电磁耦合问题的区域分解算法

Domain Decomposition Method for the Solution of Electromagnetic Field Penetration Problems

作为偏微分方程数值解新技术 ,区域分解算法对于大型复杂问题的求解表现出巨大的优越性。本文将其与频域有限差分法 ( FDFD)结合 ,对有限厚度导体平面上缝隙电磁耦合问题进行了分析。通过将所分析的结构划分为多个相对独立的规则子域 ,使原问题中差分方程的系数矩阵转换为各子域中带宽极窄的带状阵 ,从而使计算时间和计算所需内存分别下降为 O( N)和 O( max( Ni) ) ,其中 N为总网格点数 ,Ni 为第 i个子域的网格点数。数值结果与文献提供的结果吻合 ,证明了该法的有效性。同时 ,该法很容易实现并行计算 ,为进一步提高计算效率提供可能。

In this paper, a fast and rigorous algorithm is presented for the analysis of electromagnetic fields penetrating narrow slots and lapped joints in thick conducting screens. The method is to combine FDFD with Domain Decomposition Method (DDM). By splitting the original structure into several regular sub-domains through DDM, the problem was reduced into some independent small problems. Further more, these problems can be easily solved by using FDFD method with only O(N) in both computation effort and memory storage requirement. Different structures were calculated and the numerical results show good agreements with published data, which demonstrated the validity of the new method.