Based on the standard finite element method, a new finite element method which is known as nonlocal finite element method (NL-FEM) is numerically implemented in this article to study the nonlocal effects for solving 1D nonlocal elastic problem. An Eringen-type nonlocal elastic model is considered. In this model, the constitutive stress-strain law is expressed interms of integral equation which ...

The element-by-element finite element method (EBEFEM) combined with the preconditioned conjugate gradient (PCG) technique is employed in this paper to calculate the coupling capacitances of multi-level high-density three-dimensional interconnects (3DIs). All capacitive coupling 3DIs can be captured, with the effects of all geometric and physical parameters taken into account. It is numerically ...

The purpose of this paper is to present a new fictitious domain approach inspired by the extended finite element method introduced by Moës, Dolbow and Belytschko in [18]. An optimal method is obtained thanks to an additional stabilization technique. Some a priori estimates are established and numerical experiments illustrate different aspects of the method. The presentation is made on a simple ...

The recovery type error estimators introduced by Zienkiewicz and Zhu use a recovered stress field evaluated from the Finite Element (FE) solution. Their accuracy depends on the quality of the recovered field. In this sense, accurate results are obtained using recovery procedures based on the Superconvergent Patch Recovery technique (SPR). These error estimators can be easily implemented and pro...

The paper examines three selective schemes for the smoothed finite element method (SFEM) which was formulated by incorporating a cell-wise strain smoothing operation into the standard compatible finite element method (FEM). These selective SFEM schemes were formulated based on three selective integration FEM schemes with similar properties found between the number of smoothing cells in the SFEM...

Accuracy and speed are two of the most important problems in the real-time Finite Element Method (FEM)-based simulations of surgical cutting [1][2]. While the latter can be gradually eased through GPU-based acceleration[3][4], the former hasn't been properly addressed even until recently. To enable realistic and accurate simulation, the cutting line should follow the exact movement of the user-...

Only very recently, Sayas [The validity of Johnson-Nédélec's BEM-FEM coupling on polygonal interfaces. SIAM J Numer Anal 2009;47:3451-63] proved that the Johnson-Nédélec one-equation approach from [On the coupling of boundary integral and finite element methods. Math Comput 1980;35:1063-79] provides a stable coupling of finite element method (FEM) and boundary element method (BEM). In our work,...

This paper reformulates a time-discontinuous finite element method (TD-FEM) based on a new class of shape functions, called complex Fourier hereafter, for solving two-dimensional elastodynamic problems. These shape functions, which are derived from their corresponding radial basis functions, have some advantages such as the satisfaction of exponential and trigonometric function fields in comple...

Three dimensional image reconstruction for multi-modality optical spectroscopy systems needs computationally efficient forward solvers with minimum meshing complexity, while allowing the flexibility to apply spatial constraints. Existing models based on the finite element method (FEM) require full 3D volume meshing to incorporate constraints related to anatomical structure via techniques such a...