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...

The FETI-DP domain decomposition method is extended to address the iterative solution of a class of indefinite problems of the form (K−σM)x = b, and a class of complex problems of the form (K − σM + iσD)x = b, where K, M, and D are three real symmetric positive semi-definite matrices arising from the finite element discretization of either second-order elastodynamic problems or fourth-order pla...