After a short historical review, we present four popular substructuring methods: FETI-1, BDD, FETI-DP, BDDC, and derive the primal versions to the two FETI methods, called PFETI-1 and P-FETI-DP, as proposed by Fragakis and Papadrakakis. The formulation of the BDDC method shows that it is the same as P-FETI-DP and the same as a preconditioner introduced by Cros. We prove the equality of eigenval...

FETI-DP method is a substructuring method that uses Lagrange multipliers to match the continuity condition on the subdomain boundaries. For the FETI-DP method on nonmatching grids, two different formulations are known with respect to how to employ the mortar matching condition. Keeping step with the developments of the FETI-DP methods, a variety of preconditioners for the FETI-DP operator have ...

A simple explicit-implicit FETI transient analysis procedure is presented, which utilizes the same basic FETI solver developed for static structural analysis problems. A key concept for the present algorithm is to integrate d’Alembert-Lagrange principal equations, viz., the domain-by-domain floating dynamic selfequilibrium equations, by an explicit algorithm. The remaining deformation modes are...

We consider a FETI-DP formulation of the Stokes problem with mortar methods. To solve the Stokes problem correctly and efficiently, redundant continuity constraints are introduced. Lagrange multipliers corresponding to the redundant constraints are treated as primal variables in the FETI-DP formulation. We propose a preconditioner for the FETI-DP operator and show that the condition number of t...

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...

We first review our recent results concerning optimal algorithms for the solution of bound and/or equality constrained quadratic programming problems. The unique feature of these algorithms is the rate of convergence in terms of bounds on the spectrum of the Hessian of the cost function. Then we combine these estimates with some results on the FETI method (FETI-DP, FETI and Total FETI) to get t...

The Balanced Domain Decomposition (BDD) method and the Finite Element Tearing and Interconnecting (FETI) method are two commonly used non-overlapping domain decomposition methods. Due to strong theoretical and numerical similarities, these two methods are generally considered as being equivalently efficient. However, for some particular cases, such as for structures with strong heterogeneities,...

The solution of nonlinear problems, e.g., in material science requires fast and highly scalable parallel solvers. FETI-DP (Finite Element Tearing and Interconnecting) domain decomposition methods are parallel solution methods for implicit problems discretized by finite elements. Recently, nonlinear versions of the well-known FETI-DP methods for linear problems have been introduced. In these met...

Domain Decomposition methods often exhibit very poor performance when applied to engineering problems with large heterogeneities. In particular for heterogeneities along domain interfaces the iterative techniques to solve the interface problem are lacking an efficient preconditioner. Recently a robust approach, named FETI-Geneo, was proposed where troublesome modes are precomputed and deflated ...

Iron and titanium form two known stable intermetallic compounds, FeTi and Fe2Ti. exists above 1000°C , decomposing to FeTi and T i below that temperature. We have briefly noted previousl;’ that one of these compounds, FeTi, will react directly with hydrogen to form a n easily decomposed hydride which may be useful as a hydrogen storage medium. Our primary purpose here is to discuss the Fe-Ti-H ...