FETI-DP: A dual-primal unified FETI method part I: A faster alternative to the two-level FETI method

The FETI method and its two-level extension (FETI-2) are two numerically scalable domain decomposition methods with Lagrange multipliers for the iterative solution of second-order solid mechanics and fourth-order beam, plate and shell structural problems, respectively. The FETI-2 method distinguishes itself from the basic or one-level FETI method by a second set of Lagrange multipliers that are introduced at the subdomain cross-points to enforce at each iteration the exact continuity of a subset of the displacement field at these specific locations. In this paper, we present a dual-primal formulation of the FETI-2 concept that eliminates the need for that second set of Lagrange multipliers, and unifies all previously developed one-level and two-level FETI algorithms into a single dual-primal FETI-DP method. We show that this new FETI-DP method is numerically scalable for both second-order and fourth-order problems. We also show that it is more robust and more computationally efficient than existing FETI solvers, particularly when the number of subdomains and/or processors is very large.