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Lower bounds for nonoverlapping domain decomposition preconditioners in two dimensions


Authors: Susanne C. Brenner and Li-Yeng Sung
Journal: Math. Comp. 69 (2000), 1319-1339
MSC (1991): Primary 65N55, 65N30
Published electronically: April 12, 2000
MathSciNet review: 1710656
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Abstract:

Lower bounds for the condition numbers of the preconditioned systems are obtained for the Bramble-Pasciak-Schatz substructuring preconditioner and the Neumann-Neumann preconditioner in two dimensions. They show that the known upper bounds are sharp.


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Additional Information

Susanne C. Brenner
Affiliation: Department of Mathematics, University of South Carolina, Columbia, SC 29208
Email: brenner@math.sc.edu

Li-Yeng Sung
Affiliation: Department of Mathematics, University of South Carolina, Columbia, SC 29208
Email: sung@math.sc.edu

DOI: https://doi.org/10.1090/S0025-5718-00-01236-9
Keywords: Lower bounds, nonoverlapping domain decomposition preconditioners, Bramble-Pasciak-Schatz, Neumann-Neumann, two dimensions
Received by editor(s): May 22, 1998
Published electronically: April 12, 2000
Additional Notes: The work of the first author was supported in part by the National Science Foundation under Grant No. DMS-96-00133.
Article copyright: © Copyright 2000 American Mathematical Society