A Neumann-dirichlet Preconditioner for a Feti-dp Formulation with Mortar Methods

In this article, we review a dual-primal FETI (FETI-DP) method with mortar methods. The mortar matching condition is used as the continuity constraints for the FETI-DP formulation. A Neumann-Dirichlet preconditioner is investigated and it is shown that the condition number of the preconditioned FETI-DP operator for the two-dimensional elliptic problem is bounded by C maxi=1,...,N{(1 + log (Hi/hi))}, where Hi and hi are sizes of subdomain and mesh for each subdomain, respectively, and C is a constant independent of Hi and hi. For the three-dimensional elliptic problem and the two-dimensional Stokes problem, edge average constraints are further introduced as primal constraints to solve the problem correctly and to obtain a scalable FETI-DP algorithm. The Neumann-Dirichlet preconditioner is shown to give the same condition number bound as for the two-dimensional elliptic problem. For the three dimensional elasticity problem, a relatively large set of primal constraints, which include average and momentum constraints over interfaces (faces) as well as vertex constraints, is introduced. With the preconditioner, the same condition number bound is then obtained for the elasticity problems with discontinuous material parameters when only some faces are chosen as primal faces on which the average and momentum constraints is imposed.