Substructuring preconditioners for the three fields domain decomposition method
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Abstract:
We study a class of preconditioners based on substructuring, for the discrete Steklov-Poincaré operator arising in the three fields formulation of domain decomposition in two dimensions. Under extremely general assumptions on the discretization spaces involved, an upper bound is provided on the condition number of the preconditioned system, which is shown to grow at most as $\log (H/h)^2$ ($H$ and $h$ denoting, respectively, the diameter and the discretization mesh-size of the subdomains). Extensive numerical tests—performed on both a plain and a stabilized version of the method—confirm the optimality of such bound.References
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Additional Information
- Silvia Bertoluzza
- Affiliation: Istituto di Matematica Applicata e Tecnologie Informatiche del Consiglio Nazionale delle Ricerche, v. Ferrata 1, 27100 Pavia, Italy
- Email: silvia.bertoluzza@imati.cnr.it
- Received by editor(s): November 6, 2000
- Received by editor(s) in revised form: February 22, 2002
- Published electronically: October 17, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp. 73 (2004), 659-689
- MSC (2000): Primary 65N55, 65N22
- DOI: https://doi.org/10.1090/S0025-5718-03-01550-3
- MathSciNet review: 2031400