### 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 |

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) | 1439-7358 |

### Other

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

City | Jerusalem |

Period | 1/12/08 → 1/17/08 |

### ASJC Scopus subject areas

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

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## Cite this

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