Une version parallèle des MAN par décomposition de domaine
Keywords:
Asymptotic numerical method, parallel solver, FETI, iteratives solvers, domain decompositionAbstract
This paper is concerned with the implementation of the asymptotic-numerical method on a parallel computer, with a domain decomposition technique. After some recalls on the ANM principles and on the particularities of the linear systems that have to be solved, it is shown that the so-called ’for repeted right-hand-side’ FETI domain decomposition method is well adapted. The performance of this combination MAN+FETI is dicussed and analysed on various examples taken from geometrically non linear elasticity.
Downloads
References
[AZR 93] AZRAR L., COCHELIN B., DAMIL N., POTIER-FERRY M., « An asymptotic numerical
method to compute the post-buckling behavior of elastic plates and shells », International
Journal for Numerical Methods in Engineering, vol. 36, 1993, p. 1251-1277.
[COC 94] COCHELIN B., DAMIL N., POTIER-FERRY M., « The Asymptotic-Numerical-
Method : an efficient perturbation technique for nonlinear structural mechanics », Revue
Européenne des Éléments Finis, vol. 3, 1994, p. 281-297.
[FAR 91] FARHAT C., ROUX F. X., « A method of finite element tearing and interconnecting
and its parallel solution algorithm », International Journal for Numerical Methods in
Engineering, vol. 32, 1991, p. 1205-1227.
[FAR 94a] FARHAT C., CRIVELLI L., ROUX F. X., « Extending substructure based iterative
solvers to multiple loads and repeated analysis », Computer Methods in Applied Mechanics
and Engineering, vol. 117, 1994, p. 195-209.
[FAR 94b] FARHAT C., ROUX F. X., « Implicit parallel processing in structural mechanics »,
Computational Mechanics Advances, vol. 2, 1994, p. 47-72, NÆ1.
[FAR 00] FARHAT C., PIERSON K., LESOINNE M., « The second generation FETI methods
and their application to parallel solution of large-scale linear and geometrically non-linear
structural analysis problems », Computer Methods in Applied Mechanics and Engineering,
vol. 184, 2000, p. 333-374.
[GAL 00] GALLIET I., « Une version parallèle des méthodes asymptotiques numériques. Application
à des structures complexes à base d’élastomères », Mémoire de Thèse de Doctorat,
École Supérieure de Mécanique de Marseille, Université d’Aix-Marseille II, 2000.
[NAJ 98] NAJAH A., COCHELIN B., DAMIL N., POTIER-FERRY M., « A critical review of
Asymptotic Numerical Methods », Archives of Computational Methods in Engineering,
vol. 5, 1998, p. 31-50.
[NOO 80] NOOR A., PETERS J., « Reduced basis technique for non linear analysis of structures
», AIAA, vol. 18, 1980, p. 455-462.
[REY 96] REY C., LÉNÉ F., « Reuse of Krylov spaces in the solution of large scale nonlinear
elasticity problems », Ninth international Conference on Domain Decomosition Methods,
Norway, June 1996.
[ZAH 99] ZAHROUNI H., COCHELIN B., POTIER-FERRY M., « Asymptotic Numerical Method
for shells with finite rotation », Computer Methods in Applied Mechanics and Engineering,
vol. 175, 1999, p. 271-285.
