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
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)1439-7358

Other

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

ASJC Scopus subject areas

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

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    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 (pp. 247-254). (Lecture Notes in Computational Science and Engineering; Vol. 60). https://doi.org/10.1007/978-3-540-75199-1_28