A FETI-DP Formulation for Compressible Elasticity with Mortar Constraints

Abstract

A FETI-DP formulation for three dimensional elasticity problems on non-matching grids is considered. To resolve the nonconformity of the finite elements, a mortar matching condition is imposed on subdomain interfaces. The mortar matching condition are considered as weak continuity constraints in the FETIDP formulation. A relatively large set of primal constraints, which include average and moment constraints over interfaces (faces) as well as vertex constraints, is further introduced to achieve a scalable FETI-DP method. A condition number bound, C(1+log(H/h)), for the FETI-DP formulation with a Neumann-Dirichlet preconditioner is then proved for elasticity problems with discontinuous material parameters when the primal constraints are enforced on only some of the faces instead of all of them. These faces are called primal faces. An algorithm for selecting a quite small number of primal faces is described in [5].