We present a novel approach for stochastic finite-element (FE) modeling of the electromagnetic field in ferrites, combining a thin shell model (TSM) for highly permittive grain boundaries with a Voronoi-tessellation-based geometry generation algorithm. The TSM is validated in the case of a periodic grain structure in a linear 2-D time-harmonic case over a frequency range of 10 kHz–1 GHz, and problems related to standard FE discretization are discussed. The TSM is then applied in a stochastic study for simulating the effect of varying grain structure on the effective resistivity, losses, and reactive power densities of a ferrite core.

中文翻译：

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使用壳单元和随机晶粒结构对铁氧体进行电磁建模

我们提出了一种对铁氧体中电磁场进行随机有限元 (FE) 建模的新方法，将用于高介电晶界的薄壳模型 (TSM) 与基于 Voronoi 镶嵌的几何生成算法相结合。TSM 在 10 kHz–1 GHz 频率范围内的线性二维时谐情况下的周期性晶粒结构的情况下得到验证，并讨论了与标准 FE 离散化相关的问题。然后将 TSM 应用于随机研究，以模拟不同晶粒结构对铁氧体磁芯的有效电阻率、损耗和无功功率密度的影响。