FETI-DP, BDDC, and block Cholesky methods

Jing Li, Olof B. Widlund

Research output: Contribution to journalArticlepeer-review

Abstract

The FETI-DP and BDDC algorithms are reformulated using Block Cholesky factorizations, an approach which can provide a useful framework for the design of domain decomposition algorithms for solving symmetric positive definite linear system of equations. Instead of introducing Lagrange multipliers to enforce the coarse level, primal continuity constraints in these algorithms, a change of variables is used such that each primal constraint corresponds to an explicit degree of freedom. With the new formulation of these algorithms, a simplified proof is provided that the spectra of a pair of FETI-DP and BDDC algorithms, with the same set of primal constraints, are essentially the same. Numerical experiments for a two-dimensional Laplace's equation also confirm this result.

Original languageEnglish (US)
Pages (from-to)250-271
Number of pages22
JournalInternational Journal for Numerical Methods in Engineering
Volume66
Issue number2
DOIs
StatePublished - Apr 9 2006

Keywords

  • BDDC
  • Block Cholesky
  • Domain decomposition
  • FETI
  • Neumann-Neumann
  • Primal constraints

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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