A domain decomposition approach is presented for the transient analysis of three-dimensional wave propagation problems. The subdomains are modelled using the FEM and/or the BEM, and the coupling of the subdomains is performed in an iterative manner, employing a sequential Neumann–Dirichlet interface relaxation algorithm which also allows for an independent choice of the time step length in each...

and this problem can be solved analytically: u (x) = x − sinhx/sinh1. The purpose of starting with this problem is to demonstrate the fundamental concepts and pitfalls in FEM in a situation where we know the correct answer, so that we will know where our approximation is good and where it is poor. In cases of practical interest we will look at ODEs and PDEs that are too complex to be solved ana...

Finite element methods are based on the variational formulation of partial differential equations which only need to compute the gradient of a function. Although unknowns are still associated to nodes, the function composed by piece-wise polynomials on each element and thus the gradient can be computed element-wise. Finite element spaces can thus be constructed on general triangulations and thi...

An analysis of developing and fully developed turbulent flow was carried out when different techniques have been used in a zone close to the solid wall. In this paper, wall element technique based on the finite element method (FEM) has been adopted and compared with other techniques for determination of confined turbulent flow with a one equation model used to depict the turbulent viscosity is ...

This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique advantages of the smoothed finite element method and resolve the existence, linearity and posi-tivity deficiencies pointed out in [1]. We show that Wachspress in...

1 EXECUTIVE SUMMARY In a low frequency analysis of vibration in a built-up structure, the eigen frequencies and the corresponding eigenmodes help the understanding of how and why the structure behaves as it does. These eigen solutions are also useful in calculations of forced response by modal super-position procedures. However, as frequency increases there are more and more modes with increasi...

The Extended Finite Element Method (XFEM) is a technique used in fracture mechanics to predict how objects deform as cracks form and propagate through them. Here, we propose the use of XFEM to model the deformations resulting from cutting through organ tissues. We show that XFEM has the potential for being the technique of choice for modelling tissue retraction and resection during surgery. Can...