### Abstract

Original language | English |
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Title of host publication | Domain Decomposition Methods in Science and Engineering XXI |

Subtitle of host publication | Lecture Notes in Computational Science and Engineering |

Editors | Jocelyne Erhel , Martin J Gander , Laurence Halpern , Geraldine Pichot , Taiufik Sassi , Olof Widlund |

Publisher | Springer |

Pages | 447-455 |

Number of pages | 10 |

Volume | 98 |

ISBN (Electronic) | 9783319057897 |

ISBN (Print) | 9783319057880 |

DOIs | |

Publication status | Published - 21 Apr 2014 |

Event | 21st International Conference on Domain Decomposition Methods in Science and Engineering, DD 2014 - Rennes, UK United Kingdom Duration: 25 Jun 2012 → 29 Jun 2012 |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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Volume | 98 |

ISSN (Print) | 14397358 |

### Conference

Conference | 21st International Conference on Domain Decomposition Methods in Science and Engineering, DD 2014 |
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Country | UK United Kingdom |

City | Rennes |

Period | 25/06/12 → 29/06/12 |

### Cite this

*Domain Decomposition Methods in Science and Engineering XXI : Lecture Notes in Computational Science and Engineering*(Vol. 98, pp. 447-455). (Lecture Notes in Computational Science and Engineering; Vol. 98). Springer. https://doi.org/10.1007/978-3-319-05789-7_42

**Achieving robustness through coarse space enrichment in the two level Schwarz framework.** / Spillane, Nicole; Dolean, Victorita; Hauret, Patrice; Nataf, Frédéric; Pechstein, Clemens; Scheichl, Robert.

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

*Domain Decomposition Methods in Science and Engineering XXI : Lecture Notes in Computational Science and Engineering.*vol. 98, Lecture Notes in Computational Science and Engineering, vol. 98, Springer, pp. 447-455, 21st International Conference on Domain Decomposition Methods in Science and Engineering, DD 2014, Rennes, UK United Kingdom, 25/06/12. https://doi.org/10.1007/978-3-319-05789-7_42

}

TY - CHAP

T1 - Achieving robustness through coarse space enrichment in the two level Schwarz framework

AU - Spillane, Nicole

AU - Dolean, Victorita

AU - Hauret, Patrice

AU - Nataf, Frédéric

AU - Pechstein, Clemens

AU - Scheichl, Robert

PY - 2014/4/21

Y1 - 2014/4/21

N2 - As many DD methods the two level Additive Schwarz method may suffer from a lack of robustness with respect to coefficient variation. This is the case in particular if the partition into is not aligned with all jumps in the coefficients. The theoretical analysis traces this lack of robustness back to the so called stable splitting property. In this work we propose to solve a generalized eigenvalue problem in each subdomain which identifies which vectors are responsible for violating the stable splitting property. These vectors are used to span the coarse space and taken care of by a direct solve while all remaining components behave well. The result is a condition number estimate for the two level method which does not depend on the number of subdomains or any jumps in the coefficients.

AB - As many DD methods the two level Additive Schwarz method may suffer from a lack of robustness with respect to coefficient variation. This is the case in particular if the partition into is not aligned with all jumps in the coefficients. The theoretical analysis traces this lack of robustness back to the so called stable splitting property. In this work we propose to solve a generalized eigenvalue problem in each subdomain which identifies which vectors are responsible for violating the stable splitting property. These vectors are used to span the coarse space and taken care of by a direct solve while all remaining components behave well. The result is a condition number estimate for the two level method which does not depend on the number of subdomains or any jumps in the coefficients.

UR - http://www.scopus.com/inward/record.url?scp=84910647594&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1007/978-3-319-05789-7_42

UR - http://dd21.inria.fr/index.php?url=DD21_proceedings

U2 - 10.1007/978-3-319-05789-7_42

DO - 10.1007/978-3-319-05789-7_42

M3 - Chapter

SN - 9783319057880

VL - 98

T3 - Lecture Notes in Computational Science and Engineering

SP - 447

EP - 455

BT - Domain Decomposition Methods in Science and Engineering XXI

A2 - Erhel , Jocelyne

A2 - Gander , Martin J

A2 - Halpern , Laurence

A2 - Pichot , Geraldine

A2 - Sassi , Taiufik

A2 - Widlund , Olof

PB - Springer

ER -