This paper describes a modal analysis technique to approximate the vibrations of incompressible elastic solids using stabilized finite element method associated eigenvalue problem. It is explained why residual based formulations are not appropriate in this case, and formulation involving only pressure gradient employed. The effect stabilization term compared Galerkin approach detailed, both der...

It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A + |B|]$, we can create a new unique solvability condition for the absolute value equation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive deniteness of a certain point matrix...

We investigate the efficient computation of a few of the lowest eigenvalues of a symmetric eigenvalue problem occurring in quantum dynamical molecular simulations. The large sparse system of order n is highly structured such that its multiplication with a vector costs O(n logn) floating point operations only. We compare a number of eigensolvers: subspace iteration, two variants of the restarted...

In this paper, a detailed description of CG for evaluating eigenvalue problems by minimizing the Rayleigh quotient is presented from both theoretical and computational viewpoints. Three variants of CG together with their asymptotic behaviours and restarted schemes are discussed. In addition, it is shown that with a generally selected preconditioning matrix the actual performance of the PCG sche...

1. Abstract The present paper describes a solution to a non-parametric shape optimization problem of a brake model suppressing squeal noise. The brake model consists of a rotor and a pad between which the Coulomb friction occurs. A main problem is defined as a complex eigenvalue problem of the brake model obtained from the equation of motion. As an objective cost function, we use the positive r...

We derive a new formula for the asymptotic eigenvalue distribution of stiffness matrices obtained by applying P1 Finite Elements with standard mesh refinement to the semi elliptic PDE of second order in divergence form −∇(K∇Tu) = f on Ω, u = g on ∂Ω. Here Ω ⊂ R and K is supposed to be piecewise continuous and pointwise symmetric semi positive definite. The symbol describing this asymptotic eige...

A C++ code for the solution of the relativistic Hartree-Bogoliubov theory in coordinatespace is presented. The theory describes a nucleus as a relativistic system of baryons andmesons. The RHB model is applied in the self-consistent mean-field approximation to thedescription of ground state properties of spherical nuclei. Finite range interactions areincluded to describe pai...

Mathematics (ABSTRACT) This work is concerned with the construction of preconditioners for indefinite linear systems. The systems under investigation arise in the numerical solution of quadratic programming problems, for example in the form of Karush–Kuhn–Tucker (KKT) optimality conditions or in interior–point methods. Therefore, the system matrix is referred to as a KKT matrix. It is not the p...

Various methods have been developed for computing the correlation matrix nearest in the Frobenius norm to a given matrix. We focus on a quadratically convergent Newton algorithm recently derived by Qi and Sun. Various improvements to the efficiency and reliability of the algorithm are introduced. Several of these relate to the linear algebra: the Newton equations are solved by minres instead of...

Abstract. Matrix completion with prescribed eigenvalues is a special type of inverse eigenvalue problems. The goal is to construct a matrix subject to the structural constraint of prescribed entries and the spectral constraint of prescribed spectrum. The challenge of such a completion problem lies in the intertwining of the cardinality and the location of the prescribed entries so that the inve...