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 eld at these speci c 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 uni es 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 e cient than existing FETI solvers, particularly when the number of subdomains and=or processors is very large