A domain decomposition algorithm, similar to classical iterative substructuring algorithms, is presented for two-dimensional problems in the space H0(curl; Ω). It is defined in terms of a coarse space and local subspaces associated with individual edges of the subdomains into which the domain of the problem has been subdivided. The algorithm differs from others in three basic respects. First, i...

In the past two decades, the FETI method introduced in [10] and its variants have become a class of popular methods for the parallel solution of large-scale finite element problems, see e.g. [11], [9], [14], [15], [8]. A key ingredient in this class of methods is a good preconditioner for the dual Schur complement system whose operator is a weighted sum of subdomain Neumann to Dirichlet (NtD) m...

Semi-definite problems are encountered in a wide variety of engineering problems. Most domain decomposition methods efficient for parallel computing are based on iterative schemes and rarely address the problem of checking the problem’s singularity and computing the null space. In this paper we present a simple and efficient method for checking the singularity of an operator and for computing a...

The active set based MPRGP (modified proportioning with reduced gradient projection) [1] for the solution of partially bound constrained quadratic programming problems turned out to be an important ingredient in development of scalable algorithms for the solution of variational inequalities by FETI [3] and BETI [4] domain decomposition methods. The algorithm was proved to have R-linear rate of ...

Most of computations (subdomain problems) appearing in FETI-type methods are purely local and therefore parallelizable without any data transfers. However, if we want to accelerate also dual actions, some communication is needed due to primal-dual transition. Distribution of primal matrices is quite straightforward. Each of cores works with local part associated with its subdomains. A natural e...

Measurements of the superconducting transition temperatures for Al-doped, Cdoped and neutron-damaged-annealed MgB2 samples under pressure up to ∼ 8 kbar are presented. The dTc/dP values change systematically with the decrease of the ambient pressure Tc in a regular fashion. The evolution of the pressure derivatives can be understood assuming that the change in phonon spectrum is a dominant cont...

FETI205 A conforming FEM for (2.7) results in the discrete optimality system K1 0 BT1 00 K̃2−B2 −C2 ΥB1 −B2 0 00−ΥC2 0 Υ  u1u2λμ = f1f200(2.8) where K̃2 ≡ K2+C2 ΥC2.Elimination of the primal variables in (2.8) results in the coarse grid problem[B1K−11 B T1 +B2K̃−12 ...