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 ...

We consider FETI-DP solvers (see Farhat et al. [2001], Mandel and Tezaur [2001], Klawonn et al. [2002]) for the fast (and parallel) solution of this system, and we follow the structure described in [Toselli and Widlund, 2005, Sect 6.4]. To this end, we partition the domain Ω into non-overlapping subdomains Ωi, i = 1, . . . ,N such that the global mesh T (Ω) resolves the interface ⋃ i 6= j ∂Ωi∩ ...