Ab initio molecular dynamics, supported by inelastic neutron scattering and nuclear resonant inelastic x-ray scattering, showed an anomalous thermal softening of the M_{5}^{-} phonon mode in B2-ordered FeTi that could not be explained by phonon-phonon interactions or electron-phonon interactions calculated at low temperatures. A computational investigation showed that the Fermi surface undergoe...

We shall first briefly review our results related to solving of the convex box constrained quadratic programming problems by combination of the active set strategy and the conjugate gradient method with projections [1]. In particular, we shall show that with proper modification of the proportioning algorithm with projection [2], it is possible give the rate of convergence in terms of the spectr...

The FETI-DP algorithms, proposed by the authors in [SIAM J. Numer. Anal., 51 (2013), pp. 1235–1253] and [Internat. J. Numer. Methods Engrg., 94 (2013), pp. 128–149] for solving incompressible Stokes equations, are extended to three-dimensional problems. A new analysis of the condition number bound for using the Dirichlet preconditioner is given. The algorithm and analysis are valid for mixed fi...

In the theory for domain decomposition algorithms of the iterative substructuring family, each subdomain is typically assumed to be the union of a few coarse triangles or tetrahedra. This is an unrealistic assumption, in particular if the subdomains result from the use of a mesh partitioner, in which case they might not even have uniformly Lipschitz continuous boundaries. The purpose of this st...

We propose adaptive selection of the coarse space of the BDDC and FETI-DP iterative substructuring methods by adding coarse degrees of freedom (dofs) on faces between substructures constructed using eigenvectors associated with the faces. Provably the minimal number of coarse dofs on the faces is added to decrease the condition number estimate under a target value specified a priori. It is assu...

A BDDC (balancing domain decomposition by constraints) method is developed for elliptic equations, with discontinuous coefficients, discretized by mortar finite element methods for geometrically nonconforming partitions in both two and three space dimensions. The coarse component of the preconditioner is defined in terms of one mortar constraint for each edge/face, which is the intersection of ...

Convergence theories and a deluxe dual and primal finite element tearing and interconnecting algorithm are developed for a hybrid staggered DG finite element approximation of H(curl) elliptic problems in two dimensions. In addition to the advantages of staggered DG methods, the basis functions of the new hybrid staggered DG method are all locally supported in the triangular elements, and a Lagr...

The Finite Element Tearing and Interconnecting (FETI) method is an iterative substructuring method using Lagrange multipliers to enforce the continuity of the nite element solution across the subdomain interface. Mortar nite elements are nonconforming nite elements that allow for a geometrically nonconforming decomposition of the computational domain into subregions and, at the same time, for t...

A distributed optimal control problem with the constraint of a linear elliptic partial differential equation is considered. A necessary optimality condition for this problem forms a saddle point system, the efficient and accurate solution of which is crucial. A new factorization of the Schur complement for such a system is proposed and its characteristics discussed. The factorization introduces...

We consider the coupling across an interface of a fluid flow and a porous media flow. The differential equations involve Stokes equations in the fluid region and Darcy equations in the porous region, and a coupling through an interface with Beaver-Joseph-Saffman transmission conditions. The discretization consists of P2/P1 triangular Taylor-Hood finite elements in the fluid region, the lowest o...