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首页> 外文期刊>Journal of Computational Physics >Improving accuracy of the numerical solution of Maxwell's equations by processing edge singularities of the electromagnetic field
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Improving accuracy of the numerical solution of Maxwell's equations by processing edge singularities of the electromagnetic field

机译：通过加工电磁场边缘奇异性提高Maxwell方程式数值解的准确性

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摘要

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. (C) 2021 Elsevier Inc. All rights reserved.
机译：在本文中，我们提出了一种方法，通过考虑楔形结构几何边缘附近的电磁场行为，提高求解麦克斯韦方程组的频域数值方法的精度并加速其收敛。以解析模态法和谱元法为例，讨论了将奇异性处理纳入二维结构麦克斯韦方程组求解方法的几种算法。在我们使用衍射光栅的测试计算中，证明了显著的精度提高和收敛加速。在考虑谱方法的情况下，观察到从代数到指数或接近指数的收敛性增强。计算了由于介电常数的特殊值，传统方法无法收敛的光栅衍射效率。（c）2021爱思唯尔公司保留所有权利。

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