Isogeometric bddc preconditioners with deluxe scaling

L. Beirão Da Veiga, L. F. Pavarino, S. Scacchi, O. B. Widlund, S. Zampini

Research output: Contribution to journalArticlepeer-review

66 Scopus citations

Abstract

A balancing domain decomposition by constraints (BDDC) preconditioner with a novel scaling, introduced by Dohrmann for problems with more than one variable coefficient and here denoted as deluxe scaling, is extended to isogeometric analysis of scalar elliptic problems. This new scaling turns out to be more powerful than the standard ?- and stiffness scalings considered in a previous isogeometric BDDC study. Our h-analysis shows that the condition number of the resulting deluxe BDDC preconditioner is scalable with a quasi-optimal polylogarithmic bound which is also independent of coefficient discontinuities across subdomain interfaces. Extensive numerical experiments support the theory and show that the deluxe scaling yields a remarkable improvement over the older scalings, in particular for large isogeometric polynomial degree and high regularity.

Original languageEnglish (US)
Pages (from-to)A1118-A1139
JournalSIAM Journal on Scientific Computing
Volume36
Issue number3
DOIs
StatePublished - 2014

Keywords

  • BDDC preconditioners
  • Domain decomposition
  • Elliptic problems
  • Isogeometric analysis

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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