A new parallel preconditioning algorithm for 3D nonconforming FEM elasticity systems is presented. The preconditioner is constructed in two steps. First displacement decomposition of the stiffness matrix is used. Than MIC(0) factorization is applied to a proper auxiliary M-matrix to get an approximate factorization of the obtained blockdiagonal matrix. The auxiliary matrix has a special block s...

Coincidence detection in visual and auditory cortex may also be critical for feature analysis in somatosensory cortex. We examined its role in the rat postero-medial barrel subfield (PMBSF) using high-resolution arrays of epipial electrodes. Five vibrissae, forming an arc, row, or diagonal, were simultaneously or asynchronously stimulated to simulate contact with a straight edge of different an...

How can one justify the secession of a territory from a liberal-democratic state of the kind currently prevalent in North America and Western Europe? The question does not primarily concern a mutually agreed secession, such as that of Norway from the United Kingdoms of Norway and Sweden in 1905. If the government and legislature of the ‘parent state’ freely agree to a secession of a part of its...

A methodology for preconditioning discrete stress analysis systems using robust scalar algebraic multigrid (AMG) solvers is evaluated in the context of problems that arise in microfabrication technology. The principle idea is to apply an AMG solver in a segregated way to the series of scalar block matrix problems corresponding to different displacement vector components, thus yielding a block d...

Consider the square [0, n] with points from a Poisson point process of intensity 1 distributed within it. In [4] it was shown that the length Ln of a maximal increasing path (an increasing path that contains the most number of points) when properly centered and scaled converges to the Tracy-Widom distribution. Later [16] showed that all maximal paths have a displacement of n 2 3 +o(1) from the ...

The numerical solution of 3D linear elasticity equations is considered. The problem is described by a coupled system of second-order elliptic partial differential equations. This system is discretized by trilinear parallelepipedal finite elements. The preconditioned conjugate gradient iterative method is used for solving of the large-scale linear algebraic systems arising after the finite eleme...

The numerical solution of 3D linear elasticity equations is considered. The problem is described by a coupled system of second order elliptic partial differential equations. This system is discretized by trilinear parallelepipedal finite elements. The Preconditioned Conjugate Gradient iterative method is used for solving of the large-scale linear algebraic systems arising after the Finite Eleme...

In this paper a non-diagonal regulator, based on the QFT method, is synthesized for an uncertain MIMO plant whose output and control signals are subjected to hard time-domain constraints. This procedure includes the design of a non-diagonal pre-controller based on a new simple approach, followed by the sequential design of a diagonal QFT controller. We present a new formulation for the latter s...

In an earlier paper [GKO95] we exploited the displacement structure of Cauchy-like matrices to derive for them a fast O(n) implementation of Gaussian elimination with partial pivoting. One application is to the rapid and numerically accurate solution of linear systems with Toeplitzlike coe cient matrices, based on the fact that the latter can be transformed into Cauchy-like matrices by using th...

The Cauchy-Born rule postulates that when a monatomic crystal is subjected to a small linear displacement of its boundary, then all atoms will follow this displacement. In the absence of previous mathematical results, we study the validity of this rule in the model case of a 2D cubic lattice interacting via harmonic springs between nearest and diagonal neighbours. Our main result is that for fa...