用MoM—PCG—FFT分析金属栅有限阵列的散射问题

本文用矩量法、预条件共轭梯度法和快速傅里叶变换（MoM-PCG-FFT)的混合技术来分析金属栅有限阵列的电磁散射问题。首先以等效电流作为未知函数建立积分方程组或积分－微分方程组,再用矩量法（脉冲／点匹配）获得一个线性代数方程组,其系数矩阵是一个对称二重复Toeplitz矩阵,基于这一特点,应用预条件共轭梯度法和快速傅里叶变换的结合算法（PCGFFT）来求解这个线性代数方程组,其中预条件器选用T.Chan循环预条件共轭梯度法和快速傅里叶变换的结合算法（PCGFFT）来求解这个线性代数方程组,其中预条件器选用T．Chan循环预条件器的二重分块形式。文中给出的数值算例表明该混合技术是有效的,适用于较大的金属栅有限阵列的分析。

The Application MoM-PCG-FFT to the Analysis ofScattering by a Finite Array of Plane Metallic Gratings

A mixed technique of moment method, preconditioned conjugate gradient method, and fast Fourier transform is presented to analyze the scattering by a finite array of metallic gratings. In the method, the system of integral or integro differential equations for the equivalent current is first formulated, and then turned into a linearly algebra system by MoM, whose coefficient matrix is a symmetric block Toeplitz one. Based on this characteristic, a combined algorithm of PCG and FFT is used to solve the system, where the block circulant preconditioner of T.Chan is adopted. The technique has low need for computer memory, high solving rate, and good convergence.