A family of energy minimizing coarse spaces for overlapping schwarz preconditioners

Clark R. Dohrmann, Axel Klawonn, Olof B. Widlund

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

Abstract

A simple and effective approach is presented to construct coarse spaces for overlapping Schwarz preconditioners. The approach is based on energy minimizing extensions of coarse trace spaces, and can be viewed as a generalization of earlier work by Dryja, Smith, and Widlund. The use of these coarse spaces in overlapping Schwarz preconditioners leads to condition numbers bounded by C(1 + H/δ)(1 + log(H/h)) for certain problems when coefficient jumps are aligned with subdomain boundaries. For problems without coefficient jumps, it is possible to remove the log(H/h) factor in this bound by a suitable enrichment of the coarse space. Comparisons are made with the coarse spaces of two other substructuring preconditioners. Numerical examples are also presented for a variety of problems.

Original languageEnglish (US)
Title of host publicationDomain Decomposition Methods in Science and Engineering XVII
Pages247-254
Number of pages8
Volume60
DOIs
StatePublished - 2008
Event17th International Conference on Domain Decomposition Methods - St. Wolfgang /Strobl, Austria
Duration: Jul 3 2006Jul 7 2006

Publication series

NameLecture Notes in Computational Science and Engineering
Volume60
ISSN (Print)14397358

Other

Other17th International Conference on Domain Decomposition Methods
CountryAustria
CitySt. Wolfgang /Strobl
Period7/3/067/7/06

Fingerprint

Preconditioner
Overlapping
Energy
Jump
Substructuring
Coefficient
Condition number
Trace
Family
Numerical Examples

ASJC Scopus subject areas

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

Cite this

Dohrmann, C. R., Klawonn, A., & Widlund, O. B. (2008). A family of energy minimizing coarse spaces for overlapping schwarz preconditioners. In Domain Decomposition Methods in Science and Engineering XVII (Vol. 60, pp. 247-254). (Lecture Notes in Computational Science and Engineering; Vol. 60). https://doi.org/10.1007/978-3-540-75199-1_28

A family of energy minimizing coarse spaces for overlapping schwarz preconditioners. / Dohrmann, Clark R.; Klawonn, Axel; Widlund, Olof B.

Domain Decomposition Methods in Science and Engineering XVII. Vol. 60 2008. p. 247-254 (Lecture Notes in Computational Science and Engineering; Vol. 60).

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

Dohrmann, CR, Klawonn, A & Widlund, OB 2008, A family of energy minimizing coarse spaces for overlapping schwarz preconditioners. in Domain Decomposition Methods in Science and Engineering XVII. vol. 60, Lecture Notes in Computational Science and Engineering, vol. 60, pp. 247-254, 17th International Conference on Domain Decomposition Methods, St. Wolfgang /Strobl, Austria, 7/3/06. https://doi.org/10.1007/978-3-540-75199-1_28
Dohrmann CR, Klawonn A, Widlund OB. A family of energy minimizing coarse spaces for overlapping schwarz preconditioners. In Domain Decomposition Methods in Science and Engineering XVII. Vol. 60. 2008. p. 247-254. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-540-75199-1_28
Dohrmann, Clark R. ; Klawonn, Axel ; Widlund, Olof B. / A family of energy minimizing coarse spaces for overlapping schwarz preconditioners. Domain Decomposition Methods in Science and Engineering XVII. Vol. 60 2008. pp. 247-254 (Lecture Notes in Computational Science and Engineering).
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