多尺度有限元建模非线性磁 quasi 静态问题的磁感应符合 formulations
Multiscale Finite Element Modeling of Nonlinear Magnetoquasistatic Problems Using Magnetic Induction Conforming Formulations
AI总结：
本文提出用于周期性材料非线性磁 quasi 静态问题的磁感应多尺度 formulations，通过周期性均质理论和异质多尺度方法实现细尺度问题与宏尺度问题的转换，验证了周期性软磁复合材料的二维几何结构。
摘要：
本文开发了用于涉及周期性材料的非线性磁 quasi 静态问题的磁感应符合多尺度 formulations。这些 formulations 是通过周期性均质理论推导，并应用于异质多尺度方法中。因此，细尺度问题被替换为在粗网格上定义的宏尺度问题，该粗网格覆盖整个域，并且在宏尺度网格的一些关键点（例如数值四面体点）周围定义了多个细网格的小区域的 meso 问题。本文详细解释了这些宏和 meso 问题之间的信息交换。为了验证，我们考虑了一个理想化的周期性软磁复合材料的二维几何结构。
英文摘要：
In this paper we develop magnetic induction conforming multiscale formulations for magnetoquasistatic problems involving periodic materials. The formulations are derived using the periodic homogenization theory and applied within a heterogeneous multiscale approach. Therefore the fine-scale problem is replaced by a macroscale problem defined on a coarse mesh that covers the entire domain and many mesoscale problems defined on finely-meshed small areas around some points of interest of the macroscale mesh (e.g. numerical quadrature points). The exchange of information between these macro and meso problems is thoroughly explained in this paper. For the sake of validation, we consider a two-dimensional geometry of an idealized periodic soft magnetic composite.
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