### Abstract

In the theory for domain decomposition methods, it has previously often been assumed that each subdomain is the union of a small set of coarse shape-regular triangles or tetrahedra. Recent progress is reported, which makes it possible to analyze cases with irregular subdomains such as those produced by mesh partitioners. The goal is to extend the analytic tools so that they work for problems on subdomains that might not even be Lipschitz and to characterize the rates of convergence of domain decomposition methods in terms of a few, easy to understand, geometric parameters of the subregions. For two dimensions, some best possible results have already been obtained for scalar elliptic and compressible and almost incompressible linear elasticity problems; the subdomains should be John or Jones domains and the rates of convergence are determined by parameters that characterize such domains and that of an isoperimetric inequality. Technical issues for three dimensional problems are also discussed.

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

Pages | 87-98 |

Number of pages | 12 |

Volume | 70 LNCSE |

DOIs | |

State | Published - 2009 |

Event | 18th International Conference of Domain Decomposition Methods - Jerusalem, Israel Duration: Jan 12 2008 → Jan 17 2008 |

### Publication series

Name | Lecture Notes in Computational Science and Engineering |
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Volume | 70 LNCSE |

ISSN (Print) | 14397358 |

### Other

Other | 18th International Conference of Domain Decomposition Methods |
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Country | Israel |

City | Jerusalem |

Period | 1/12/08 → 1/17/08 |

### 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 XVIII*(Vol. 70 LNCSE, pp. 87-98). (Lecture Notes in Computational Science and Engineering; Vol. 70 LNCSE). https://doi.org/10.1007/978-3-642-02677-5_8

**Accomodating irregular subdomains in domain decomposition theory.** / Widlund, Olof B.

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

*Domain Decomposition Methods in Science and Engineering XVIII.*vol. 70 LNCSE, Lecture Notes in Computational Science and Engineering, vol. 70 LNCSE, pp. 87-98, 18th International Conference of Domain Decomposition Methods, Jerusalem, Israel, 1/12/08. https://doi.org/10.1007/978-3-642-02677-5_8

}

TY - GEN

T1 - Accomodating irregular subdomains in domain decomposition theory

AU - Widlund, Olof B.

PY - 2009

Y1 - 2009

N2 - In the theory for domain decomposition methods, it has previously often been assumed that each subdomain is the union of a small set of coarse shape-regular triangles or tetrahedra. Recent progress is reported, which makes it possible to analyze cases with irregular subdomains such as those produced by mesh partitioners. The goal is to extend the analytic tools so that they work for problems on subdomains that might not even be Lipschitz and to characterize the rates of convergence of domain decomposition methods in terms of a few, easy to understand, geometric parameters of the subregions. For two dimensions, some best possible results have already been obtained for scalar elliptic and compressible and almost incompressible linear elasticity problems; the subdomains should be John or Jones domains and the rates of convergence are determined by parameters that characterize such domains and that of an isoperimetric inequality. Technical issues for three dimensional problems are also discussed.

AB - In the theory for domain decomposition methods, it has previously often been assumed that each subdomain is the union of a small set of coarse shape-regular triangles or tetrahedra. Recent progress is reported, which makes it possible to analyze cases with irregular subdomains such as those produced by mesh partitioners. The goal is to extend the analytic tools so that they work for problems on subdomains that might not even be Lipschitz and to characterize the rates of convergence of domain decomposition methods in terms of a few, easy to understand, geometric parameters of the subregions. For two dimensions, some best possible results have already been obtained for scalar elliptic and compressible and almost incompressible linear elasticity problems; the subdomains should be John or Jones domains and the rates of convergence are determined by parameters that characterize such domains and that of an isoperimetric inequality. Technical issues for three dimensional problems are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=78651586748&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78651586748&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-02677-5_8

DO - 10.1007/978-3-642-02677-5_8

M3 - Conference contribution

SN - 9783642026768

VL - 70 LNCSE

T3 - Lecture Notes in Computational Science and Engineering

SP - 87

EP - 98

BT - Domain Decomposition Methods in Science and Engineering XVIII

ER -