An Accurate Edge-based FEM for Electromagnetic Analysis with Its Applications to Multiscale Structures

TL;DR

This paper presents an edge-based smoothed finite element method (ES-FEM) that enhances electromagnetic analysis accuracy and stability, especially on distorted meshes, by using gradient smoothing over edge-associated domains.

Contribution

The paper introduces a novel ES-FEM approach for electromagnetic analysis that improves accuracy and stability over traditional FEM, particularly under mesh distortion.

Findings

ES-FEM achieves higher accuracy than traditional FEM.

ES-FEM is robust against mesh distortion.

Numerical experiments confirm improved stability and precision.

Abstract

This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of accuracy and numerical stability for mesh distortion compared with the traditional FEM. Unlike the traditional FEM, the computational domain in ES-FEM is divided into nonoverlapping smoothing domains associated with each edge of elements, triangles in two dimensional domain and tetrahedrons in three dimensional domain. Then, the gradient smoothing technique (GST) is used to smooth the gradient components in the stiff matrix of the FEM. Several numerical experiments are carried out to validate its accuracy and numerical stability. Numerical results show that the ES-FEM can obtain much more accurate results and is almost independent of mesh distortion.