Comparative Performance of Novel Nodal-to-Edge finite elements over Conventional Nodal element for Electromagnetic Analysis

TL;DR

This paper compares the performance of novel nodal-to-edge finite elements with conventional nodal elements in electromagnetic analysis, demonstrating edge elements' advantages in accuracy, robustness, and handling complex geometries.

Contribution

The study introduces and evaluates finite element formulations using edge elements alongside nodal elements, highlighting their superior performance in complex electromagnetic problems.

Findings

Edge elements directly compute field variables, reducing post-processing.

Edge elements show better accuracy on coarse meshes compared to nodal elements.

Edge elements are more robust against mesh distortion and complex geometries.

Abstract

In nodal based finite element method (FEM), degrees of freedom are associated with the nodes of the element whereas, for edge FEM, degrees of freedom are assigned to the edges of the element. Edge element is constructed based on Whitney spaces. Nodal elements impose both tangential and normal continuity of vector or scalar fields across interface boundaries. But in edge elements only tangential continuity is imposed across interface boundaries, which is consistent with electromagnetic field problems. Therefore, the required continuities in the electromagnetic analysis are directly obtained with edge elements, whereas in nodal elements they are attained through potential formulations. Hence, while using edge elements, field variables are directly calculated, but with nodal elements, post-processing is required to obtain the field variables from the potentials. Here, we present the finite element formulations with the edge element as well as with nodal elements. Thereafter, we have demonstrated the relative performances of different nodal and edge elements through a series of examples. All possible complexities like curved boundaries, non-convex domains, sharp corners, non-homogeneous domains have been addressed in those examples. The robustness of edge elements in predicting the singular eigen values for the domains with sharp edges and corners is evident in the analysis. A better coarse mesh accuracy has been observed for all the edge elements as compared to the respective nodal elements. Edge elements are also not susceptible to mesh distortion.