in this paper, single, bi-layered and three-layered tube hydroforming processes were numerically simulated using the finite element method. it was found that the final bulges heights resulted from the models were in good agreement with the experimental results. three types of modeling were kept with the same geometry, tube material and process parameters to be compared between the obtained hydr...

We study random eigenvalue problems in the context of spectral stochastic finite elements. In particular, given a parameter-dependent, symmetric positive-definite matrix operator, we explore the performance of algorithms for computing its eigenvalues and eigenvectors represented using polynomial chaos expansions. We formulate a version of stochastic inverse subspace iteration, which is based on...

Spectral elements based on Legendre polynomials are used to improve an existing finite-element method for simulating a highly nonlinear field phenomenon: fluid cavitation in an underwater-shock environment. Further improvement is provided by separation of the total field into its equilibrium, incident, and scattered components. These enhancements promise to make the finite-element method suitab...

By using the finite element $p$-Version in convection-diffusion problems, we can attain to a stabilized and accurate results. Furthermore, the fundamental of the finite element $p$-Version is augmentation degrees of freedom. Based on the fact that the finite element and the meshless methods have similar concept, it is obvious that many ideas in the finite element can be easily used in the meshl...

Spectral partitioning methods use the Fiedler vector—the eigenvector of the second-smallest eigenvalue of the Laplacian matrix—to find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extremely well. In this paper, we show that spectral partitioning methods work well on bounded-degree pl...

Several old and new finite-element preconditioners for nodal-based spectral discretizations of −∆u = f in the domain Ω = (−1, 1) (d = 2 or 3), with Dirichlet or Neumann boundary conditions, are considered and compared in terms of both condition number and computational efficiency. The computational domain covers the case of classical single-domain spectral approximations (see [5]), as well as t...

Deterministic models of fluid flow and the transport of chemicals in flows in heterogeneous porous media incorporate partial differential equations (PDEs) whose material parameters are assumed to be known exactly. To tackle more realistic stochastic flow problems, it is fitting to represent the permeability coefficients as random fields with prescribed statistics. Traditionally, large numbers o...

We present efficient domain decomposition solvers for a class of non-standard finite element methods (FEM). These methods utilize PDE-harmonic trial functions in every element of a polyhedral mesh, and use boundary element techniques locally in order to assemble the finite element stiffness matrices. For these reasons, the terms BEMbased FEM or Trefftz-FEM are sometimes used in connection with ...

This paper deals with the finite element approximation of the displacement formulation of the spectral acoustic problem on a curved non convex two-dimensional domain Ω. Convergence and error estimates are proved for Raviart-Thomas elements on a discrete polygonal domainΩh 6⊂ Ω in the framework of the abstract spectral approximation theory. Similar results have been previously proved only for po...

We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral stochastic finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions,...