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How does the partition of unity influence SORAS preconditioner?

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  • معلومة اضافية
    • Contributors:
      Inversion of Differential Equations For Imaging and physiX (IDEFIX); Inria Saclay - Ile de France; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Unité de Mathématiques Appliquées (UMA); École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-EDF R&D (EDF R&D); EDF (EDF)-EDF (EDF); 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)
    • بيانات النشر:
      HAL CCSD
      Springer Nature Switzerland
    • الموضوع:
      2024
    • نبذة مختصرة :
      International audience ; We investigate the influence of the choice of the partition of unity on the convergence of the Symmetrized Optimized Restricted Additive Schwarz (SORAS) preconditioner for the reaction-convection-diffusion equation. We focus on two kinds of partitions of unity, and study the dependence on the overlap and on the number of subdomains. In particular, the second kind of partition of unity, which is non-zero in the interior of the whole overlapping region, gives more favorable convergence properties, especially when increasing the overlap width, in comparison with the first kind of partition of unity, whose gradient is zero on the subdomain interfaces and which would be the natural choice for ORAS solver instead.
    • Relation:
      info:eu-repo/semantics/altIdentifier/arxiv/2212.03132; hal-03882577; https://hal.science/hal-03882577; https://hal.science/hal-03882577v2/document; https://hal.science/hal-03882577v2/file/authorsample.pdf; ARXIV: 2212.03132
    • الرقم المعرف:
      10.1007/978-3-031-50769-4_6
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • الرقم المعرف:
      edsbas.FCCD3019