一种新型针对快速多极子法(FMM)的预条件技术

提出了一种针对FMM近场作用矩阵块的不完全LU预条件方法。和传统单纯依靠填充参数来控制非零元素个数的ILU分解方法相比，该方法由于引入了数值丢弃阈值，因而可获得性能更好的预条件矩阵。利用该项预条件技术，迭代过程变得更健壮，而且收敛也更快，计算花费的时间也更少。数值实验表明：这种基于双丢弃准则的ILUT预条件技术，是一种非常适合FMM计算的预条件处理方法。

A New Preconditioner for FMM Implementation

In this paper, a new incomplete LU (ILU) preconditioner using the near field matrix of the fast multipole method (FMM) is given to increase the efficiency of the iterative solver. With numerical dropping strategies, the new method can yield more accurate factorization with the same amount of fill in than only using level of in methods. By using this preconditioner, we can solve more problems, moreover, fewer steps and less time is needed. Tests show the ILU preconditioner, based on double dropping rule, is quite efficient on FMM implementation.