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

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.

Comparison of 2.5D finite element formulations with perfectly matched layers for solving open axisymmetric electromagnetic cavity problems

“…The numerically computed solutions for the ansätze A2 and A3 coincide, as it has also been the case for the closed cavity problems. 3 Since this holds true for all following test cases, in particular for all n, different FE orders and PML damping functions, only one of the two ansätze is shown for the remainder of this work.…”

“…Regarding the assembly cost, we provide the number of elementary FE terms associated with the different ansätze in Table 4, which clearly shows that, while A2 and A3 demand less integration points for the assembly than A1, they require more elementary FE terms than A1. In Schnaubelt et al, 3 a discussion comparing the three ansätze in terms of accuracy with respect to the number of integration points is available. ‡…”

“…Two approaches have been proposed in the literature for the treatment of the singularity of at and to construct a suitable subspace of 1,2 . A comparison of all following strategies has been published by Schnaubelt et al 3 for closed cavity problems.…”

“…The parameters and of cannot be chosen freely but must satisfy certain constraints 6,3 . Following Schnaubelt et al, 3 we choose for and for in this work.…”

Quasi-3-D Spectral Wavelet Method for a Thermal Quench Simulation

“…To obtain a realistic quench simulation, a magneto-thermal coupling is required, which would necessitate the use of vectorial edge shape functions [15]. These are more involved than nodal ones and beyond this work's scope [16].…”