Adaptive Simultaneous-FETI: scalability results, robustness assessments and application to finite displacement problems
Résumé
Classic Domain Decomposition methods like FETI are known to slowly converge when applied to real engineering problems involving for instance, automatic partitioning, quasi-incompressible materials or large heterogeneities. To ensure robustness in those cases, the Simultaneous-FETI (S-FETI) algorithm was recently proposed [1] as an alternative to GENEO approaches [2] where an augmentation space is
preprocessed by solving a generalized eigenvalue problem.
The S-FETI method is essentially a multi preconditioned conjugate gradient that exploits the additive structure of the preconditioner. At each iteration, the S-FETI algorithm generates as many search directions as there are domains in the decomposition.
In this contribution, the parallel scalability and the robustness of the S-FETI method are assessed.
Then, observing that the search space may be oversized in some cases, an adaptive variant is introduced. At each iteration, the Adaptive Simultaneous-FETI (AS-FETI) tries to compose the smallest search space which ensures a sufficient decrease of the residual. The theoretical result driving the adaptivity process was lately proven by one of the authors [3]. Finally, slight modifications allowing SFETI to deal with large
displacement finite element problems are proposed, and we present the application of these methods to real engineering tests cases.
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