随机小介质球散射的稀疏矩阵/规则网格法分析

Sparse-Matrix/Canonical Grid Method for Scattering from Random Small Spherical Particles

利用张量电场积分方程和稀疏矩阵/规则网格 (SMCG)法分析了随机分布小介质球的散射问题 .SMCG法根据离散单元间场作用的强弱 ,将阻抗元素分解为强作用的稀疏矩阵和弱作用的补充矩阵 .在共轭梯度法迭代求解矩阵方程时 ,直接计算强作用稀疏阵与待求向量的乘积 ;而对弱作用的补充矩阵 ,则将阻抗元素在规则网格上应用Taylor级数展开 ,由于级数项中存在平移不变性的核 ,因而可利用快速傅里叶变换实现补充矩阵与待求向量的乘积 .实验算例表明 :SMCG法和矩量法的数值曲线吻合性很好 ,在分析电大目标散射时减少了计算机内存和CPU时间要求 。

Based on tensor electric integral equation, the sparse-matrix/canonical grid (SMCG) method is applied to analyze scattering of random small particles. In SMCG method, the impedance matrix is decomposed into a sparse matrix which corresponds to near interactions and its complementary matrix which corresponds to far interaction. During conjugate gradient method (CGM) interative process, the near-interaction portion of the matrix-vector multiplication is computed directly as the moment method (MOM). The far-interaction portion of matrix vector multiplication is computed indirectly using fast Fourier transforms. This is achieved by a Taylor series expansion of impedance matrix elements about the grid points of uniformly spaced canonical grid overlaying the randomly located spheres. The numerical results from SMCG are consistent with that from MOM, whereas the SMCG method is superior to MOM for analyzing electric large scalar problems when considering the requirement of CPU time and computer storage.