分析三维随机介质目标散射问题的SMCG方法

应用稀疏矩阵规则网格(sparse matrix canonical grid，SMCG)法分析了三维随机介质目标的电磁放射问题.用矩量法术解介质放射体的体积分方程时，根据放射体离放单元间场相互作用的强弱，将阻抗矩阵分解为近区强相互作用的稀疏矩阵和远区弱相互作用的补充矩阵、在用共轭梯度法迭代求解矩阵方程时，将格林函数在规则网格点上进行泰勒级数展开，进而可利用快速傅里叶变换计算弱相互作用矩阵与待求向量的乘积，而强相互作用矩阵与待求向量的乘积可以直接计算、文中对几种不同情况的随机介质目标的远区放射场进行了计算，结果表明SMCG法的计算结果与满阵矩量法的计算结果吻合良好，而所需的计算机内存和计算量却大为减少．

Sparse Matrix Canonical Grid Method for Scattering from 3D Random Dielectric Scatterers

The sparse matrix canonical grid method is employed to analyze electromagnetic scattering from three dimensional random dielectric scatterers in this paper. The method of moments was used to solve the volume integral equation for dielectric scatterers. The impedance matrix is decomposed into a sparse matrix, which corresponds to strong near field interactions, and its complementary matrix, which corresponds to weak far field interactions according to the discrete unit of scatterers. During the iterative solution of the matrix equation by the conjugate gradient method, the far interaction portion of the matrix vector multiplication is computed indirectly using fast Fourier transforms. This is achieved by a Taylor series expansion of the Green's function about the grid points of a uniformly spaced canonical grid. The near interaction portion of the matrix vector multiplication is computed directly. The far scattered fields for several examples are calculated. It is shown that the numerical results are in good agreement with the results achieved by the full matrix method of moments, while the memory requirement and operations are considerably reduced.