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Nonlinearly Preconditioned FETI Solver for Substructured Formulations of Nonlinear Problems

Author

Listed:
  • Camille Negrello

    (ENS Paris-Saclay, CNRS, 91190 Gif-sur-Yvette, France
    CEA, DAM- DIF, 91297 Arpajon, France)

  • Pierre Gosselet

    (ENS Paris-Saclay, CNRS, 91190 Gif-sur-Yvette, France
    Centrale Lille, CNRS, University of Lille, 59000 Lille, France)

  • Christian Rey

    (Safran Corporate Reseach Center, 92230 Gennevilliers, France)

Abstract

We consider the finite element approximation of the solution to elliptic partial differential equations such as the ones encountered in (quasi)-static mechanics, in transient mechanics with implicit time integration, or in thermal diffusion. We propose a new nonlinear version of preconditioning, dedicated to nonlinear substructured and condensed formulations with dual approach, i.e., nonlinear analogues to the Finite Element Tearing and Interconnecting (FETI) solver. By increasing the importance of local nonlinear operations, this new technique reduces communications between processors throughout the parallel solving process. Moreover, the tangent systems produced at each step still have the exact shape of classically preconditioned linear FETI problems, which makes the tractability of the implementation barely modified. The efficiency of this new preconditioner is illustrated on two academic test cases, namely a water diffusion problem and a nonlinear thermal behavior.

Suggested Citation

  • Camille Negrello & Pierre Gosselet & Christian Rey, 2021. "Nonlinearly Preconditioned FETI Solver for Substructured Formulations of Nonlinear Problems," Mathematics, MDPI, vol. 9(24), pages 1-25, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3165-:d:698081
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    Cited by:

    1. Mohammad Asghari & Amir M. Fathollahi-Fard & S. M. J. Mirzapour Al-e-hashem & Maxim A. Dulebenets, 2022. "Transformation and Linearization Techniques in Optimization: A State-of-the-Art Survey," Mathematics, MDPI, vol. 10(2), pages 1-26, January.

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