Abstract: Multilevel fast multipole algorithm (MLFMA) and preconditioned generalized minimal residual (GMRES) method was employed to analyze electromagnetic scattering characteristics in resonance region of 3-D complex objects in this paper. For the problem of scattering in resonance region, such as 5 to 10 wavelengths, MLFMA needs much less core memory and computing complexity than moment method and fast multipole method. How to choose the optimal parameter L, the multipole number, is discussed. Preconditioned GMRES is used to solve the MLFMA matrix equation with a large number of unknowns, which proves to be more efficient than conventional conjugate gradient (CG) method. Finally, electromagnetic scattering in resonance region of 3-D complex bodies including the missile model and stealthy airplane model are analyzed.

Key words: electromagnetic scattering, multilevel fast multipole algorithm, RCS, resonance region, GMRES

摘要： 用多层快速多极子方法（MLFMA）和预优的广义最小残差法（GMRES）计算了三维复杂目标的谐振区电磁散射特性。对于在谐振区中5～10个波长目标的电磁散射体，MLMFA比矩量法（MOM）和快速多极子法（FMM）占用内存少很多，计算速度也更快；本文讨论了MLFMA中重要参数多极子数L的优化选取，同时采用了预优的GMRES方法求解MLFMA大规模矩阵方程，这比采用传统的共轭梯度（CG）法具有更大的优越性。最后对某导弹模型和典型隐身飞机模型进行了谐振区散射特性的高效求解分析。

关键词: 电磁散射, 多层快速多极子, 雷达散射截面, 谐振区, 广义最小残差法