Sensitivity analysis is important for electromagnetic (EM)-based design. The existing adjoint EM sensitivity analysis methods have to solve large systems of EM equations repetitively for different frequencies. This article addresses this situation and proposes to speed up the EM sensitivity analysis over a frequency range by solving EM equations at only a single frequency. A new adjoint EM sensitivity analysis algorithm for the fast frequency sweep using the matrix Padé via Lanczos (MPVL) technique based on the finite-element method (FEM) is proposed in this article. MPVL is incorporated to relate the information of one frequency to the information of multiple frequencies. A large system of EM equations is then solved at a single frequency to predict the sensitivity information for the entire frequency band. Adjoint formulations are further derived to avoid the effect of the number of design variables. The adjoint EM sensitivity analysis using the proposed technique can obtain the same accuracy as the existing techniques while taking less time by avoiding repetitively solving large systems of EM equations for different frequencies and different design variables. The proposed technique is demonstrated by three EM examples of microwave components.

中文翻译：

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基于有限元法的Lanczos技术使用MatrixPadé进行快速扫频的EM伴随灵敏度分析

灵敏度分析对于基于电磁（EM）的设计非常重要。现有的伴随EM灵敏度分析方法必须针对不同的频率重复求解大型的EM方程组。本文解决了这种情况，并建议通过仅在单个频率上求解EM方程来加快某个频率范围内的EM灵敏度分析。提出了一种基于有限元法（FEM）的基于矩阵Padévia Lanczos（MPVL）技术的快速频率扫描伴随EM灵敏度分析算法。并入了MPVL，以使一个频率的信息与多个频率的信息相关。然后以单个频率求解大型的EM方程系统，以预测整个频带的灵敏度信息。进一步推导了伴随公式，以避免设计变量数量的影响。通过避免针对不同的频率和不同的设计变量重复求解大型的EM方程组，使用提出的技术进行的伴随EM灵敏度分析可以获得与现有技术相同的精度，同时花费更少的时间。微波组件的三个EM实例证明了所提出的技术。