电磁对偶元的子区域分析

Sub-region Analysis for Dual Electromagnetic Finite Element Method

点基类有限元在处理不同介质电磁场问题时,将面临不同介质界面处场分量不连续的困难,本文提出子区域分析方法,可以有效地解决这一问题。从电磁场对偶变量变分原理出发,结合新近开发的电磁对偶元,详细说明了电磁场的子区域分析方法。在子区域的层次区分内部及出口变量并首先将内部变量消去,子区域提供分界面出口变量的动力刚度阵,最后通过子区域的拼装得到整个问题的求解方案。数值算例显示了本文算法的必要性和有效性。

Discontinuity of field component at interfaces is a major difficulty for node-based finite elements to deal with electromagnetic field problems containing different media. This paper presents sub-region approach that can solve this problem efficiently. From the variational principle for dual variables and combined with the recently developed dual variables FEM, sub-region analysis approach for electromagnetic problem is presented in detail. Inner variables and outside variables are distinguished in the sub-regions, the inner variants are eliminated firstly and then the dynamic stiffness matrices corresponding to the outside variables are calculated and assembled to form the global dynamic stiffness matrix at the end. Numerical examples demonstrate the effectiveness and the necessity of our approach.