The development of coarse spaces for domain decomposition algorithms

Olof B. Widlund

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publicationDomain Decomposition Methods in Science and Engineering XVIII
Pages241-248
Number of pages8
Volume70 LNCSE
DOIs
StatePublished - 2009
Event18th International Conference of Domain Decomposition Methods - Jerusalem, Israel
Duration: Jan 12 2008Jan 17 2008

Publication series

NameLecture Notes in Computational Science and Engineering
Volume70 LNCSE
ISSN (Print)14397358

Other

Other18th International Conference of Domain Decomposition Methods
CountryIsrael
CityJerusalem
Period1/12/081/17/08

Fingerprint

Decomposition Algorithm
Domain Decomposition
Decomposition
Domain decomposition methods
Preconditioned Conjugate Gradient Method
Conjugate gradient method
Domain Decomposition Method
Preconditioner
Convergence Rate
Necessary
Alternatives
Approximation
History
Design

ASJC Scopus subject areas

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

Cite this

Widlund, O. B. (2009). The development of coarse spaces for domain decomposition algorithms. In 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.

Domain Decomposition Methods in Science and Engineering XVIII. Vol. 70 LNCSE 2009. p. 241-248 (Lecture Notes in Computational Science and Engineering; Vol. 70 LNCSE).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Widlund, OB 2009, The development of coarse spaces for domain decomposition algorithms. in 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
Widlund OB. The development of coarse spaces for domain decomposition algorithms. In Domain Decomposition Methods in Science and Engineering XVIII. Vol. 70 LNCSE. 2009. p. 241-248. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-642-02677-5_26
Widlund, Olof B. / The development of coarse spaces for domain decomposition algorithms. Domain Decomposition Methods in Science and Engineering XVIII. Vol. 70 LNCSE 2009. pp. 241-248 (Lecture Notes in Computational Science and Engineering).
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