Overlapping schwarz methods for isogeometric analysis

L. Beirão Da Veiga, D. Cho, L. F. Pavarino, S. Scacchi

Research output: Contribution to journalArticlepeer-review

77 Scopus citations

Abstract

We construct and analyze an overlapping Schwarz preconditioner for elliptic problems discretized with isogeometric analysis. The preconditioner is based on partitioning the domain of the problem into overlapping subdomains, solving local isogeometric problems on these subdomains, and solving an additional coarse isogeometric problem associated with the subdomain mesh. We develop an h-analysis of the preconditioner, showing in particular that the resulting algorithm is scalable and its convergence rate depends linearly on the ratio between subdomain and "overlap sizes" for fixed polynomial degree p and regularity k of the basis functions. Numerical results in two- and three-dimensional tests show the good convergence properties of the preconditioner with respect to the isogeometric discretization parameters h, p, k, number of subdomains N, overlap size, and also jumps in the coefficients of the elliptic operator.

Original languageEnglish
Pages (from-to)1394-1416
Number of pages23
JournalSIAM Journal on Numerical Analysis
Volume50
Issue number3
DOIs
StatePublished - 2012

Keywords

  • Domain decomposition methods
  • Finite elements
  • Isogeometric analysis
  • NURBS
  • Overlapping Schwarz
  • Scalable preconditioners

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