本文首先研究了三维MLFMA中不变项的内在性质 .它们分别是 :αmlm′l具有平移不变性 ,Vs 和Vf 在角谱空间中共轭对称 ,使用Galerkin法时 Asparse为对称矩阵并且Vs 和Vf 相等 .这些性质可用于优化不变项的计算 ,使αmlm′l的计算复杂度从O(Ml(6 3 - 33 ) )降到O(73 - 33 )甚至O((73 - 33 ) / 8) ,而Vs 和Vf 的复杂度则从O(KLN)降至O(KLN/4) ,Aji的从O(N)到O(N/ 2 ) .数值结果表明了优化的有效性 . In this paper, the intrinsic properties of invariant terms in MLFMA are studied first. They are: αmlm’l has translational invariance, Vs and Vf are conjugate symmetric in angular spectral space, Asparse is symmetric matrix when Galerkin method is used, and Vs and Vf are equal . These properties can be used to optimize the calculation of invariants and reduce the computational complexity of αmlm’l from O (Ml (6 3 - 33)) to O (73 - 33) or even O ((73 - 33) / 8) , While the complexity of Vs and Vf decreases from O (KLN) to O (KLN / 4) and Aji from O (N) to O (N / 2). Numerical results show the effectiveness of the optimization.