Title: A FETI-DP formulation of three dimensional elasticity problems with mortar discretization

(NYU-CS-TR863)

Author:  Hyea Hyun Kim

Abstract:

In this paper, a FETI-DP formulation for the three dimensional elasticity problem on non-matching grids over a geometrically conforming subdomain partition is considered. To resolve the nonconformity of the finite elements, a mortar matching condition on the subdomain interfaces (faces) is imposed. By introducing Lagrange multipliers for the mortar matching constraints, the resulting linear system becomes similar to that of a FETI-DP method. In order to make the FETI-DP method efficient for solving this linear system, a relatively large set of primal constraints, which include average and momentum constraints over interfaces (faces) as well as vertex constraints, is introduced. A condition number bound $C(1+\text{log}(H/h))2$ for the FETI-DP formulation with a Neumann-Dirichlet preconditioner is then proved for the elasticity problems with discontinuous material parameters when only some faces are chosen as primal faces on which the average and momentum constraints will be imposed. An algorithm which selects a quite small number of primal faces is also discussed.