In the present paper a method is proposed to investigate the free vibration of a partially liquid-filled cylindrical tank. The mechanical properties of the container are assumed to change continuously along the thickness according to volume fraction Power-law, Sigmoid or Exponential distribution. The liquid is supposed to be incompressible and in viscid and its velocity potential is formulated ...

A general inner-outer iteration for computing extreme eigenpairs of symmetric/positive-definite matrix pencils is proposed. The principle of the method is to produce a sequence of p-dimensional bases {Xk} that converge to a minimizer of a generalized Rayleigh quotient. The role of the inner iteration is to produce an “update” vector by (approximately) minimizing a quadratic model of the Rayleig...

An intra-cavity adaptive mirror is required to compensate for time-dependent phase aberrations to the laser beam, such as those caused by thermal lensing. A piezoelectric unimorph design can provide a small, low-cost deformable mirror for this application. The unimorph consists of a metallic disc, with a mirror finish, bonded to a piezoelectric disc. In adaptive optics the deformations that the...

In this paper we propose a Modiied Block Newton Method for approximating an invariant subspace S and the corresponding eigenvalues of a symmetric matrix A. The method generates a sequence of matrices Z (k) which span subspaces S k approximating S. The matrices Z (k) are calculated via a Newton step applied to a special formulation of the block eigenvalue problem for the matrix A, followed by a ...

We consider the solution of large-scale nonlinear algebraic Hermitian eigenproblems of the form T (λ)v = 0 that admit a variational characterization of eigenvalues. These problems arise in a variety of applications and are generalizations of linear Hermitian eigenproblems Av=λBv. In this paper, we propose a Preconditioned Locally Minimal Residual (PLMR) method for efficiently computing interior...

The Jacobi-Davidson method is suitable for computing solutions of large n-dimensional eigenvalue problems. It needs (approximate) solutions of speciic n-dimensional linear systems. Here we propose a strategy based on a nonoverlapping domain decomposition technique in order to reduce the wall clock time and local memory requirements. For a model eigenvalue problem we derive optimal coupling para...

The purpose of this note is to study the Euclidean condition number of the matrix resulting from using the well-known RayleighRitz-Galerkin method with finite dimensional subspaces of polynomial spline functions to approximate the solution of a linear, selfadjoint* two-point boundary value problem. Roughly speaking, we consider a model class of such problems of order In and determine upper boun...