Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic Problem †

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Abstract

We construct an overlapping additive Schwarz preconditioner for the biharmonic Dirichlet problems discretized by isogeometric analysis based on generalized B-splines (GB-splines) and analyze its optimal convergence rate bound that is cubic in the ratio between subdomains and overlap sizes. Our analysis is validated through a set of numerical experiments that illustrate good behavior of the proposed preconditioner with respect to the model parameters.

Original languageEnglish
Article number452
JournalAxioms
Volume12
Issue number5
DOIs
StatePublished - May 2023

Keywords

  • biharmonic problems
  • domain decomposition methods
  • effective preconditioners
  • finite element method
  • generalized B-splines
  • isogeometric analysis
  • overlapping Schwarz methods

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