多层快速多极子算法的改进措施

Improving Multilevel Fast Multipole Algorithm

为精确求解散射问题,采用混合场积分方程(CFIE)、多层快速多极子算法(MLFMA)和共轭梯度算法(CG)的收敛技术。基于传统多层快速多级子算法,详细研究了二维拉格朗日插值节点数对计算精度的影响,并改进了插值方法,在不同的层采用不同的插值节点数;提出了在不同的层采用不同的精度控制来计算多级子模式数;分析了稀疏矩阵的对称性对内存使用的影响以及磁场积分方程对迭代初始值的选择。数值计算结果表明以上改进可较大幅度地提高计算精度和计算效率,同时降低内存使用,可满足复杂目标电磁散射计算要求。

To gain a precise radar cross section （RCS） scattering from three-dimensional objects efficiently and stably, the convergence algorithm is adopted which integrates conjugate grads （CG） algorithm combined field integral equation （CFIE） and multilevel fast multipole algorithm （MLFMA）. Based on traditional MLFMA, the effect on calculation precision caused by node number used in the two-dimensional Lagrange interpolation is investigated in detail, and interpolation method is improved which chooses different node number at different levels. This article presents a method that adopted different precision control at different levels for truncation number calculation. The impact of symmetry of sparse matrix on the memory used in calculation is analyzed, and the selection of iterative initial value for magnetic field integral equation （MFIE） is discussed. The improvements can enhance the precision and efficiency of calculation notably and reduce memory, as illustrated by the numerical results. They can meet the algorithm requirements of electromagnetic scattering for complex three-dimensional targets.