Electromagnetic analysis is subjected to uncertainties due to variations in material properties, excitation functions, boundary conditions, or the geometry itself. In this letter, the stochastic response is obtained using the Neumann expansion method, which is implemented alongside Galerkin’s formulation of vector finite elements for the variations in the properties of the electromagnetic material. Using the proposed approach, a constraint on the maximum allowed variations in permittivity is estimated. The Neumann expansion with a third-order approximation passes the Kolmogorov–Smirnov test resulting in output response matching with that of the Monte Carlo method. Since accurate stochastic simulations are possible within less computational time, we extend the analysis to the full operating frequency range with this method. It has also been shown that the computational complexity of the Neumann expansion method does not scale with number of stochastic regions considered.

中文翻译：

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基于 Neumann 展开的 FEM 用于电容率变化的不确定性量化

由于材料特性、激励函数、边界条件或几何本身的变化，电磁分析会受到不确定性的影响。在这封信中，随机响应是使用诺依曼展开方法获得的，该方法与伽辽金针对电磁材料特性变化的矢量有限元公式一起实施。使用所提出的方法，估计介电常数的最大允许变化的约束。三阶近似的诺依曼展开式通过了 Kolmogorov-Smirnov 检验，导致输出响应与蒙特卡罗方法的输出响应匹配。由于可以在更短的计算时间内进行准确的随机模拟，因此我们使用这种方法将分析扩展到整个工作频率范围。