Isogeometric schwarz preconditioners for the biharmonic problem

D. Cho, L. F. Pavarino, S. Scacchi

Research output: Contribution to journalArticlepeer-review

Abstract

A scalable overlapping Schwarz preconditioner for the biharmonic Dirichlet problem discretized by isogeometric analysis is constructed, and its convergence rate is analyzed. The proposed preconditioner is based on solving local biharmonic problems on overlapping subdomains that form a partition of the CAD domain of the problem and on solving an additional coarse biharmonic problem associated with the subdomain coarse mesh. An h-analysis of the preconditioner shows an optimal convergence rate bound that is scalable in the number of subdomains and is cubic in the ratio between subdomain and overlap sizes. Numerical results in 2D and 3D confirm this analysis and also illustrate the good convergence properties of the preconditioner with respect to the isogeometric polynomial degree p and regularity k.

Original languageEnglish
Pages (from-to)81-102
Number of pages22
JournalElectronic Transactions on Numerical Analysis
Volume49
DOIs
StatePublished - 2018

Keywords

  • B-splines
  • Biharmonic problem
  • Domain decomposition methods
  • Finite elements
  • Isogeometric analysis
  • NURBS
  • Overlapping Schwarz
  • Scalable preconditioners

Fingerprint

Dive into the research topics of 'Isogeometric schwarz preconditioners for the biharmonic problem'. Together they form a unique fingerprint.

Cite this