用于薄结构中电磁场计算的三维高精度壳体矢量单元

A General 3D High-Fidelity Shell Vector Element for Electromagnetic Computation in Thin Structures

提出了一种适用于薄结构中电磁场计算的通用三维高精度壳体矢量单元。该类壳体单元在薄结构厚度方向对场矢量采用一阶矢量插值,而在薄结构面方向采用二阶矢量插值,能够很容易地应用于平面和曲面薄结构问题的建模与求解。文中应用该壳体矢量单元与2阶六面体矢量单元对比做了两个算例,结果表明:使用该壳体矢量单元建模计算薄层结构不仅可以达到高的计算精度,而且能节约未知量数目一半以上,节约计算时间达80%以上。

The modeling of thin structures is a difficult problem in electromagnetic computation with finite element method. Recent research papers have made some progress utilizing simplified boundary conditions in modeling thin conductor and air gap, but they are still quite difficult to apply in general engineering computation. In this paper, a novel general 3D high-fidelity shell vector element for modeling thin structures is presented. Taking into account the nature of much smaller size of thickness than the others of in-plane in thin structures, the vector shell element adopts one-order vector basis functions of interpolation along the thickness orientation of thin structures and two-order ones along the other orientations, which can be easily applied to model the thin structure with beth fiat and curved surfaces. Two eigen-value problems for rectangular cavities with different dielectric thin structures are solved; in which the thin structures are modeled by two-order hexahedra vector elements and the proposed shell vector elements respectively. The CPU time to calculate individual element matrix of the shell vector element is much less than that of the two-order hexahedra vector element, saving more than 84.16% . The cases show that applying the proposed shell vector element to model thin structures can not only achieve the same precision as hexahedra vector element, but also save unknowns largely, more than 51% . Moreover, the 3D high-fidelity shell vector element can be easily expanded into higher order shell vector element by virtue of hierarchical function.