### 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 language | English (US) |
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Title of host publication | Domain Decomposition Methods in Science and Engineering XVI |

Pages | 413-420 |

Number of pages | 8 |

Volume | 55 |

State | Published - 2007 |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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Volume | 55 |

ISSN (Print) | 14397358 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Domain Decomposition Methods in Science and Engineering XVI.*vol. 55, Lecture Notes in Computational Science and Engineering, vol. 55, pp. 413-420.

}

TY - CHAP

T1 - A BDDC Preconditioner for Saddle Point Problems

AU - Li, Jing

AU - Widlund, Olof

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84880338064&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880338064&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:84880338064

SN - 9783540344681

VL - 55

T3 - Lecture Notes in Computational Science and Engineering

SP - 413

EP - 420

BT - Domain Decomposition Methods in Science and Engineering XVI

ER -