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A GenEO Domain Decomposition method for Saddle Point problems

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  • معلومة اضافية
    • Contributors:
      Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)); Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité); Algorithms and parallel tools for integrated numerical simulations (ALPINES); Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques (INSMI-CNRS)-Inria de Paris; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)); Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité); This work was granted access to the HPC resources of OCCIGEN@CINES under the allocation 2020-067730 granted by GENCI
    • بيانات النشر:
      HAL CCSD
      Académie des sciences (Paris)
    • الموضوع:
      2023
    • Collection:
      Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe)
    • نبذة مختصرة :
      International audience ; We introduce an adaptive element-based domain decomposition (DD) method for solving saddle point problems defined as a block two by two matrix. The algorithm does not require any knowledge of the constrained space. We assume that all sub matrices are sparse and that the diagonal blocks are spectrally equivalent to a sum of positive semi definite matrices. The latter assumption enables the design of adaptive coarse space for DD methods that extends the GenEO theory to saddle point problems. Numerical results on three dimensional elasticity problems for steel-rubber structures discretized by a finite element with continuous pressure are shown for up to one billion degrees of freedom.
    • Relation:
      hal-02343808; https://hal.science/hal-02343808; https://hal.science/hal-02343808v6/document; https://hal.science/hal-02343808v6/file/saddle_point_geneo.pdf
    • الرقم المعرف:
      10.5802/crmeca.175
    • الدخول الالكتروني :
      https://hal.science/hal-02343808
      https://hal.science/hal-02343808v6/document
      https://hal.science/hal-02343808v6/file/saddle_point_geneo.pdf
      https://doi.org/10.5802/crmeca.175
    • Rights:
      http://creativecommons.org/licenses/by/ ; info:eu-repo/semantics/OpenAccess
    • الرقم المعرف:
      edsbas.5F89F5D3