A BDDC Preconditioner for Saddle Point Problems

Jing Li, Olof Widlund

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The purpose of this paper is to extend the BDDC (balancing domain decomposition by constraints) algorithm to saddle point problems that arise when mixed finite element methods are used to approximate the system of incompressible Stokes equations. The BDDC algorithms are defined in terms of a set of primal continuity constraints, which are enforced across the interface between the subdomains, and which provide a coarse space component of the preconditioner. Sets of such constraints are identified for which bounds on the rate of convergence can be established that are just as strong as previously known bounds for the elliptic case. The preconditioned operator is positive definite and a conjugate gradient method can be used. A close connection is also established between the BDDC and FETI-DP algorithms for the Stokes case.

Original languageEnglish (US)
Title of host publicationDomain Decomposition Methods in Science and Engineering XVI
Pages413-420
Number of pages8
Volume55
StatePublished - 2007

Publication series

NameLecture Notes in Computational Science and Engineering
Volume55
ISSN (Print)14397358

Fingerprint

Saddle Point Problems
Domain Decomposition
Preconditioner
Balancing
Decomposition
Conjugate gradient method
FETI-DP
Mixed Finite Element Method
Stokes Equations
Finite element method
Conjugate Gradient Method
Stokes
Positive definite
Rate of Convergence
Operator

ASJC Scopus subject areas

  • Engineering(all)
  • Computational Mathematics
  • Modeling and Simulation
  • Control and Optimization
  • Discrete Mathematics and Combinatorics

Cite this

Li, J., & Widlund, O. (2007). A BDDC Preconditioner for Saddle Point Problems. In Domain Decomposition Methods in Science and Engineering XVI (Vol. 55, pp. 413-420). (Lecture Notes in Computational Science and Engineering; Vol. 55).

A BDDC Preconditioner for Saddle Point Problems. / Li, Jing; Widlund, Olof.

Domain Decomposition Methods in Science and Engineering XVI. Vol. 55 2007. p. 413-420 (Lecture Notes in Computational Science and Engineering; Vol. 55).

Research output: Chapter in Book/Report/Conference proceedingChapter

Li, J & Widlund, O 2007, A BDDC Preconditioner for Saddle Point Problems. in Domain Decomposition Methods in Science and Engineering XVI. vol. 55, Lecture Notes in Computational Science and Engineering, vol. 55, pp. 413-420.
Li J, Widlund O. A BDDC Preconditioner for Saddle Point Problems. In Domain Decomposition Methods in Science and Engineering XVI. Vol. 55. 2007. p. 413-420. (Lecture Notes in Computational Science and Engineering).
Li, Jing ; Widlund, Olof. / A BDDC Preconditioner for Saddle Point Problems. Domain Decomposition Methods in Science and Engineering XVI. Vol. 55 2007. pp. 413-420 (Lecture Notes in Computational Science and Engineering).
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