A Comparison Between Different Formulations for Solving Axisymmetric Time-Harmonic Electromagnetic Wave Problems

TL;DR

This paper compares various finite element formulations for solving axisymmetric time-harmonic electromagnetic problems, focusing on handling singularities, spurious modes, and convergence with high-order elements to improve computational efficiency.

Contribution

It introduces a comparative analysis of different formulations addressing singularities and spurious modes in 2D reductions of 3D electromagnetic problems with axial symmetry.

Findings

Certain formulations better suppress spurious modes.

High-order elements improve convergence.

Some methods effectively handle singularities.

Abstract

In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried out on a two-dimensional (2D) angular cross section of the problem, thus significantly reducing the computational effort. However, the transition from a full 3D problem to a 2D analysis introduces additional difficulties such as, among others, a singularity in the variational formulation. In this work, we compare and discuss different finite element formulations to deal with these obstacles. Particular attention is paid to spurious modes and to the convergence behavior when using high-order elements.