P. Letallec et T. Sassi, DOMAIN DECOMPOSITION WITH NONMATCHING GRIDS - AUGMENTED LAGRANGIAN APPROACH, Mathematics of computation, 64(212), 1995, pp. 1367-1396
We propose and study a domain decomposition method which treats the co
nstraint of displacement continuity at the interfaces by augmented Lag
rangian techniques and solves the resulting problem by a parallel vers
ion of the Peaceman-Rachford algorithm. We prove that this algorithm i
s equivalent to the fictitious overlapping method introduced by P.L. L
ions. We also prove its linear convergence independently of the discre
tization step h, even if the finite element grids do not match at the
interfaces. A new preconditioner using fictitious overlapping and well
adapted to three-dimensional elasticity problems is also introduced a
nd is validated on several numerical examples.