitive with direct solvers. In this study, the performance of some general preconditioning techniques on shell problems is examined. PRECONDITIONING TECHNIQUES In this paper, the iterative solution of the discretized equilibrium equations of shells, written as a system of linear equations Ax b 1 is considered. The stiness matrix A is large, sparse and symmetric. In most cases it is also positive de®nite, but can be inde®nite at some stage in non-linear analyses. However, the number of negative eigenvalues is usually small, mostly one, on unstable equilibrium paths which are of practical interest. The preconditioned conjugate gradient (PCG) method is a powerful tool for solving such a system. Even though it is foolproof only for positive de®nite matrices, in practice it usually performs well without breakdowns. To speed up the convergence of the conjugate gradient iteration, preconditioning of the original system (1) is introduced: M À1 Ax M À1 b

show abstract

Section: Numerical Experimentsmentioning

confidence: 99%