小波变换在电磁场数值计算中的应用

Applications of Wavelet Transform in Electromagnetic Numerical Computations

本文从算子展开的角度将小波矩量法（Ｗａｖｅｌｅｔ－ＭｏＭ）应用于解电场积分方程，分析了其系数矩阵的精确度、稀疏性及条件数等，并在以上几个方面同一般的分域基矩量法进行了比较，指出小波矩量法形成的系数矩阵是一个稀疏矩阵，但是它的条件数高。我们分析了系数矩阵的稀疏原理，并解释了矩阵性态不好的原因，给出了改善矩阵性态的方法，最后以一个无限长的薄导体片在ＴＭ平面波入射下的感应电流为计算对象，验证了我们的结论。

In this paper, wavelet-method of moment (Wavelet-MoM) is applied in solving elecric field integral equations(EFIE).Accuracy, sparsity and condition number of the expansion matrix are analyzed, comparison with the general used subdomain moment is made. The results show that Wavelet-MoM leads to a sparse expansion matrix, with a higher condition number as its cost. We analyze the sparsity principle and give an explanation to the mechanism of higher condition number. At last, a numerical example is presented to verify our conclusions.