A Preconditioner for the FETI-DP Formulation with Mortar Methods in Two Dimensions

In this paper, we consider a dual-primal FETI (FETI-DP) method for elliptic problems on nonmatching grids. The FETI-DP method is a domain decomposition method that uses Lagrange multipliers to match solutions continuously across subdomain boundaries in the sense of dual-primal variables. We use the mortar matching condition as the continuity constraints for the FETI-DP formulation. We construct a preconditioner for the FETI-DP operator and show that the condition number of the preconditioned FETI-DP operator is bounded by C max i=1,... ,N {(1 + log (Hi/hi))}, where Hi and hi are sizes of domain and mesh for each subdomain, respectively, and C is a constant independent of Hi’s and hi’s. We allow jumps of coefficients of elliptic problems across subdomain boundaries. Numerical results are included.