### Abstract

A simple and effective approach is presented to construct coarse spaces for overlapping Schwarz preconditioners. The approach is based on energy minimizing extensions of coarse trace spaces, and can be viewed as a generalization of earlier work by Dryja, Smith, and Widlund. The use of these coarse spaces in overlapping Schwarz preconditioners leads to condition numbers bounded by C(1 + H/δ)(1 + log(H/h)) for certain problems when coefficient jumps are aligned with subdomain boundaries. For problems without coefficient jumps, it is possible to remove the log(H/h) factor in this bound by a suitable enrichment of the coarse space. Comparisons are made with the coarse spaces of two other substructuring preconditioners. Numerical examples are also presented for a variety of problems.

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

Pages | 247-254 |

Number of pages | 8 |

Volume | 60 |

DOIs | |

State | Published - 2008 |

Event | 17th International Conference on Domain Decomposition Methods - St. Wolfgang /Strobl, Austria Duration: Jul 3 2006 → Jul 7 2006 |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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Volume | 60 |

ISSN (Print) | 14397358 |

### Other

Other | 17th International Conference on Domain Decomposition Methods |
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Country | Austria |

City | St. Wolfgang /Strobl |

Period | 7/3/06 → 7/7/06 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Domain Decomposition Methods in Science and Engineering XVII*(Vol. 60, pp. 247-254). (Lecture Notes in Computational Science and Engineering; Vol. 60). https://doi.org/10.1007/978-3-540-75199-1_28

**A family of energy minimizing coarse spaces for overlapping schwarz preconditioners.** / Dohrmann, Clark R.; Klawonn, Axel; Widlund, Olof B.

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

*Domain Decomposition Methods in Science and Engineering XVII.*vol. 60, Lecture Notes in Computational Science and Engineering, vol. 60, pp. 247-254, 17th International Conference on Domain Decomposition Methods, St. Wolfgang /Strobl, Austria, 7/3/06. https://doi.org/10.1007/978-3-540-75199-1_28

}

TY - GEN

T1 - A family of energy minimizing coarse spaces for overlapping schwarz preconditioners

AU - Dohrmann, Clark R.

AU - Klawonn, Axel

AU - Widlund, Olof B.

PY - 2008

Y1 - 2008

N2 - A simple and effective approach is presented to construct coarse spaces for overlapping Schwarz preconditioners. The approach is based on energy minimizing extensions of coarse trace spaces, and can be viewed as a generalization of earlier work by Dryja, Smith, and Widlund. The use of these coarse spaces in overlapping Schwarz preconditioners leads to condition numbers bounded by C(1 + H/δ)(1 + log(H/h)) for certain problems when coefficient jumps are aligned with subdomain boundaries. For problems without coefficient jumps, it is possible to remove the log(H/h) factor in this bound by a suitable enrichment of the coarse space. Comparisons are made with the coarse spaces of two other substructuring preconditioners. Numerical examples are also presented for a variety of problems.

AB - A simple and effective approach is presented to construct coarse spaces for overlapping Schwarz preconditioners. The approach is based on energy minimizing extensions of coarse trace spaces, and can be viewed as a generalization of earlier work by Dryja, Smith, and Widlund. The use of these coarse spaces in overlapping Schwarz preconditioners leads to condition numbers bounded by C(1 + H/δ)(1 + log(H/h)) for certain problems when coefficient jumps are aligned with subdomain boundaries. For problems without coefficient jumps, it is possible to remove the log(H/h) factor in this bound by a suitable enrichment of the coarse space. Comparisons are made with the coarse spaces of two other substructuring preconditioners. Numerical examples are also presented for a variety of problems.

UR - http://www.scopus.com/inward/record.url?scp=70349607199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349607199&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-75199-1_28

DO - 10.1007/978-3-540-75199-1_28

M3 - Conference contribution

AN - SCOPUS:70349607199

SN - 9783540751984

VL - 60

T3 - Lecture Notes in Computational Science and Engineering

SP - 247

EP - 254

BT - Domain Decomposition Methods in Science and Engineering XVII

ER -