In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solving Maxwell's equations in the frequency domain by taking into account the behavior of the electromagnetic field near the geometric edges of wedge-shaped structures. Several algorithms for incorporating treatment of singularities into methods for solving Maxwell's equations in two-dimensional structures by the examples of the analytical modal method and the spectral element method are discussed. In test calculations, for which we use diffraction gratings, the significant accuracy improvement and convergence acceleration were demonstrated. In the considered cases of spectral methods an enhancement of convergence from algebraic to exponential or close to exponential is observed. Diffraction efficiencies of the gratings, for which the conventional methods fail to converge due to the special values of permittivities, were calculated.

在本文中，我们考虑到电磁场在楔形结构几何边缘附近的行为，提出了一种提高精度并加快数值方法的收敛性的方法，以解决频域中麦克斯韦方程组的问题。讨论了几种将奇异性处理纳入二维结构麦克斯韦方程组求解方法的算法，其中以解析模态法和谱元法为例。在我们使用衍射光栅的测试计算中，证明了显着的精度改进和会聚加速。在考虑频谱方法的情况下，观察到从代数到指数或接近指数的收敛性增强。