Abstract:

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 preconditioners 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.

Key words: multi-level fast multipole algorithm (MLFMA), LU decomposition, conjugate gradient method, preconditioner