对三维多层快速多极子方法中不变项计算的优化

Optimization of the Invariant Terms′ Calculation in Three Dimensional MLFMA

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 qualities of invariant terms in 3D MLFMA are discussed at first.They are α m lm′ l ′s invariance of translation,the central conjugate symmetry of V s or V f on space,and the symmetric sparse matrix sparse and equivalency between V s and V f while using Galerking method.Using these factors,we can optimize the invatriant terms′ calculation in MLFMA program.As a result,the complexity of calculating α m lm′ l is reduced from O(M l(6 3-3 3)) to O(7 3-3 3) and even to O ((7 3-3 3)/8), V s and V f are reduced from O(K LN) to O(K LN/4) ,and A ji from O(N) to O(N/2) .Numerical results show the validity of optimizing.