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Mathematics of Computation

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Substructuring preconditioners for the three fields domain decomposition method

Author: Silvia Bertoluzza
Journal: Math. Comp. 73 (2004), 659-689
MSC (2000): Primary 65N55, 65N22
Published electronically: October 17, 2003
MathSciNet review: 2031400
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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.

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Silvia Bertoluzza
Affiliation: Istituto di Matematica Applicata e Tecnologie Informatiche del Consiglio Nazionale delle Ricerche, v. Ferrata 1, 27100 Pavia, Italy

Keywords: Three fields formulation, domain decomposition, stabilized methods, preconditioning
Received by editor(s): November 6, 2000
Received by editor(s) in revised form: February 22, 2002
Published electronically: October 17, 2003
Article copyright: © Copyright 2003 American Mathematical Society