论文标题
通过处理电磁场的边缘奇异性来提高麦克斯韦方程的数值解决方案的准确性
Improving accuracy of the numerical solution of Maxwell's equations by processing edge singularities of the electromagnetic field
论文作者
论文摘要
在本文中，我们提出了一种方法，用于提高频率域中麦克斯韦方程的数值方法的准确性和加速度，并考虑到楔形结构几何边缘附近的电磁场的范围。讨论了通过分析模态方法的示例和光谱元素方法将奇异性处理到二维结构中求解麦克斯韦方程的方法中的几种算法。在我们使用衍射光栅的测试计算中，证明了明显的准确性提高和收敛性交流 - 旋转。在考虑的情况下，观察到从代数到指数或接近指数的收敛增强。计算了光栅的衍射效率，该光栅的衍射效率是由于特殊的介电值而无法收敛的。
In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior 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 ac-celeration 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.
