### Abstract

The importance of using coarse components, and thus at least one additional level, in the design of domain decomposition methods has been understood for at least twenty years. For many problems of interest, such a device, which provides at least a minimal amount of global transfer of information in each step, is necessary in order to obtain convergence rates which are independent of the number of subdomains. An historical overview, colored by the scientific history of its author, is given of the development of such coarse components of the domain decomposition algorithms. These algorithms are all preconditioned conjugate gradient methods or they are accelerated by using some alternative Krylov space method. The preconditioners are built from solvers of the given problem restricted to subdomains and a coarse approximation which often can be quite exotic.

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

Pages | 241-248 |

Number of pages | 8 |

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
- Modeling and Simulation
- Control and Optimization
- Discrete Mathematics and Combinatorics

### Cite this

*Domain Decomposition Methods in Science and Engineering XVIII*(Vol. 70 LNCSE, pp. 241-248). (Lecture Notes in Computational Science and Engineering; Vol. 70 LNCSE). https://doi.org/10.1007/978-3-642-02677-5_26

**The development of coarse spaces for domain decomposition algorithms.** / 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. 241-248, 18th International Conference of Domain Decomposition Methods, Jerusalem, Israel, 1/12/08. https://doi.org/10.1007/978-3-642-02677-5_26

}

TY - GEN

T1 - The development of coarse spaces for domain decomposition algorithms

AU - Widlund, Olof B.

PY - 2009

Y1 - 2009

N2 - The importance of using coarse components, and thus at least one additional level, in the design of domain decomposition methods has been understood for at least twenty years. For many problems of interest, such a device, which provides at least a minimal amount of global transfer of information in each step, is necessary in order to obtain convergence rates which are independent of the number of subdomains. An historical overview, colored by the scientific history of its author, is given of the development of such coarse components of the domain decomposition algorithms. These algorithms are all preconditioned conjugate gradient methods or they are accelerated by using some alternative Krylov space method. The preconditioners are built from solvers of the given problem restricted to subdomains and a coarse approximation which often can be quite exotic.

AB - The importance of using coarse components, and thus at least one additional level, in the design of domain decomposition methods has been understood for at least twenty years. For many problems of interest, such a device, which provides at least a minimal amount of global transfer of information in each step, is necessary in order to obtain convergence rates which are independent of the number of subdomains. An historical overview, colored by the scientific history of its author, is given of the development of such coarse components of the domain decomposition algorithms. These algorithms are all preconditioned conjugate gradient methods or they are accelerated by using some alternative Krylov space method. The preconditioners are built from solvers of the given problem restricted to subdomains and a coarse approximation which often can be quite exotic.

UR - http://www.scopus.com/inward/record.url?scp=78651573016&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78651573016&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-02677-5_26

DO - 10.1007/978-3-642-02677-5_26

M3 - Conference contribution

SN - 9783642026768

VL - 70 LNCSE

T3 - Lecture Notes in Computational Science and Engineering

SP - 241

EP - 248

BT - Domain Decomposition Methods in Science and Engineering XVIII

ER -