We present a short survey of multigrid–based solvers for symmetric eigenvalue problems. We concentrate our attention on “of the shelf” and “black box” methods, which should allow solving eigenvalue problems with minimal, or no, effort on the part of the developer, taking advantage of already existing algorithms and software. We consider a class of such methods, where the multigrid only appears ...

The linear finite element approximation of a general linear diffusion problem with arbitrary anisotropic meshes is considered. The conditioning of the resultant stiffness matrix and the Jacobi preconditioned stiffness matrix is investigated using a density function approach proposed by Fried in 1973. It is shown that the approach can be made mathematically rigorous for general domains and used ...

Abstract—In this paper, the specific sound Transmission Loss (TL) of the Laminated Composite Plate (LCP) with different material properties in each layer is investigated. The numerical method to obtain the TL of the LCP is proposed by using elastic plate theory. The transfer matrix approach is novelty presented for computational efficiency in solving the numerous layers of dynamic stiffness mat...

In this work, we introduce a numerical method to approximate differential operators and integrals on point clouds sampled from a two dimensional manifold embedded in Rn. Global mesh structure is usually hard to construct in this case. While our method only relies on the local mesh structure at each data point, which is constructed through local triangulation in the tangent space obtained by loc...

We study catastrophic filter divergence in data assimilation procedures whereby the forecast model develops severe numerical instabilities leading to a blow up of the solution. Catastrophic filter divergence occurs in sparse observational grids with small observational noise for intermediate 5 observation intervals and finite ensemble sizes. Using a minimal five dimensional model we establish t...

In the present paper, the aeroelastic stability of helicopter rotor blade is determined using Aeroelastic Frequency Response Function. The conventional methods of aeroelastic stability usually use an iterative procedure while the present method does not require such approach. Aeroelastic Frequency Response Functions are obtained by inverting dynamic stiffness matrix of the aeroelastic system. S...

Wave propagation in a stratified fluid / porous medium is studied here using analytical and numerical methods. The semi-analytical method is based on an exact stiffness matrix method coupled with a matrix conditioning procedure, preventing the occurrence of poorly conditioned numerical systems. Special attention is paid to calculating the Fourier integrals. The numerical method is based on a hi...

A defect-free rolling element bearing has a varying stiffness. The variation of stiffness depends on number of rolling elements, their configuration and cage frequency. The time-varying characteristics of the stiffness results in a parametric excitation. This may lead to instability which is manifested as high vibration levels. An FEM simulation is performed to evaluate stiffness in each config...

Because of the substantial difference in stiffness between matrix and nanotube in CNT composite, the stress transfer between them controls their mechanical properties. This paper investigates the said issue, analytically and numerically, in axial load using representative volume element (RVE). The analytical model was established based on the modified Cox’s shear lag model with the use of some ...

An interaction integral method for evaluating mixed-mode stress intensity factors (SIFs) for two dimensional crack problems using NURBS-based isogeometric analysis method is investigated. The interaction integral method is based on the path independent J-integral. By introducing a known auxiliary field solution, the mixed-mode SIFs are calculated simultaneously. Among features of B-spline basis...