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.
翻译:在许多时间调和电磁波问题中,经过考虑的几何学表现为轴对称性。在这种情况下,通过利用方正正方形方向的Fourier扩张,可以对问题的二维(2D)角交叉部分进行完全三维(3D)计算,从而大大减少了计算努力。然而,从完全的三维问题向二维分析的过渡带来了额外的困难,例如变异配方的独一性等。在这项工作中,我们比较和讨论不同的有限元素配方,以应对这些障碍。特别注意假造模式和使用高阶元素时的趋同行为。