Abstract. In this paper, a FETI-DP formulation for the three dimensional elasticity problem on non-matching grids over a geometrically conforming subdomain partition is considered. To resolve the nonconformity of the finite elements, a mortar matching condition on the subdomain interfaces (faces) is imposed. By introducing Lagrange multipliers for the mortar matching constraints, the resulting ...

In this article we give a new rigorous condition number estimate of the finite element tearing and interconnecting (FETI) method and a variant thereof, all-floating FETI. We consider the scalar elliptic equation in a twoor three-dimensional domain with a highly heterogeneous (multiscale) diffusion coefficient. This coefficient is allowed to have large jumps not only across but also along subdom...

In this article we give a new rigorous condition number estimate of the finite element tearing and interconnecting (FETI) method and a variant thereof, all-floating FETI. We consider the scalar elliptic equation in a twoor three-dimensional domain with a highly heterogeneous (multiscale) diffusion coefficient. This coefficient is allowed to have large jumps not only across but also along subdom...

Iterative substructuring methods with Lagrange multipliers for the elliptic system of linear elasticity are considered. The algorithms belong to the family of dual-primal FETI methods which was introduced for linear elasticity problems in the plane by Farhat et al. [2001] and then extended to three dimensional elasticity problems by Farhat et al. [2000]. In dual-primal FETI methods, some contin...

Robust FETI-DP methods for heterogeneous, linear elasticity problems in three dimensions were developed and analyzed in Klawonn and Widlund [2004]. For homogeneous problems or materials with only small jumps in the Young moduli, the primal constraints can be chosen as edge averages of the displacement components over well selected edges; see Klawonn and Widlund [2004] and for numerical experime...

FETI 3 Theorem 2.1 (u1, u2, λ) solves (2.4) if and only if (u1, u2, λ, μ = c(u2)) solves (2.7). Proof. The theorem is easily established by using the stabilized constraints (2.5) and recalling that τ = 0. The theorem demonstrates that (2.5) represents a consistent stabilization. The impact of this innocuous sleight of hand is that the resulting coarse grid problem is equivalently stabilized. We...

Theoretical and experimental results concerning a new FETI based algorithm for numerical solution of variational inequalities are reviewed. A discretized model problem is first reduced by the duality theory of convex optimization to the quadratic programming problem with bound and equality constraints. The latter is then optionally modified by means of orthogonal projectors to the natural coars...

Finite Element Tearing and Interconnecting (FETI) methods are a powerful approach to designing solvers for large-scale problems in computational mechanics. The numerical simulation problem is subdivided into a number of independent sub-problems, which are then coupled in appropriate ways. NURBS- (Non-Uniform Rational B-spline) based isogeometric analysis (IGA) applied to complex geometries requ...

Advanced High Strength Steels (AHSS) provide a good combination of both strength and formability and are therefore applied extensively in the automotive industry, especially in the crash relevant parts of the vehicle. Dual-phase (DP) steel is an example for such AHSS which is widely employed. The excellent macroscopic behavior of this steel is a result of the inherent micro-heterogeneity and co...