A BDDC Preconditioner for Saddle Point Problems

Jing Li; Olof Widlund

doi:10.1007/978-3-540-34469-8_51

A BDDC Preconditioner for Saddle Point Problems

Jing Li, Olof Widlund

Mathematics

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

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)
Title of host publication	Domain Decomposition Methods in Science and Engineering XVI
Publisher	Springer Verlag
Pages	413-420
Number of pages	8
ISBN (Print)	9783540344681
DOIs	https://doi.org/10.1007/978-3-540-34469-8_51
State	Published - 2007

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	55
ISSN (Print)	1439-7358

ASJC Scopus subject areas

Modeling and Simulation
General Engineering
Discrete Mathematics and Combinatorics
Control and Optimization
Computational Mathematics

Access to Document

10.1007/978-3-540-34469-8_51

Cite this

@inbook{af45a4ab45bc424285341851c712203d,

title = "A BDDC Preconditioner for Saddle Point Problems",

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.",

author = "Jing Li and Olof Widlund",

year = "2007",

doi = "10.1007/978-3-540-34469-8_51",

language = "English (US)",

isbn = "9783540344681",

series = "Lecture Notes in Computational Science and Engineering",

publisher = "Springer Verlag",

pages = "413--420",

booktitle = "Domain Decomposition Methods in Science and Engineering XVI",

}

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

U2 - 10.1007/978-3-540-34469-8_51

DO - 10.1007/978-3-540-34469-8_51

M3 - Chapter

AN - SCOPUS:84880338064

SN - 9783540344681

T3 - Lecture Notes in Computational Science and Engineering

SP - 413

EP - 420

BT - Domain Decomposition Methods in Science and Engineering XVI

PB - Springer Verlag

ER -

A BDDC Preconditioner for Saddle Point Problems

Abstract

Publication series

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this