In this note, we discuss iterative substructuring methods for a scalar elliptic model problem with a strongly varying diffusion coefficient that is typically discontinuous and exhibits large jumps. Opposed to earlier theory, we treat the case where the jumps happen on a small spatial scale and can in general not be resolved by a domain decomposition. We review the available theory of FETI metho...

Iterative substructuring methods with Lagrange multipliers for elliptic problems are considered. The algorithms belong to the family of dual-primal FETI methods which were introduced for linear elasticity problems in the plane by Farhat et al. [2001] and were later extended to three dimensional elasticity problems by Farhat et al. [2000]. Recently, the family of algorithms for scalar diffusion ...

In this paper, certain iterative substructuring methods with Lagrange multipliers are considered for elliptic problems in three dimensions. The algorithms belong to the family of dual{ primal FETI methods which have recently been introduced and analyzed successfully for elliptic problems in the plane. The family of algorithms for three dimensions is extended and a full analysis is provided for ...

Dual-Primal FETI methods are nonoverlapping domain decomposition methods where some of the continuity constraints across subdomain boundaries are required to hold throughout the iterations, as in primal iterative substructuring methods, while most of the constraints are enforced by Lagrange multipliers, as in one-level FETI methods. The purpose of this article is to develop strategies for selec...

In our earlier work [4], a dual iterative substructuring method for two dimensional problems was proposed, which is a variant of the FETI-DP method. The proposed method imposes continuity on the interface by not only the pointwise matching condition but also uses a penalty term which measures the jump across the interface. For a large penalization parameter, it was proven that the condition num...

FETI 205 A conforming FEM for (2.7) results in the discrete optimality system   K1 0 B T 1 0 0 K̃2 −B2 −C2 Υ B1 −B2 0 0 0 −ΥC2 0 Υ     u1 u2 λ μ   =   f1 f2 0 0   (2.8) where K̃2 ≡ K2 +C2 ΥC2. Elimination of the primal variables in (2.8) results in the coarse grid problem [ B1K −1 1 B T 1 +B2K̃ −1 2 B T 2 B2K̃ −1 2 C T 2 Υ ΥC2K̃ −1 2 B T 2 ΥC2K̃ −1 2 C T 2 Υ−Υ ] [ λ μ ] = [ d1 d1 ] ...

A special finite element method based on approximate component mode synthesis (ACMS) was introduced in [U. Hetmaniuk, R. Lehoucq, A special finite element method based on component mode synthesis, ESAIM: Mathematical Modelling and Numerical Analysis, 44 (2010), 401-420]. ACMS was developed for second order elliptic partial differential equations with rough or highly varying coefficients. Here, ...