FETI‐DP: a dual–primal unified FETI method—part I: A faster alternative to the two‐level FETI method

Abstract

SUMMARYThe 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 ÿeld at these speciÿc 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 uniÿes 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. Copyright ? 2001 John Wiley & Sons, Ltd.KEY WORDS: domain decomposition; numerical scalability; iterative methods BACKGROUNDThe ÿnite element tearing and interconnecting (FETI) methods are a family of domain decomposition (DD) algorithms with Lagrange multipliers that have been developed during the last decade for the fast sequential and parallel iterative solution of large-scale systems of equations arising from the ÿnite element discretization of partial di erential equations. From a mechanical viewpoint, a FETI method can be viewed as an iterative substructuring method where Lagrange multipliers are introduced at the substructure interfaces to enforce the continuity of the displacement ÿeld. By

Scattered Field Computation With an Extended Feti-Dpem2 Method

“…In addition, in order to further improve the convergence of the iterative process and the scalability of the method, one can notice the existence of two techniques: the first one uses the plane wave spectrum operator [21], the second one uses dual-primal techniques which can be seen as coarse grid corrections [22,26,28,36]. In this last method, the corner nodes in 2D or the corner edges in 3D (we denote by "corner" the geometrical entities which belong to more than two subdomains) are extracted from each subdomain and are globally and uniquely numbered.…”

An Overview of Scalable FETI—DP Algorithms for Variational Inequalities

“…After introducing a socalled "natural coarse grid", Farhat, Mandel and Roux [13] modified the basic FETI method to obtain a numerically scalable algorithm. A similar result was achieved by the Dual-Primal FETI method (FETI-DP) introduced by Farhat et al [12]; see also [15]. In this paper, we use the FETI-DP method to develop scalable algorithms for the numerical solution of elliptic variational inequalities.…”

On the Applicability of Lions’ Energy Estimates in the Analysis of Discrete Optimized Schwarz Methods with Cross Points

“…Thus, it suffices to introduce one extra variable (typically a coarse-grid basis function that has the value one at the cross point), and the PDE constraint is used as part of the coarse problem. This approach is similar to FETI-DP [3], except it is usually formulated with Neumann rather than Robin traces. 2.…”