The performance of multigrid methods for the standard Poisson problem and for the consistent Poisson problem arising in spectral element discretizations of the Navier-Stokes equations is investigated. It is demonstrated that overlapping additive Schwarz methods are effective smoothers, provided that the solution in the overlap region is weighted by the inverse counting matrix. It is also shown ...

the purpose of this study is to compare the results of different probabilistic methods such as the perturbation method, stochastic finite element method (sfem) and monte carlo method. these methods were used to study the convergence of direct approach for slope stability analysis and are developed for a linear soil behavior. in this study, two dimensional random fields are used and both the fir...

A coupled Legendre-Laguerre spectral element method is proposed for the Stokes and Navier-Stokes equations in unbounded domains. The method combines advantages of the high accuracy of the Laguerre-spectral method for unbounded domains and the geometric flexibility of the spectral-element method. Rigorous stability and error analysis for the Stokes problem is carried out. Numerical results indic...

The objective of this research is to study the free vibration a cantilever Euler-Bernoulli beam carrying point mass with moment inertia at end using spectral element method (SEM). Typically, shape (or interpolation) functions used in Spectral are derived from exact solutions governing differential equations motion frequency domain. was discretized by single which connected end. dynamic stiffnes...

in this paper, an advanced formulation of the spectral finite element method (sfem) is presented and applied in order to carry out site response analysis of 2d topographic structures subjected to vertically propagating incident in-plane waves in time-domain. the accuracy, efficiency and applicability of the formulation are demonstrated by solving some wave scattering examples. a numerical param...

in this study, a new efficient semi-analytical method is introduced to give approximate solutions of strongly nonlinear oscillators. the proposed method is based on combination of two different methods, the multi-step homotopy analysis method and spectral method, called the multi-step spectral homotopy analysis method (msham). in this method, firstly, we propose a new spectral homotopy analysis...

Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, tota...