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本文用高次有限元法求解了任意横截面形状波导的本征值问题;提出了一种便于编制计算机程序的区域剖分方法。为了比较高次元和线性元的解题效能,以此两方法计算了三种不同形状波导主模和高次模的本征值。结果显示:二次元方法的精度比线性元可提高一至三个数量级。由于高次元对计算高次模特别有效,本法尤其适用于对多模元件的分析和设计。
In this paper, the problem of eigenvalue of waveguide with arbitrary cross-section is solved by high-order finite element method. A method of region division is presented to facilitate the preparation of computer program. In order to compare the solving performance of higher-order elements and linear elements, the eigenvalues of the three modes of waveguide main mode and high-order mode are calculated by these two methods. The results show that the accuracy of the quadratic method can be increased by one to three orders of magnitude compared with linear elements. This high-order element is particularly useful for the analysis and design of multimode components, since high-order elements are particularly effective in computing high-order models.