### Abstract

Iterative substructuring methods with Lagrange multipliers for elliptic problems are considered. The algorithms belong to the family of dual-primal FETI methods which were introduced for linear elasticity problems in the plane by Farhat et al. [2001] and were later extended to three dimensional elasticity problems by Farhat et al. [2000]. Recently, the family of algorithms for scalar diffusion problems was extended to three dimensions and successfully analyzed by Klawonn et al. [2002a,b]. It was shown that the condition number of these dual-primal FETI algorithms can be bounded polylogarithmically as a function of the dimension of the individual subregion problems and that the bounds are otherwise independent of the number of subdomains, the mesh size, and jumps in the diffusion coefficients. In this article, numerical results for some of these algorithms are presented and their relation to the theoretical bounds is studied. The algorithms have been implemented in PETSc, see Balay et al. [2001], and their parallel scalability is analyzed.

Original language | English (US) |
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Title of host publication | Domain Decomposition Methods in Scienceand Engineering |

Pages | 361-368 |

Number of pages | 8 |

Volume | 40 |

State | Published - 2005 |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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Volume | 40 |

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 Scienceand Engineering*(Vol. 40, pp. 361-368). (Lecture Notes in Computational Science and Engineering; Vol. 40).

**Some computational results for dual-primal FETI methods for elliptic problems in 3D.** / Klawonn, Axel; Rheinbach, Oliver; Widlund, Olof B.

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

*Domain Decomposition Methods in Scienceand Engineering.*vol. 40, Lecture Notes in Computational Science and Engineering, vol. 40, pp. 361-368.

}

TY - CHAP

T1 - Some computational results for dual-primal FETI methods for elliptic problems in 3D

AU - Klawonn, Axel

AU - Rheinbach, Oliver

AU - Widlund, Olof B.

PY - 2005

Y1 - 2005

N2 - Iterative substructuring methods with Lagrange multipliers for elliptic problems are considered. The algorithms belong to the family of dual-primal FETI methods which were introduced for linear elasticity problems in the plane by Farhat et al. [2001] and were later extended to three dimensional elasticity problems by Farhat et al. [2000]. Recently, the family of algorithms for scalar diffusion problems was extended to three dimensions and successfully analyzed by Klawonn et al. [2002a,b]. It was shown that the condition number of these dual-primal FETI algorithms can be bounded polylogarithmically as a function of the dimension of the individual subregion problems and that the bounds are otherwise independent of the number of subdomains, the mesh size, and jumps in the diffusion coefficients. In this article, numerical results for some of these algorithms are presented and their relation to the theoretical bounds is studied. The algorithms have been implemented in PETSc, see Balay et al. [2001], and their parallel scalability is analyzed.

AB - Iterative substructuring methods with Lagrange multipliers for elliptic problems are considered. The algorithms belong to the family of dual-primal FETI methods which were introduced for linear elasticity problems in the plane by Farhat et al. [2001] and were later extended to three dimensional elasticity problems by Farhat et al. [2000]. Recently, the family of algorithms for scalar diffusion problems was extended to three dimensions and successfully analyzed by Klawonn et al. [2002a,b]. It was shown that the condition number of these dual-primal FETI algorithms can be bounded polylogarithmically as a function of the dimension of the individual subregion problems and that the bounds are otherwise independent of the number of subdomains, the mesh size, and jumps in the diffusion coefficients. In this article, numerical results for some of these algorithms are presented and their relation to the theoretical bounds is studied. The algorithms have been implemented in PETSc, see Balay et al. [2001], and their parallel scalability is analyzed.

UR - http://www.scopus.com/inward/record.url?scp=33751110027&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33751110027&partnerID=8YFLogxK

M3 - Chapter

SN - 3540225234

SN - 9783540225232

VL - 40

T3 - Lecture Notes in Computational Science and Engineering

SP - 361

EP - 368

BT - Domain Decomposition Methods in Scienceand Engineering

ER -