关于CFIE-MLFMA算法的一类预条件方法

A Class of Preconditioners for MLFMA Based on CFIE

研究了多层快速多极子算法(MLFMA)的预条件加速技术.利用MLFMA的近场矩阵的结构特征,先将其分裂为对角块阵、不完全下三角块阵和不完全上三角块阵,再将对角块作LU分解,就可以构造出一系列的预条件阵DILU.与不用预条件或只用对角块预条件相比,这些预条件阵能大幅度地减少迭代次数,节省计算时间.一部分预条件阵不会增加存储量,而另外一部分只增加很少的存储量.文中给出的数值算例比较了几种不同预条件阵的优缺点,也验证了这些预条件加速方法的正确性和有效性.

In this paper, preconditioners for multi-level fast multipole algorithm （MLFMA） are investigated, Based on its structure, the near-part of MLFMA matrix is split into a block-diagonal matrix, and incomplete lower matrix, and an incomplete upper block matrix. The block-diagonal matrices are LU decomposition. A series of preconditioners （DILU） are constructed. These preconditioners can save CPU time by greatly reducing the number of iterations. Some precondifioners require slightly increased memory size, while others even do not need any additional memory. Numerical examples compare efficiency of the preconditioners, and show validity of the accelerated algorithms.