FETI-DP, BDDC, and block Cholesky methods

Jing Li, Olof B. Widlund

Research output: Contribution to journalArticle

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

Fingerprint

FETI-DP
Cholesky
Cholesky factorisation
Change of Variables
Linear system of equations
Decomposition Algorithm
Domain Decomposition
Laplace's equation
Lagrange multipliers
Positive definite
Laplace equation
Factorization
Degree of freedom
Numerical Experiment
Linear systems
Formulation
Decomposition
Experiments

Keywords

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

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Applied Mathematics
  • Computational Mechanics

Cite this

FETI-DP, BDDC, and block Cholesky methods. / Li, Jing; Widlund, Olof B.

In: International Journal for Numerical Methods in Engineering, Vol. 66, No. 2, 09.04.2006, p. 250-271.

Research output: Contribution to journalArticle

Li, Jing ; Widlund, Olof B. / FETI-DP, BDDC, and block Cholesky methods. In: International Journal for Numerical Methods in Engineering. 2006 ; Vol. 66, No. 2. pp. 250-271.
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