A preconditioner for the FETI-DP formulation with mortar methods in two dimensions

Abstract

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 (H-i/h(i)))(2)}, where H-i and h(i) are sizes of domain and mesh for each subdomain, respectively, and C is a constant independent of H-i's and h(i)'s. We allow jumps of coefficients of elliptic problems across subdomain boundaries. Numerical results are included.