Substructuring Preconditioners for the Three Fields Domain
Decomposition Method
S. Bertoluzza
We study a class of preconditioners based on substructuring, for the discrete
Steklov-Poincare 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 the square of log(H/h)
(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.
Pubbl. I.A.N. n 1192 (2000)
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