This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two-dimensional cylindrical and three-dimensional Cartesian systems, which shows much better performance in terms of accuracy and numerical stability for mesh distortion compared with the traditional FEM. Unlike the traditional FEM, the computational domain in ES-FEM is divided into non-overlapping smoothing domains associated with each edge of elements, triangles in two-dimensional domain and tetrahedrons in three-dimensional domain. Then, the gradient smoothing technique is used to smooth the gradient components in the stiff matrix of the FEM. Several numerical experiments are carried out to validate its accuracy and numerical stability. Results show that the ES-FEM can obtain much more accurate results compared with the traditional FEM and is almost independent of mesh distortion.

中文翻译：

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用于电磁分析的精确基于边缘的 FEM 及其在多尺度结构中的应用

本文介绍了一种精确的基于边缘的平滑有限元方法 (ES-FEM)，用于二维圆柱和三维笛卡尔系统的电磁分析，与网格畸变相比，该方法在精度和数值稳定性方面表现出更好的性能。传统的有限元法。与传统的 FEM 不同，ES-FEM 中的计算域被划分为与元素的每条边相关联的非重叠平滑域、二维域中的三角形和三维域中的四面体。然后，使用梯度平滑技术来平滑 FEM 刚性矩阵中的梯度分量。进行了多次数值实验以验证其准确性和数值稳定性。