DOMAIN DECOMPOSITION WITH NONMATCHING GRIDS - AUGMENTED LAGRANGIAN APPROACH

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.