电大尺寸物体电磁辐射与散射特性几种分析方法的比较研究

Comparison Research on Several Analysis Methods for the Radiation and the Scattering Problems of Electrical Large Bodies

在一定的规则剖分下，矩量法中的系数矩阵为Ｔｏｅｐｌｉｔｚ矩阵或多重Ｔｏｅｐｌｉｔｚ矩阵。利用这一特征而提出的共轭梯度（ＣＧＭ）和快速付里叶变换（ＦＦＴ）算法已成为目前国际上分析电大尺寸问题的一种有效手段。虽然ＣＧＭ—ＦＦＴ将普通矩量法中正比于Ｎ２（Ｎ为系数矩阵的阶数）的存储量压缩为正比于Ｎ的存储量，但其迭代算法使所花ＣＰＵ时间仍与普通矩量法相当。本文采用基于递推的Ｌｉｖｅｎｓｏｎ算法和一种库软件处理同样的问题，所花ＣＰＵ时间和普通矩量法相比降低两个量级，而且存储量比ＣＧＭ—ＦＦＴ技术还要小。本文以直导线的辐射和散射问题为例介绍了几种算法的基本原理，并对他们的计算时间和存储空间等进行了比较研究，得出了一些重要结论。

The coefficient matrix for the method of moments (MoM ) should be a single or multiple stage Toeplitz matrix in the case of regular division. By using the characteristic of the Toeplitz matrix,the combination of the conjugate gradient method (CGM) and fast Fourier transform (FFT)has currently become an efficient algorithm for the electrical large problems. Although the necessary storage space for CGMFFT has been reduced to be proportional to N while that for the traditional MoM is proportional to N2(N is the dimension of the coefficient matrix),the computational efficiency of both methods is nearly at the same level. In this paper,the Livenson algorithm and a program in the library Linpack are used to analyze the same problems. Because both of them are the recurrent basis methods,the CPU time for them is two orders of magnitude less than that for the traditional MoM. Besides, the necessary storage space for these two methods is even less than that for the CGMFFT technique. The scattering and the radiation problems Of a straight wire are used to illustrate the principle of these algorithms,and the comparisons of CPU time and storage space for these algorithms are presented. Based on these, some important conclusions are made.